
@C4@M@bScene Description Language


The Scene Description Language allows you to describe the world in a readable
and convenient way. Files are created in plain ASCII text using an editor of
your choice. The input file name is specified using the Input_File_Name=file
option or +Ifile switch. By default the files have the extension .pov.
POV-Ray reads the file, processes it by creating an internal model of the
scene and then renders the scene.

The overall syntax of a scene is a file that contains any number of the
following items in any order.

   LANGUAGE_DIRECTIVES
   camera { CAMERA_ITEMS }
   OBJECT_STATEMENTS
   ATMOSPHERE_STATEMENTS
   global_settings { GLOBAL_ITEMS }


See section "Language Directives", section "Objects", section "Camera",
section "Atmospheric Effects" and section "Global Settings" for details.

7.1              Language Basics

The POV-Ray language consists of identifiers, reserved keywords, floating
point expressions, strings, special symbols and comments. The text of a
POV-Ray scene file is free format. You may put statements on separate lines
or on the same line as you desire. You may add blank lines, spaces or
indentations as long as you do not split any keywords or identifiers.

7.1.1            Identifiers and Keywords

POV-Ray allows you to define identifiers for later use in the scene file. An
identifier may be 1 to 40 characters long. It may consist of upper or lower
case letters, the digits 0 through 9 or an underscore character ("_"). The
first character must be an alphabetic character. The declaration of
identifiers is covered later.

POV-Ray has a number of reserved keywords which are listed below.


aa_level                 fog_offset           reciprocal
aa_threshold             fog_type             recursion_limit
abs                      frequency            red
acos                     gif                  reflection
acosh                    global_settings      refraction
adaptive                 glowing              render
adc_bailout              gradient             repeat
agate                    granite              rgb
agate_turb               gray_threshold       rgbf
all                      green                rgbft
alpha                    halo                 rgbt
ambient                  height_field         right
ambient_light            hexagon              ripples
angle                    hf_gray_16           rotate
aperture                 hierarchy            roughness
arc_angle                hollow               samples
area_light               hypercomplex         scale
asc                      if                   scallop_wave
asin                     ifdef                scattering
asinh                    iff                  seed
assumed_gamma            image_map            shadowless
atan                     incidence            sin
atan2                    include              sine_wave
atanh                    int                  sinh
atmosphere               interpolate          sky
atmospheric_attenuation  intersection         sky_sphere
attenuating              inverse              slice
average                  ior                  slope_map
background               irid                 smooth
bicubic_patch            irid_wavelength      smooth_triangle
black_hole               jitter               sor
blob                     julia_fractal        specular
blue                     lambda               sphere
blur_samples             lathe                spherical_mapping
bounded_by               leopard              spiral
box                      light_source         spiral1
box_mapping              linear               spiral2
bozo                     linear_spline        spotlight
break                    linear_sweep         spotted
brick                    location             sqr
brick_size               log                  sqrt
brightness               looks_like           statistics
brilliance               look_at              str
bumps                    low_error_factor     strcmp
bumpy1                   mandel               strength
bumpy2                   map_type             strlen
bumpy3                   marble               strlwr
bump_map                 material_map         strupr
bump_size                matrix               sturm
camera                   max                  substr
case                     max_intersections    superellipsoid
caustics                 max_iteration        switch
ceil                     max_trace_level      sys
checker                  max_value            t
chr                      merge                tan
clipped_by               mesh                 tanh
clock                    metallic             test_camera_1
color                    min                  test_camera_2
color_map                minimum_reuse        test_camera_3
colour                   mod                  test_camera_4
colour_map               mortar               text
component                nearest_count        texture
composite                no                   texture_map
concat                   normal               tga
cone                     normal_map           thickness
confidence               no_shadow            threshold
conic_sweep              number_of_waves      tightness
constant                 object               tile2
control0                 octaves              tiles
control1                 off                  torus
cos                      offset               track
cosh                     omega                transform
count                    omnimax              translate
crackle                  on                   transmit
crand                    once                 triangle
cube                     onion                triangle_wave
cubic                    open                 true
cubic_spline             orthographic         ttf
cylinder                 panoramic            turbulence
cylindrical_mapping      pattern1             turb_depth
debug                    pattern2             type
declare                  pattern3             u
default                  perspective          ultra_wide_angle
degrees                  pgm                  union
dents                    phase                up
difference               phong                use_color
diffuse                  phong_size           use_colour
direction                pi                   use_index
disc                     pigment              u_steps
distance                 pigment_map          v
distance_maximum         planar_mapping       val
div                      plane                variance
dust                     png                  vaxis_rotate
dust_type                point_at             vcross
eccentricity             poly                 vdot
else                     polygon              version
emitting                 pot                  vlength
end                      pow                  vnormalize
error                    ppm                  volume_object
error_bound              precision            volume_rendered
exp                      prism                vol_with_light
exponent                 pwr                  vrotate
fade_distance            quadratic_spline     v_steps
fade_power               quadric              warning
falloff                  quartic              warp
falloff_angle            quaternion           water_level
false                    quick_color          waves
file_exists              quick_colour         while
filter                   quilted              width
finish                   radial               wood
fisheye                  radians              wrinkles
flatness                 radiosity            x
flip                     radius               y
floor                    rainbow              yes
focal_point              ramp_wave            z
fog                      rand

fog_alt                  range


All reserved words are fully lower case. Therefore it is recommended
that your identifiers contain at least one upper case character so it
is sure to avoid conflict with reserved words.

The following keywords are in the above list of reserved keywords but
are not currently used by POV-Ray however they remain reserved.

  bumpy1               test_camera_1
  bumpy2               test_camera_2
  bumpy3               test_camera_3
  incidence            test_camera_4
  pattern1             track
  pattern2             volume_object
  pattern3             volume_rendered
  spiral               vol_with_light


7.1.2            Comments

Comments are text in the scene file included to make the scene file easier to
read or understand. They are ignored by the ray-tracer and are there for your
information. There are two types of comments in POV-Ray.

Two slashes are used for single line comments. Anything on a line after a
double slash (//) is ignored by the ray-tracer. For example:

  // This line is ignored


You can have scene file information on the line in front of the comment as
in:

  object { FooBar }  // this is an object


The other type of comment is used for multiple lines. It starts with "/*" and
ends with "*/". Everything in-between is ignored. For example:

  /* These lines
     are ignored
     by the
     ray-tracer */


This can be useful if you want to temporarily remove elements from a scene
file. /* ... */ comments can comment out lines containing other // comments
and thus can be used to temporarily or permanently comment out parts of a
scene. /* ... */ comments can be nested, the following is legal:

  /* This is a comment
  // This too
  /* This also */
  */


Use comments liberally and generously. Well used, they really improve the
readability of scene files.

7.1.3            Float Expressions

Many parts of the POV-Ray language require you to specify one or more
floating point numbers. A floating point number is a number with a decimal
point. Floats may be specified using literals, identifiers or functions which
return float values. You may also create very complex float expressions from
combinations of any of these using various familiar operators.

Where POV-Ray needs an integer value it allows you to specify a float value
and it truncates it to an integer. When POV-Ray needs a logical or boolean
value it interprets any non-zero float as true and zero as false. Because
float comparisons are subject to rounding errors POV-Ray accepts values
extremely close to zero as being false when doing boolean functions.
Typically values whose absolute values are less than a preset value epsilon
are considered false for logical expressions. The value of epsilon is system
dependent but is generally about 1.0e-10. Two floats a and b are considered
to be equal if abs(a-b) < epsilon.

7.1.3.1          Float Literals

Float literals are represented by an optional sign ("+" or "-") digits, an
optional decimal point and more digits. If the number is an integer you may
omit the decimal point and trailing zero. If it is all fractional you may
omit the leading zero. POV-Ray supports scientific notation for very large or
very small numbers. The following are all valid float literals:

  -2.0    -4    34    3.4e6    2e-5    .3    0.6


7.1.3.2          Float Identifiers

Float identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. An identifier is declared as follows.

  #declare IDENTIFIER = EXPRESSION


Where IDENTIFIER is the name of the identifier up to 40 characters long and
EXPRESSION is any valid expression which evaluates to a float value. Here are
some examples.

  #declare Count = 0
  #declare Rows = 5.3
  #declare Cols = 6.15
  #declare Number = Rows*Cols
  #declare Count = Count+1


As the last example shows, you can re-declare a float identifier and may use
previously declared values in that re-declaration. There are several built-in
identifiers which POV-Ray declares for you. See "Built-in Identifiers" for
details.

7.1.3.3          Float Operators

Arithmetic float expressions can be created from float literals, identifiers
or functions using the following operators in this order of precedence...

  ()             expressions in parentheses first
  +A   -A   !A   unary minus, unary plus and logical "not"
  A*B  A/B       multiplication and division
  A+B  A-B       addition and subtraction


Relational, logical and conditional expressions may also be created. However
there is a restriction that these types of expressions must be enclosed in
parentheses first. This restriction, which is not imposed by most computer
languages, is necessary because POV-Ray allows mixing of float and vector
expressions. Without the parentheses there is an ambiguity problem.
Parentheses are not required for the unary logical not operator "!" as shown
above. The operators and their precedence are shown here.

Relational expressions: The operands are arithmetic expressions and the
result is always boolean with 1 for true and 0 for false. All relational
operators have the same precedence.

  (A > B))A is greater than Br equal to Bbs(A-B)>=EPSILON)


Logical expressions: The operands are converted to boolean values of 0 for
false and 1 for true. The result is always boolean. All logical operators
have the same precedence. Note that these are not bit-wise operations, they
are logical.

  (A | B)true if either A or B or both are truelse otherwise


Conditional expressions: The operand C is boolean while operands A and B are
any expressions. The result is of the same type as A and B.

  (C ? A : B)if C then A else B


Assuming the various identifiers have been declared, the following are
examples of valid expressions...

  1+2+3       2*5         1/3         Row*3       Col*5
  (Offset-5)/2            This/That+Other*Thing
  ((This<That) & (Other>=Thing)?Foo:Bar)


Expressions are evaluated left to right with innermost parentheses evaluated
first, then unary +, - or !, then multiply or divide, then add or subtract,
then relational, then logical, then conditional.

7.1.4            Vector Expressions

POV-Ray often requires you to specify a vector. A vector is a set of related
float values. Vectors may be specified using literals, identifiers or
functions which return vector values. You may also create very complex vector
expressions from combinations of any of these using various familiar
operators.

POV-Ray vectors may have from two to five components but the vast majority of
vectors have three components. Unless specified otherwise, you should assume
that the word vector means a three component vector. POV-Ray operates in a 3D
x, y, z coordinate system and you will use three component vectors to specify
x, y and z values. In some places POV-Ray needs only two coordinates. These
are often specified by a 2D vector called an UV vector. Fractal objects use
4D vectors. Color expressions use 5D vectors but allow you to specify 3, 4 or
5 components and use default values for the unspecified components. Unless
otherwise noted, all 2, 4 or 5 component vectors work just like 3D vectors
but they have a different number of components.

7.1.4.1          Vector Literals

Vectors consist of two to five float expressions that are bracketed by angle
brackets < and >. The terms are separated by commas. For example here is a
typical three component vector:

  < 1.0, 3.2, -5.4578 >


The commas between components are necessary to keep the program from thinking
that the 2nd term is the single float expression 3.2-5.4578 and that there is
no 3rd term. If you see an error message such as Float expected but '>' found
instead you probably have missed a comma.

Sometimes POV-Ray requires you to specify floats and vectors side-by-side.
The rules for vector expressions allow for mixing of vectors with vectors or
vectors with floats so commas are required separators whenever an ambiguity
might arise. For example < 1,2,3>-4 evaluates as a mixed float and vector
expression where 4 is subtracted from each component resulting in <
-3,-2,-1>. However the comma in <1,2,3>,-4 means this is a vector followed by
a float.

Each component may be a full float expression. For example <
This+3,That/3,5*Other_Thing> is a valid vector.

7.1.4.2          Vector Identifiers

Vector identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. An identifier is declared as follows...

  #declare IDENTIFIER = EXPRESSION


Where IDENTIFIER is the name of the identifier up to 40 characters long and
EXPRESSION is any valid expression which evaluates to a vector value. Here
are some examples...

  #declare Here = <1,2,3>
  #declare There = <3,4,5>
  #declare Jump = <Foo*2,Bar-1,Bob/3>
  #declare Route = There-Here
  #declare Jump = Jump+<1,2,3>


Note that you invoke a vector identifier by using its name without any angle
brackets. As the last example shows, you can re-declare a vector identifier
and may use previously declared values in that re-declaration. There are
several built-in identifiers which POV-Ray declares for you. See section
"Built-in Identifiers" for details.

7.1.4.3          Vector Operators

Vector literals, identifiers and functions may also be combined in
expressions the same as float values. Operations are performed on a
component-by-component basis. For example <1,2,3> + <4,5,6> evaluates the
same as < 1+4,2+5,3+6> or <5,7,9>. Other operations are done on a similar
component-by-component basis. For example (< 1,2,3> = <3,2,1>) evaluates to <
0,1,0> because the middle components are equal but the others are not.
Admittedly this isn't very useful but its consistent with other vector
operations.

Conditional expressions such as (C ? A : B) require that C is a float
expression but A and B may be vector expressions. The result is that the
entire conditional evaluates as a valid vector. For example if Foo and Bar
are floats then

  Foo < Bar ? <1,2,3> : <5,6,7>
evaluates as the vector <1,2,3> if Foo is less than Bar and evaluates as
<5,6,7> otherwise.

You may use the dot operator to extract a single component from a vector.
Suppose the identifier Spot was previously defined as a vector. Then Spot.x
is a float value that is the first component of this x, y, z vector.
Similarly Spot.y and Spot.z reference the 2nd and 3rd components. If Spot was
a two component UV vector you could use Spot.u and Spot.v to extract the
first and second component. For a 4D vector use .x, .y, .z and .t to extract
each float component. The dot operator is also used in color expressions
which are covered later.

7.1.4.4          Operator Promotion

You may use a lone float expression to define a vector whose components are
all the same. POV-Ray knows when it needs a vector of a particular type and
will promote a float into a vector if need be. For example the POV-Ray scale
statement requires a three component vector. If you specify scale 5 then
POV-Ray interprets this as scale <5,5,5> which means you want to scale by 5
in every direction.

Versions of POV-Ray prior to 3.0 only allowed such use of a float as a vector
in various limited places such as scale and turbulence. However you may now
use this trick anywhere. For example...

  box{0,1}    // Same as box{<0,0,0>,<1,1,1>}
  sphere{0,1} // Same as sphere{<0,0,0>,1}


When promoting a float into a vector of 2, 3, 4 or 5 components, all
components are set to the float value, however when promoting a vector of a
lower number of components into a higher order vector, all remaining
components are set to zero. For example if POV-Ray expects a 4D vector and
you specify 9 the result is <9,9,9,9> but if you specify <7,6> the result is
< 7,6,0,0>.

7.1.5            Specifying Colors

POV-Ray often requires you to specify a color. Colors consist of five values
or color components. The first three are called red, green and blue. They
specify the intensity of the primary colors red, green and blue using an
additive color system like the one used by the red, green and blue color
phosphors on a color monitor.

The 4th component, called filter, specifies the amount of filtered
transparency of a substance. Some real-world examples of filtered
transparency are stained glass windows or tinted cellophane. The light
passing through such objects is tinted by the appropriate color as the
material selectively absorbs some frequencies of light while allowing others
to pass through. The color of the object is subtracted from the light passing
through so this is called subtractive transparency.

The 5th component, called transmit, specifies the amount of non-filtered
light that is transmitted through a surface. Some real-world examples of
non-filtered transparency are thin see-through cloth, fine mesh netting and
dust on a surface. In these examples, all frequencies of light are allowed to
pass through tiny holes in the surface. Although the amount of light passing
through is diminished, the color of the light passing through is unchanged.
The color of the object is added to the light passing through so this is
called additive transparency.

Note that early versions of POV-Ray used the keyword alpha to specify
filtered transparency. However that word is often used to describe
non-filtered transparency. For this reason alpha is no longer used.

Each of the five components of a color are float values which are normally in
the range between 0.0 and 1.0. However any values, even negatives may be
used.

Colors may be specified using vectors, keywords with floats or identifiers.
You may also create very complex color expressions from combinations of any
of these using various familiar operators. The syntax for specifying a color
has evolved since POV-Ray was first released. We have maintained the original
keyword-based syntax and added a short-cut vector notation. Either the old or
new syntax is acceptable however the vector syntax is easier to use when
creating color expressions.

7.1.5.1          Color Vectors

The syntax for a color vector is any of the following...

  color rgb VECTOR3
  color rgbf VECTOR4
  color rgbt VECTOR4
  color rgbft VECTOR5


where VECTOR3, VECTOR4 or VECTOR5 are any valid vector expressions of 3, 4 or
5 components. For example

  color rgb <1.0, 0.5, 0.2>


This specifies a color whose red component is 1.0 or 100% of full intensity.
The green component is 0.5 or 50% of full intensity and the blue component is
0.2 or 20% of full intensity. Although the filter and transmit components are
not explicitly specified, they exist and are set to their default values of 0
or no transparency.

The rgbf keyword requires a four component vector. The 4th component is the
filter component and the transmit component defaults to zero. Similarly the
rgbt keyword requires four components where the 4th value is moved to the 5th
component which is transmit and then the filter component is set to zero.

The rgbft keyword allows you to specify all five components. Internally in
expressions all five are always used.

Under most circumstances the keyword color is optional and may be omitted. We
also support the British or Canadian spelling colour. Under some
circumstances, if the vector expression is a 5 component expression or there
is a color identifier in the expression then the rgbtf keyword is optional.

7.1.5.2          Color Keywords

The older keyword method of specifying a color is still useful and many users
prefer it. Like a color vector, you begin with the optional keyword color.
This is followed by any of five additional keywords red, green, blue, filter
or transmit. Each of these component keywords is followed by a float
expression. For example

  color red 1.0 green 0.5


This specifies a color whose red component is 1.0 or 100% of full intensity
and the green component is 0.5 or 50% of full intensity. Although the blue,
filter and transmit components are not explicitly specified, they exist and
are set to their default values of 0. The component keywords may be given in
any order and if any component is unspecified its value defaults to zero.

7.1.5.3          Color Identifiers

Color identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. A color identifier is declared as either of the following...

  #declare IDENTIFIER = COLOR_VECTOR
  #declare IDENTIFIER = COLOR_KEYWORDS...


Where IDENTIFIER is the name of the identifier up to 40 characters long and
COLOR_VECTOR or COLOR_KEYWORDS are any valid color specifications as
described in the two previous sections of this document. Here are some
examples...

  #declare White = rgb <1,1,1>
  #declare Cyan = color blue 1.0  green 1.0
  #declare Weird = rgb <Foo*2,Bar-1,Bob/3>
  #declare LightGray = White*0.8
  #declare LightCyan = Cyan red 0.6


As the LightGray example shows you do not need any color keywords when
creating color expressions based on previously declared colors. The last
example shows you may use a color identifier with the keyword style syntax.
Make sure that the identifier comes first before any other component
keywords.

Like floats and vectors, you may re-define colors throughout a scene but the
need to do so is rare.

7.1.5.4          Color Operators

Color vectors may be combined in expressions the same as float or vector
values. Operations are performed on a component-by-component basis. For
example rgb <1.0, 0.5 0.2> * 0.9 evaluates the same as rgb <1.0, 0.5 0.2> *
<0.9, 0.9, 0.9> or rgb <0.9, 0.45,  0.18>. Other operations are done on a
similar component-by-component basis.

You may use the dot operator to extract a single component from a color.
Suppose the identifier Shade was previously defined as a color. Then
Shade.red is the float value of the red component of Shade. Similarly
Shade.green, Shade.blue, Shade.filter and Shade.transmit extract the float
value of the other color components.

7.1.5.5          Common Color Pitfalls

The variety and complexity of color specification methods can lead to some
common mistakes. Here are some things to consider when specifying a color.

When using filter transparency, the colors which come through are multiplied
by the primary color components. For example if gray light such as rgb
<0.9,0.9,0.9> passes through a filter such as rgbf <1.0,0.5,0.0,1.0> the
result is rgb <0.9,0.45,0.0> with the red let through 100%, the green cut in
half from 0.9 to 0.45 and the blue totally blocked. Often users mistakenly
specify a clear object by

  color filter 1.0


but this has implied red, green and blue values of zero. You've just
specified a totally black filter so no light passes through. The correct way
is either

  color red 1.0   green 1.0   blue 1.0   filter 1.0


or

  color transmit 1.0


In the 2nd example it doesn't matter what the rgb values are. All of the
light passes through untouched.

Another pitfall is the use of color identifiers and expressions with color
keywords. For example...

  color My_Color red 0.5


this substitutes whatever was the red component of My_Color with a red
component of 0.5 however...

  color My_Color + red 0.5


adds 0.5 to the red component of My_Color and even less obvious...

  color My_Color * red 0.5


that cuts the red component in half as you would expect but it also
multiplies the green, blue, filter and transmit components by zero! The part
of the expression after the multiply operator evaluates to rgbft
<0.5,0,0,0,0> as a full 5 component color.

The following example results in no change to My_Color.

  color red 0.5 My_Color


This is because the identifier fully overwrites the previous value. When
using identifiers with color keywords, the identifier should be first.

One final issue, some POV-Ray syntax allows full color specifications but
only uses the rgb part. In these cases it is legal to use a float where a
color is needed. For example:

  finish { ambient 1 }


The ambient keyword expects a color so the value 1 is promoted to <1,1,1,1,1>
which is no problem. However

  pigment { color 0.4 }


is legal but it may or may not be what you intended. The 0.4 is promoted to
<0.4,0.4,0.4,0.4,0.> with the filter and transmit set to 0.4 as well. It is
more likely you wanted...

  pigment { color rgb 0.4 }


in which case a 3 component vector is expected. Therefore the 0.4 is promoted
to <0.4,0.4,0.4,0.0,0.0> with default zero for filter and transmit.

7.1.6            Strings

The POV-Ray language requires you to specify a string of characters to be
used as a file name, text for messages or text for a text object. Strings may
be specified using literals, identifiers or functions which return string
values. Although you cannot build string expressions from symbolic operators
such as are used with floats, vectors or colors, you may perform various
string operations using string functions. Some applications of strings in
POV-Ray allow for non-printing formatting characters such as newline or
form-feed.

7.1.6.1          String Literals

String literals begin with a double quote mark '"' which is followed by up to
256 printable ASCII characters and are terminated by another double quote
mark. The following are all valid string literals:

  "Here"   "There"    "myfile.gif"    "textures.inc"


Note if you need to specify a quote mark in a string literal you must preceed
it with a backslash. For example

  "Joe said \"Hello\" as he walked in."


is converted to

  Joe said "Hello" as he walked in.


If you need to specify a backslash, most of the time you need do nothing
special. However if the string ends in a backslash, you will have to specify
two. For example:

  "This is a backslash  and so is this"


Is converted to:

  This is a backslash  and so is this\


The

regardless usage however other formating codes such as \n for new line are
supported in user message streams. See "Text Formatting" for details.

7.1.6.2          String Identifiers

String identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. An identifier is declared as follows...

  #declare IDENTIFIER = STRING


Where IDENTIFIER is the name of the identifier up to 40 characters long and
STRING is a string literal, string identifier or function which returns a
string value. Here are some examples...

  #declare Font_Name = "ariel.ttf"
  #declare Inc_File = "myfile.inc"
  #declare Name = "John"
  #declare Name = concat(Name," Doe")


As the last example shows, you can re-declare a string identifier and may use
previously declared values in that re-declaration.

7.1.7            Built-in Identifiers

There are several built-in float and vector identifiers. You can use them to
specify values or to create expressions but you cannot re-declare them to
change their values.

7.1.7.1          Constant Built-in Identifiers

Most built-in identifiers never change value. They are defined as though the
following lines were at the start of every scene.

  #declare pi = 3.1415926535897932384626
  #declare true = 1
  #declare yes = 1
  #declare on = 1
  #declare false = 0
  #declare no = 0
  #declare off = 0
  #declare u = <1,0>
  #declare v = <0,1>
  #declare x = <1,0,0>
  #declare y = <0,1,0>
  #declare z = <0,0,1>
  #declare t = <0,0,0,1>


The built-in float identifier pi is obviously useful in math expressions
involving circles.

The built-in float identifiers on,off, yes, no, true and false are designed
for use as boolean constants.

The built-in vector identifiers x, y and z provide much greater readability
for your scene files when used in vector expressions. For example....

  plane { y, 1}        // The normal vector is obviously "y".
  plane { <0,1,0>, 1}  // This is harder to read.

  translate 5*x        // Move 5 units in the "x" direction.
  translate <5,0,0>    // This is less obvious.


An expression like 5*x evaluates to 5 <1,0,0> or <5,0,0>.

Similarly u and v may be used in 2D vectors. When using 4D vectors you should
use x, y, z, and t and POV-Ray will promote x, y and z to 4D when used where
4D is required.

7.1.7.2          Built-in Identifier 'clock'

The built-in float identifier clock is used to control animations in POV-Ray.
Unlike some animation packages, the action in POV-Ray animated scenes does
not depend upon the integer frame numbers. Rather you should design your
scenes based upon the float identifier clock. For non-animated scenes its
default value is 0 but you can set it to any float value using the INI file
option Clock=n.n or the command-line switch +Kn.n to pass a single float
value your scene file.

Other INI options and switches may be used to animate scenes by automatically
looping through the rendering of frames using various values for clock. By
default, the clock value is 0 for the initial frame and 1 for the final
frame. All other frames are interpolated between these values. For example if
your object is supposed to rotate one full turn over the course of the
animation you could specify rotate 360*clock*y. Then as clock runs from 0 to
1, the object rotates about the y-axis from 0 to 360 degrees.

Although the value of clock will change from frame-to-frame, it will never
change throughout the parsing of a scene.


7.1.7.3          Built-in Identifier 'version'

The built-in float identifier version contains the current setting of the
version compatibility option. Although this value defaults to 3 which is the
current POV-Ray version number, the initial value of version may be set by
the INI file option Version=n.n or by the +MVn.n command-line switch. This
tells POV-Ray to parse the scene file using syntax from an earlier version of
POV-Ray.

The INI option or switch only affects the initial setting. Unlike other
built-in identifiers, you may change the value of version throughout a scene
file. You do not use #declare to change it though. The #version language
directive is used to change modes. Such changes may occur several times
within scene files.

Together with the built-in version identifier the #version directive allows
you to save and restore the previous values of this compatibility setting.
For example suppose mystuff.inc is in version 1 format. At the top of the
file you could put:

  #declare Temp_Vers = version    // Save previous value
  #version 1.0                    // Change to 1.0 mode

  ... // Version 1.0 stuff goes here...

  #version Temp_Vers              // Restore previous version


7.1.8            Functions

POV-Ray defines a variety of built-in functions for manipulating floats,
vectors and strings. The functions are listed grouped according to their
usage and not by the type of value they return. For example vdot computes the
dot product of two vectors and is listed as a vector function even though it
returns a single float value.

Function calls consist of a keyword which specifies the name of the function
followed by a parameter list enclosed in parentheses. Parameters are
separated by commas. For example:

  keyword(param1,param2)


Functions evaluate to values that are floats, vectors or strings and may be
used in expressions or statements anywhere that literals or identifiers of
that type may be used.

7.1.8.1          Float Functions

The following are the functions which take one or more float parameters and
return float values. Assume that A and B are any valid expression that
evaluates to a float. See section "Vector Functions" and section "String
Functions" for other functions which return float values but whose primary
purpose is more closely related to vectors and strings.

abs(A): Absolute value of A. If A is negative, returns -A otherwise returns
A.

acos(A): Arc-cosine of A. Returns the angle, measured in radians, whose
cosine is A.

asin(A): Arc-sine of A. Returns the angle, measured in radians, whose sine is
A.

atan2(A,B): Arc-tangent of (A/B). Returns the angle, measured in radians,
whose tangent is (A/B). Returns appropriate value even if B is zero. Use
atan2(A,1) to compute usual atan(A) function.

ceil(A): Ceiling of A. Returns the smallest integer greater than A. Rounds up
to the next higher integer.

cos(A): Cosine of A. Returns the cosine of the angle A, where A is measured
in radians.

degrees(A): Convert radians to degrees. Returns the angle measured in degrees
whose value in radians is A. Formula is degrees=A/pi*180.0.

div(A,B): Integer division. The integer part of (A/B).

exp(A): Exponential of A. Returns the value of e raised to the power A where
e is the base of the natural logarithm, i.e. the non-repeating value
approximately equal to 2.71828182846.

floor(A): Floor of A. Returns the largest integer less than A. Rounds down to
the next lower integer.

int(A): Integer part of A. Returns the truncated integer part of A. Rounds
towards zero.

log(A): Natural logarithm of A. Returns the natural logarithm base e of the
value A.

max(A,B): Maximum of A and B. Returns A if A larger than B. Otherwise returns
B.

min(A,B): Minimum of A and B. Returns A if A smaller than B. Otherwise
returns B.

mod(A,B): Value of A modulo B. Returns the remainder after the integer
division of A/B. Formula is mod=((A/B)-int(A/B))*B.

pow(A,B): Exponentiation. Returns the value of A raised to the power B.

radians(A): Convert degrees to radians. Returns the angle measured in radians
whose value in degrees is A. Formula is radians=A*pi/180.0.

rand(A): Returns the next pseudo-random number from the stream specified by
the positive integer A. You must call seed() to initialize a random stream
before calling rand(). The numbers are uniformly distributed, and have values
between 0.0 and 1.0, inclusively. The numbers generated by separate streams
are independent random variables.

seed(A): Initializes a new pseudo-random stream with the initial seed value
A. The number corresponding to this random stream is returned. Any number of
pseudo-random streams may be used as shown in the example below:

  #declare R1 = seed(0)
  #declare R2 = seed(12345)

  #sphere { <rand(R1), rand(R1), rand(R1)>, rand(R2) }


Multiple random generators are very useful in situations where you use rand()
to place a group of objects, and then decide to use rand() in another
location earlier in the file to set some colors or place another group of
objects. Without separate rand() streams, all of your objects would move when
you added more calls to rand(). This is very annoying.

sin(A): Sine of A. Returns the sine of the angle A, where A is measured in
radians.

sqrt(A): Square root of A. Returns the value whose square is A.

tan(A): Tangent of A. Returns the tangent of the angle A, where A is measured
in radians.

7.1.8.2          Vector Functions

The following are the functions which take one or more vector and float
parameters and return vector or float values. All of these functions support
only three component vectors. Assume that A and B are any valid expression
that evaluates to a three component vector and that F is any valid expression
that evaluates to a float.

vaxis_rotate(A,B,F): Rotate A about B by F. Given the x,y,z coordinates of a
point in space designated by the vector A, rotate that point about an
arbitrary axis defined by the vector B. Rotate it through an angle specified
in degrees by the float value F. The result is a vector containing the new
x,y,z coordinates of the point.

vcross(A,B): Cross product of A and B. Returns a vector that is the vector
cross product of the two vectors. The resulting vector is perpendicular to
the two original vectors and its length is proportional to the angle between
them. See the animated demo scene VECT2.POV for an illustration.

vdot(A,B): Dot product of A and B. Returns a float value that is the dot
product (sometimes called scaler product of A with B. Formula is vdot=A.x*B.x
+ A.y*B.y + A.z*B.z. See the animated demo scene VECT2.POV for an
illustration.

vlength(A): Length of A. Returns a float value that is the length of vector
A. Can be used to compute the distance between two points. Dist=vlength(B-A).
Formula is vlength=sqrt(vdot(A,A)).

vnormalize(A): Normalize vector A. Returns a unit length vector that is the
same direction as A. Formula is vnormalize=A/vlength(A).

vrotate(A,B): Rotate A about origin by B. Given the x,y,z coordinates of a
point in space designated by the vector A, rotate that point about the origin
by an amount specified by the vector B. Rotate it about the x-axis by an
angle specified in degrees by the float value B.x. Similarly B.y and B.z
specify the amount to rotate in degrees about the y-axis and z-axis. The
result is a vector containing the new x,y,z coordinates of the point.

7.1.8.3          String Functions

The following are the functions which take one or more string and float
parameters and return string or float values. Assume that S1 and S2 are any
valid strings and that A, L and P are any valid expressions that evaluate to
floats.

asc(S1): ASCII value of S1. Returns an integer value in the range 0 to 255
that is the ASCII value of the first character of S1. For example asc("ABC")
is 65 because that is the value of the character "A".

chr(A): Character whose ASCII value is A. Returns a single character string.
The ASCII value of the character is specified by an integer A which must be
in the range 0 to 255. For example chr(70) is the string "F". When rendering
text objects you should be aware that the characters rendered for values of A
> 127 are dependent on the (TTF) font being used. Many (TTF) fonts use the
Latin-1 (ISO 8859-1) character set, but not all do.

concat(S1,S2,[S3...]): Concatenate strings S1 and S2. Returns a string that
is the concatenation of all parameter strings. Must have at least 2
parameters but may have more. For example:

  concat("Value is ", str(A,3,1), " inches")


If the float value A was 12.34 the result is "Value is 12.3 inches" which is
a string.

file_exists(S1): Search for file specified by S1. Attempts to open the file
whose name is specified by the string S1. The current directory and all
directories specified in any Library_Path INI options or +L command line
switches are searched. File is immediately closed. Returns a boolean value 1
on success and 0 on failure.

str(A,L,P): Convert float A to a formatted string. Returns a formatted string
representation of float value A. The float parameter L specifies the minimum
length of the string and the type of left padding used if the string's
representation is shorter than the minimum. If L is positive then the padding
is with blanks. If L is negative then the padding is with zeros. The overall
minimum length of the formatted string is abs(L). If the string needs to be
longer, it will be made as long as necessary to represent the value.

The float parameter P specifies the number of digits after the decimal point.
If P is negative then a compiler-specific default precision is use. Here are
some examples:

  str(123.456,0,3)   "123.456"
  str(123.456,4,3)   "123.456"
  str(123.456,9,3)   "  123.456"
  str(123.456,-9,3)  "00123.456"
  str(123.456,0,2)   "123.46"
  str(123.456,0,0)   "123"
  str(123.456,5,0)   "  123"
  str(123.000,7,2)   " 123.00"
  str(123.456,0,-1)  "123.456000" (platform specific)


strcmp(S1,S2): Compare string S1 to S2. Returns a float value zero if the
strings are equal, a positive number if S1 comes after S2 in the ASCII
collating sequence, else a negative number.

strlen(S1): Length of S1. Returns an integer value that is the number of
characters in the string S1.

strlwr(S1): Lower case of S1. Returns a new string in which all upper case
letters in the string S1 are converted to lower case. The original string is
not affected. For example strlwr("Hello There!") results in "hello there!".

substr(S1,P,L): Sub-string from S1. Returns a string that is a subset of the
characters in parameter S1 starting at the position specified by the integer
value P for a length specified by the integer value L. For example
substr("ABCDEFGHI",4,2) evaluates to the string "EF". If P+L>strlen(S1) an
error occurs.

strupr(S1): Upper case of S1. Returns a new string in which all lower case
letters in the string S1 are converted to upper case. The original string is
not affected. For example strupr("Hello There!") results in "HELLO THERE!".

val(S1): Convert string S1 to float. Returns a float value that is
represented by the text in S1. For example val("123.45") is 123.45 as a
float.

7.2              Language Directives

The POV Scene Language contains several statements called language
directives which tell the file parser how to do its job. These directives can
appear in almost any place in the scene file - even in the middle of some
other statements. They are used to include other text files in the stream of
commands, to declare identifiers, to define conditional or looped parsing and
to control other important aspects of scene file processing.

Each directive begins with the hash character # (often called a number sign
or pound sign). It is followed by a keyword and optionally other parameters.

In versions of POV-Ray prior to 3.0, the use of this # character was
optional. Language directives could only be used between objects, camera or
light_source statements and could not appear within those statements. The
exception was the #include which could appear anywhere. Now that all language
directives can be used almost anywhere, the # character is mandatory.

The following keywords introduce language directives.


#break              #default            #statistics
#case               #else               #switch
#debug              #end                #version
#declare            #render             #warning


Earlier versions of POV-Ray considered the keyword
#max_intersections and the keyword #max_trace_level to
be language directives but they have been moved to the
global_settings statement. Their use as a directive still works
but it generates a warning and may be discontinued in the future.


7.2.1            Include Files

The language allows include files to be specified by placing the line

  #include "filename.inc"


at any point in the input file. The filename may be specified by any valid
string expression but it usually is a literal string enclosed in double
quotes. It may be up to 40 characters long (or your computer's limit),
including the two double-quote characters.

The include file is read in as if it were inserted at that point in the file.
Using include is the same as actually cutting and pasting the entire contents
of this file into your scene.

Include files may be nested. You may have at most 10 nested include files.
There is no limit on un-nested include files.

Generally, include files have data for scenes but are not scenes in
themselves. By convention scene files end in .pov and include files end with
.inc.

It is legal to specify drive and directory information in the file
specification however it is discouraged because it makes scene files less
portable between various platforms.

It is typical to put standard include files in a special sub-directory.
POV-Ray can only read files in the current directory or one referenced by the
Library_Path option (See section "Library Paths").

7.2.2            Declare

Identifiers may be declared and later referenced to make scene files more
readable and to parametrize scenes so that changing a single declaration
changes many values. There are several built-in identifiers which POV-Ray
declares for you. See section "Built-in Identifiers"  for details.

7.2.2.1          Declaring identifiers

An identifier is declared as follows.

  #declare IDENTIFIER = ITEM


Where IDENTIFIER is the name of the identifier up to 40 characters long and
ITEM is any of the following

  float, vector, color or string expressions
  objects (all kinds)
  texture, pigment, normal, finish or halo
  color_map, pigment_map, slope_map, normal_map
  camera, light_source
  atmosphere
  fog
  rainbow
  sky_sphere
  transform


Here are some examples.

  #declare Rows = 5
  #declare Count = Count+1
  #declare Here = <1,2,3>
  #declare White = rgb <1,1,1>
  #declare Cyan = color blue 1.0  green 1.0
  #declare Font_Name = "ariel.ttf"
  #declare Ring = torus {5,1}
  #declare Checks = pigment { checker White, Cyan }

  object{ Rod scale y*5 }         // not "cylinder { Rod }"
  object {
    Ring
    pigment { Checks scale 0.5 }
    transform Skew
  }


Declarations, like most language directives, can appear anywhere in the file
- even within other statements. For example:

  #declare Here=<1,2,3>
  #declare Count=0                   // initialize Count

  union {
    object { Rod translate Here*Count }
    #declare Count=Count+1           // re-declare inside union
    object { Rod translate Here*Count }
    #declare Count=Count+1           // re-declare inside union
    object { Rod translate Here*Count }
  }


As this example shows, you can re-declare an identifier and may use
previously declared values in that re-declaration. However if you attempt to
re-declare an identifier as anything other than its original type, it will
generate a warning message.

Declarations may be nested inside each other within limits. In the example in
the previous section you could declare the entire union as a object. However
for technical reasons you may not use any language directive inside the
declaration of floats, vectors or color expressions.

7.2.3            Default Directive

POV-Ray creates a default texture when it begins processing. You may change
those defaults as described below. Every time you specify a texture
statement, POV-Ray creates a copy of the default texture. Anything you put in
the texture statement overrides the default settings. If you attach a
pigment, normal or finish to an object without any texture statement then
POV-Ray checks to see if a texture has already been attached. If it has a
texture then the pigment, normal or finish will modify the existing texture.
If no texture has yet been attached to the object then the default texture is
copied and the pigment, normal or finish will modify that texture.

You may change the default texture, pigment, normal or finish using the
language directive #default as follows:

  #default {
    texture {
      pigment {...}
      normal  {...}
      finish  {...}
    }
  }


Or you may change just part of it like this:

  #default {
    pigment {...}
  }


This still changes the pigment of the default texture. At any time there is
only one default texture made from the default pigment, normal and finish.
The example above does not make a separate default for pigments alone. Note
that the special textures tiles and material_map or a texture with a
texture_map may not be used as defaults.

You may change the defaults several times throughout a scene as you wish.
Subsequent #default statements begin with the defaults that were in effect at
the time. If you wish to reset to the original POV-Ray defaults then you
should first save them as follows:

  //At top of file
  #declare Original_Default = texture {}


later after changing defaults you may restore it with...

  #default {texture {Original_Default}}


If you do not specify a texture for an object then the default texture is
attached when the object appears in the scene. It is not attached when an
object is declared. For example:

  #declare My_Object =
    sphere{ <0,0,0>, 1 }  // Default texture not applied
  object { My_Object }    // Default texture added here


You may force a default texture to be added by using an empty texture
statement as follows:

  #declare My_Thing =
    sphere { <0,0,0>, 1 texture {} }  // Default texture applied


The original POV-Ray defaults for all items are given throughout the
documentation under each appropriate section.

7.2.4            Version Directive

While many language changes have been made for POV-Ray 3.0, all of version
2.0 syntax and most of version 1.0 syntax still works. Whenever possible we
try to maintain backwards compatibility. One feature introduced in 2.0 that
was incompatible with any 1.0 scene files is the parsing of float
expressions. Setting +MV1.0 command line switch or the Version=1.0 INI option
turns off expression parsing as well as many warning messages so that nearly
all 1.0 files will still work. The changes between 2.0 and 3.0 are not as
extensive. Setting Version=2.0 is only necessary to eliminate some warning
messages. Naturally the default setting for this option is Version=3.0.

The #version language directive is used to change modes within scene files.
This switch or INI options only affects the initial setting.

Together with the built-in version identifier the #version directive allows
you to save and restore the previous values of this compatibility setting.
For example suppose mystuff.inc is in version 1.0 format. At the top of the
file you could put:

  #declare Temp_Vers = version // Save previous value
  #version 1.0                    // Change to 1.0 mode

  ... // Version 1.0 stuff goes here ...

  #version Temp_Vers              // Restore previous version


Previous versions of POV-Ray would not allow you to change versions inside an
object or declaration but that restriction has been lifted for POV-Ray 3.0.

Future versions of POV-Ray may not continue to maintain full backward
compatibility even with the #version directive. We strongly encourage you to
phase in 3.0 syntax as much as possible.

7.2.5            Conditional Directives

POV-Ray 3.0 allows a variety of new language directives to implement
conditional parsing of various sections of your scene file. This is
especially useful in describing the motion for animations but it has other
uses as well. Also available is a #while loop directive. You may nest
conditional directives 200 levels deep.

7.2.5.1          IF ELSE Directives

The simplest conditional directive is a traditional #if directive. It is of
the form...

  #if (COND)
    // This section is
    //  parsed if COND is true
  #else
    // This section is
    // parsed if COND is false
  #end // End of conditional part


where (COND) is a float expression that evaluates to a boolean value. A value
of 0.0 is false and any non-zero value is true. Note that extremely small
values of about 1e-10 are considered zero in case of round off errors. The
parentheses around the condition are required. The #else directive is
optional. The #end directive is required.

7.2.5.2          IFDEF Directives

The #ifdef directive is similar to the #if directive however it is used to
determine if an identifier has been previously declared. After the #ifdef
directive instead of a boolean expression you put a lone identifier enclosed
in parentheses. For example:

 #ifdef (User_Thing)
   // This section is parsed if the
   // identifier "User_Thing" was
   // previously declared
   object{User_Thing} // invoke identifier
 #else
   // This section is parsed if the
   // identifier "User_Thing" was not
   // previously declared
   box{<0,0,0>,<1,1,1>} // use a default
 #end
   // End of conditional part


7.2.5.3          IFNDEF Directives

The #ifndef directive is similar to the #ifdef directive however it is used
to determine if the given identifier isn't declared yet. For example:

 #ifndef (User_Thing)
   // This section is parsed if the
   // identifier "User_Thing" was not
   // previously declared
   box{<0,0,0>,<1,1,1>} // use a default
 #else
   // This section is parsed if the
   // identifier "User_Thing" was
   // previously declared
   object{User_Thing} // invoke identifier
 #end
   // End of conditional part


7.2.5.4          SWITCH CASE and RANGE Directives

A more powerful conditional is the #switch directive. The syntax is as
follows...

  #switch (VALUE)
    #case (TEST_1)
      // This section is parsed if VALUE=TEST_1
    #break  //First case ends

    #case (TEST_2)
      // This section is parsed if VALUE=TEST_2
    #break  //Second case ends

    #range (LOW_1,HIGH_1)
      // This section is parsed if (VALUE>=LOW_1)&(VALUE<=HIGH_1)
    #break  //Third case ends

    #range (LOW_2,HIGH_2)
      // This section is parsed if (VALUE>=LOW_2)&(VALUE<=HIGH_2)
    #break  //Fourth case ends

    #else
      // This section is parsed if no other case or
      // range is true.
  #end // End of conditional part


The float expression VALUE following the #switch directive is evaluated and
compared to the values in the #case or #range directives. When using #case,
it is followed by a float expression TEST_1 in parentheses. It is compared to
the VALUE. As usual in POV-Ray, float comparisons are considered equal if
their difference is under 1e-10. If the values are equal, parsing continues
normally until a #break, #else or #end directive is reached. If the
comparison fails POV-Ray skips until another #case or #range is found.

If you use the #range directive it is followed by two float expressions LOW_1
and HIGH_1 which are enclosed in parentheses and separated by a comma. If the
switch VALUE is in the range specified then parsing continues normally until
a #break, #else or #end directive is reached. If the VALUE is outside the
range the comparison fails and POV-Ray skips until another #case or #range is
found.

If no #case or #range succeeds the #else section is parsed. The #else
directive is optional. If no #else is specified and no match succeeds then
parsing resumes after the #end directive.

There may be any number of #case or #range directives in any order you want.
If a segment evaluates true but no #break is specified, the parsing will fall
through to the next #case or #range and will continue until a #break, #else
or #end. Hitting a #break while parsing a successful section causes an
immediate jump to the #end without processing subsequent sections, even if a
subsequent condition would also have been satisfied.

7.2.5.5          WHILE Directive

The #while directive is a looping feature that makes it easy to place
multiple objects in a pattern or other uses. The #while directive is followed
by a float expression that evaluates to a boolean value. A value of 0.0 is
false and any non-zero value is true. Note that extremely small values of
about 1e-10 are considered zero in case of round off errors. The parentheses
around the expression are required. If the condition is true parsing
continues normally until an #end directive is reached. At the end, POV-Ray
loops back to the #while directive and the condition is re-evaluated. Looping
continues until the condition fails. When it fails, parsing continues after
the #end directive. For example:

  #declare Count=0
  #while (Count < 5)
    object{MyObject translate x*3*Count}
    #declare Count=Count+1
  #end


This example places five copies of MyObject in a row spaced three units apart
in the x-direction.

7.2.6            User Message Directives

With the addition of conditional and loop directives, the POV-Ray language
has the potential to be more like an actual programming language. This means
that it will be necessary to have some way to see what is going on when
trying to debug loops and conditionals. To fulfill this need we have added
the ability to print text messages to the screen. You have a choice of five
different text streams to use including the ability to generate a fatal error
if you find it necessary. Limited formatting is available for strings output
by this method.

7.2.6.1          Text Message Streams

The syntax for a text message is any of the following:

  #debug      STRING
  #error      STRING
  #render     STRING
  #statistics STRING
  #warning    STRING


Where STRING is any valid string of text including string identifiers or
functions which return strings. For example:

  #switch (clock*360)
    #range (0,180)
      #render "Clock in 0 to 180 range\n"
    #break

    #range (180,360)
      #render "Clock in 180 to 360 range\n"
    #break

    #else
      #warning "Clock outside expected range\n"
      #warning concat("Value is:",str(clock*360,5,0),"\n")
  #end


There are seven distinct text streams that POV-Ray uses for output. You may
output only to five of them. On some versions of POV-Ray, each stream is
designated by a particular color. Text from these streams are displayed
whenever it is appropriate so there is often an intermixing of the text. The
distinction is only important if you choose to turn some of the streams off
or to direct some of the streams to text files. On some systems you may be
able to review the streams separately in their own scroll-back buffer. See
"Console Text Output" for details on re-directing the streams to a text file.


Here is a description of how POV-Ray uses each stream. You may use them for
whatever purpose you want except note that use of the #error stream causes a
fatal error after the text is displayed.

DEBUG: This stream displays debugging messages. It was primarily designed for
developers but this and other streams may also be used by the user to display
messages from within their scene files.

FATAL: This stream displays fatal error messages. After displaying this text,
POV-Ray will terminate. When the error is a scene parsing error, you may be
shown several lines of scene text that leads up to the error.

RENDER: This stream displays information about what options you have
specified to render the scene. It includes feedback on all of the major
options such as scene name, resolution, animation settings, anti-aliasing and
others.

STATISTICS: This stream displays statistics after a frame is rendered. It
includes information about the number of rays traced, the length of time of
the processing and other information.

WARNING: This stream displays warning messages during the parsing of scene
files and other warnings. Despite the warning, POV-Ray can continue to render
the scene.


7.2.6.2          Text Formatting

Some escape sequences are available to include non-printing control
characters in your text. These sequences are similar to those used in string
literals in the C programming language. The sequences are:

  "\""Double quote 0x2209D 0x0A


For example:

  #debug "This is one line.\nBut this is another"


Depending on what platform you are using, they may not be fully supported for
console output. However they will appear in any text file if you re-direct a
stream to a file.

Note that most of these control characters only apply in text message
directives. They are not implemented for other string usage in POV-Ray such
as text objects or file names.

The exceptions are the


7.3              POV-Ray Coordinate System

Objects, lights and the camera are positioned using a typical 3D coordinate
system. The usual coordinate system for POV-Ray has the positive y-axis
pointing up, the positive x-axis pointing to the right and the positive
z-axis pointing into the screen. The negative values of the axes point the
other direction as shown in the images in section "Understanding POV-Ray's
Coordinate System".

Locations within that coordinate system are usually specified by a three
component vector. The three values correspond to the x, y and z directions
respectively. For example, the vector < 1,2,3> means the point that's one
unit to the right, two units up and three units in front of the center of the
universe at <0,0,0>.

Vectors are not always points though. They can also refer to an amount to
size, move or rotate a scene element or to modify the texture pattern applied
to an object.

The supported transformations are rotate, scale and translate. They are used
to turn, size and translate an object or texture. A transformation matrix may
also be used to specify complex transformations directly.

7.3.1            Transformations

The supported transformations are rotate, scale and translate. They are used
to turn, size and translate an object or texture.

  rotate <VECTOR>
  scale <VECTOR>
  translate <VECTOR>


7.3.1.1          Translate

An object or texture pattern may be moved by adding a translate parameter. It
consists of the keyword translate followed by a vector expression. The terms
of the vector specify the number of units to move in each of the x, y and z
directions. Translate moves the element relative to it's current position.
For example

  sphere { <10, 10, 10>, 1
    pigment { Green }
    translate <-5, 2, 1>
  }


will move the sphere from <10,10,10> to < 5,12,11>. It does not move it to
the absolute location <-5,2,1>. Translating by zero will leave the element
unchanged on that axis. For example:

  sphere { <10, 10, 10>, 1
    pigment { Green }
    translate 3*x // evaluates to <3,0,0> so move 3 units
                  // in the x direction and none along y or z
  }


7.3.1.2          Scale

You may change the size of an object or texture pattern by adding a scale
parameter. It consists of the keyword scale followed by a vector expression.
The 3 terms of the vector specify the amount of scaling in each of the x, y
and z directions.

Scale is used to stretch or squish an element. Values larger than one stretch
the element on that axis while values smaller than one are used to squish it.
Scale is relative to the current element size. If the element has been
previously re-sized using scale then scale will size relative to the new
size. Multiple scale values may used.

For example

  sphere { <0,0,0>, 1
    scale <2,1,0.5>
  }


will stretch and smash the sphere into an ellipsoid shape that is twice the
original size along the x-direction, remains the same size in the y-direction
and is half the original size in the z-direction.

If a lone float expression is specified it is promoted to a three component
vector whose terms are all the same. Thus the item is uniformly scaled by the
same amount in all directions. For example:

  object {
    MyObject
    scale 5 // Evaluates as <5,5,5> so uniformly scale
            // by 5 in every direction.
  }


7.3.1.3          Rotate

You may change the orientation of an object or texture pattern by adding a
rotate parameter. It consists of the keyword rotate followed by a vector
expression. The three terms of the vector specify the number of degrees to
rotate about each of the x-, y- and z-axes.

Note that the order of the rotations does matter. Rotations occur about the
x-axis first, then the y-axis, then the z-axis. If you are not sure if this
is what you want then you should only rotate on one axis at a time using
multiple rotation statements to get a correct rotation. As in

  rotate <0, 30, 0>  // 30 degrees around Y axis then,
  rotate <-20, 0, 0> // -20 degrees around X axis then,
  rotate <0, 0, 10>  // 10 degrees around Z axis.


Rotation is always performed relative to the axis. Thus if an object is some
distance from the axis of rotation it will not only rotate but it will orbit
about the axis as though it was swinging around on an invisible string.

To work out the rotation directions you must perform the famous Computer
Graphics Aerobics exercise as explained in the section "Understanding
POV-Ray's Coordinate System".

7.3.1.4          Matrix Keyword

The matrix keyword can be used to explicitly specify the transformation
matrix to be used for objects or textures. Its syntax is:

  matrix < m00, m01, m02,
           m10, m11, m12,
           m20, m21, m22,
           m30, m31, m32 >


Where m00 through m32 are float expressions that specify the elements of a
4*4 matrix with the fourth column implicitly set to <0,0,0,1>. A point P,
P=<px, py, pz>, is transformed into Q, Q=<qx, qy, qz> by

  qx = M00 * px + M10 * py + M20 * pz + M30
  qy = M01 * px + M11 * py + M21 * pz + M31
  qz = M02 * px + M12 * py + M22 * pz + M32


Normally you won't use the matrix keyword because it's less descriptive than
the transformation commands and harder to visualize. There is an intersecting
aspect of the matrix command though. It allows more general transformation
like shearing. The following matrix causes an object to be sheared along the
y-axis.

  object {
    MyObject
    matrix < 1, 1, 0,
             0, 1, 0,
             0, 0, 1,
             0, 0, 0 >
  }


7.3.2            Transformation Order

Because rotations are always relative to the axis and scaling is relative to
the origin, you will generally want to create an object at the origin and
scale and rotate it first. Then you may translate it into its proper
position. It is a common mistake to carefully position an object and then to
decide to rotate it because a rotation of an object causes it to orbit about
the axis, the position of the object may change so much that it orbits out of
the field of view of the camera!

Similarly scaling after translation also moves an object unexpectedly. If you
scale after you translate the scale will multiply the translate amount. For
example

  translate <5, 6, 7>
  scale 4


will translate to <20,24,28> instead of < 5,6,7>. Be careful when
transforming to get the order correct for your purposes.

7.3.3            Transform Identifiers

At times it is useful to combine together several transformations and apply
them in multiple places. A transform identifier may be used for this purpose.
Transform identifiers are declared as follows:

  #declare IDENT = transform { TRANSFORMATION... }


Where IDENT is the identifier to be declared and TRANSFORMATION is one or
more translate, rotate, scale or matrix specifications or a previously
declared transform identifier. A transform identifier is invoked by the
transform keyword without any brackets as shown here:

  object {
    MyObject           // Get a copy of MyObject
    transform MyTrans  // Apply the transformation
    translate -x*5     // Then move it 5 units left
  }
  object {
    MyObject           // Get another copy of MyObject
    transform MyTrans  // Apply the same transformation
    translate -x*5     // Then move this one 5 units right
  }


On extremely complex CSG objects with lots of components it may speed up
parsing if you apply a declared transformation rather than the individual
translate, rotate, scale or matrix specifications. The transform is attached
just once to each component. Applying each individual translate, rotate,
scale or matrix specifications takes long. This only affects parsing -
rendering works the same either way.

7.3.4            Transforming Textures and Objects

When an object is transformed all textures attached to the object at that
time are transformed as well. This means that if you have a translate,
rotate, scale or matrix in an object before a texture the texture will not be
transformed. If the transformation is after the texture then the texture will
be transformed with the object. If the transformation is inside the texture
statement then only the texture is affected. The shape remains the same. For
example:

  sphere { 0, 1
    texture { Jade }  // texture identifier from TEXTURES.INC
    scale 3           // this scale affects both the
                      // shape and texture
  }

  sphere { 0, 1
    scale 3           // this scale affects the shape only
    texture { Jade }
  }

  sphere { 0, 1
    texture {
      Jade
      scale 3         // this scale affects the texture only
    }
  }


Transformations may also be independently applied to pigment patterns and
surface normal patterns. Note that scaling a normal pattern affects only the
width and spacing. It does not affect the apparent height or depth of the
bumps. For example:

  box { <0, 0, 0>, <1, 1, 1>
    texture {
      pigment {
        checker Red, White
        scale 0.25 // This affects only the color pattern
      }
      normal {
        bumps 0.3  // This specifies apparent height of bumps
        scale 0.2  // Scales diameter and space between bumps
                   // but not the height. Has no effect on
                   // color pattern.
      }
      rotate y*45  // This affects the entire texture but
    }              // not the object.
  }


7.4              Camera

The camera definition describes the position, projection type and properties
of the camera viewing the scene. Its syntax is:

  camera {
    [ perspective | orthographic | fisheye |
      ultra_wide_angle | omnimax | panoramic |
      cylinder FLOAT ]
    location <VECTOR>
    look_at <VECTOR>
    right <VECTOR>
    up <VECTOR>
    direction <VECTOR>
    sky <VECTOR>
    right <VECTOR>
    angle FLOAT
    blur_samples FLOAT
    aperture FLOAT
    focal_point <VECTOR>
    normal { NORMAL }
  }


Depending on the projection type some of the parameters are required, some
are optional and some aren't used. If no projection type is given the
perspective camera will be used (pinhole camera). If no camera is specified a
default camera is used.

Regardless of the projection type all cameras use the location, look_at,
right, up, direction and sky keywords to determine the location and
orientation of the camera. Their meaning differs with the projection type
used. A more detailed explanation of the camera placement follows later.

7.4.1            Type of Projection

The following list explains the different projection types that can be used
with the camera. The most common types are the perspective and orthographic
projections.

Perspective projection: This projection represents the classic pinhole
camera. The (horizontal) viewing angle is either determined by the ratio
between the length of the direction vector and the length of the right vector
or by the optional keyword angle, which is the preferred way. The viewing
angle has to be larger than 0 degrees and smaller than 180 degrees. See the
figure below for the geometry of the perspective camera.

The perspective camera.

Orthographic projection: This projection uses parallel camera rays to create
an image of the scene. The size of the image is determined by the lengths of
the right and up vectors.

If you add the orthographic keyword after all other parameters of a
perspective camera you'll get an orthographic view with the same image area,
i.e. the size of the image is the same. In this case you needn't specify the
lengths of the right and up vector because they'll be calculated
automatically. You should be aware though that the visible parts of the scene
change when switching from perspective to orthographic view. As long as all
objects of interest are near the look_at location they'll be still visible if
the orthographic camera is used. Objects farther away may get out of view
while nearer objects will stay in view.

Fisheye projection: This is a spherical projection. The viewing angle is
specified by the angle keyword. An angle of 180 degrees creates the
"standard" fisheye while an angle of 360 degrees creates a super-fisheye
("I-see-everything-view"). If you use this projection you should get a
circular image. If this isn't the case, i.e. you get an elliptical image, you
should read "Aspect Ratio".

Ultra wide angle projection: This projection is somewhat similar to the
fisheye but it projects the image onto a rectangle instead of a circle. The
viewing angle can be specified using the angle keyword.

Omnimax projection: The omnimax projection is a 180 degrees fisheye that has
a reduced viewing angle in the vertical direction. In reality this projection
is used to make movies that can be viewed in the dome-like Omnimax theaters.
The image will look somewhat elliptical. The angle keyword isn't used with
this projection.

Panoramic projection: This projection is called "cylindrical equirectangular
projection". It overcomes the degeneration problem of the perspective
projection if the viewing angle approaches 180 degrees. It uses a type of
cylindrical projection to be able to use viewing angles larger than 180
degrees with a tolerable lateral-stretching distortion. The angle keyword is
used to determine the viewing angle.

Cylindrical projection: Using this projection the scene is projected onto a
cylinder. There are four different types of cylindrical projections depending
on the orientation of the cylinder and the position of the viewpoint. The
viewing angle and the length of the up or right vector determine the
dimensions of the camera and the visible image. The camera to use is
specified by a number. The types are:

  4 horizontal cylinder, viewpoint moves along the cylinder's axis


If the perspective camera is used the angle keyword overrides the viewing
angle specified by the direction keyword and vice versa. Each time angle is
used the length of the direction vector is adjusted to fit the new viewing
angle.

There is no limitation to the viewing angle except for the perspective
projection. If you choose viewing angles larger than 360 degrees you'll see
repeated images of the scene (the way the repetition takes place depends on
the camera). This might be useful for special effects.

You should note that the vista buffer can only be used with the perspective
and orthographic camera.

7.4.2            Focal Blur

Simulates focal depth-of-field by shooting a number of sample rays from
jittered points within each pixel and averaging the results.

The aperture keyword determines the depth of the sharpness zone. Large
apertures give a lot of blurring, while narrow apertures will give a wide
zone of sharpness. Note that, while this behaves as a real camera does, the
values for aperture are purely arbitrary and are not related to f-stops.

The center of the zone of sharpness is the focal_point vector (the default
focal_point is <0,0,0>).

The blur_samples value controls the maximum number of rays to use for each
pixel. More rays give a smoother appearance but is slower, although this is
controlled somewhat by an adaptive mechanism that stops shooting rays when a
certain degree of confidence has been reached that shooting more rays would
not result in a significant change.

The confidence and variance keywords control the adaptive function. The
confidence value is used to determine when the samples seem to be close
enough to the correct color. The variance value specifies an acceptable
tolerance on the variance of the samples taken so far. In other words, the
process of shooting sample rays is terminated when the estimated color value
is very likely (as controlled by the confidence probability) near the real
color value.

Since the confidence is a probability its values can range from 0 to 1 (the
default is 0.9, i. e. 90%). The value for the variance should be in the range
of the smallest displayable color difference (the default is 1/128).

Larger confidence values will lead to more samples, slower traces and better
images. The same holds for smaller variance thresholds.

By default no focal blur is used, i. e. the default aperture is 0 and the
default number of samples is 0.

7.4.3            Camera Ray Perturbation

The optional keyword normal may be used to assign a normal pattern to the
camera. All camera rays will be perturbed using this pattern. This lets you
create special effects. See the animated scene camera2.pov for an example.

7.4.4            Placing the Camera

In the following sections the placing of the camera will be further
explained.

7.4.4.1          Location and Look_At

Under many circumstances just two vectors in the camera statement are all you
need to position the camera: location and look_at. For example:

  camera {
    location <3,5,-10>
    look_at  <0,2,1>
  }


The location is simply the x, y, z coordinates of the camera. The camera can
be located anywhere in the ray-tracing universe. The default location is <0,
0, 0>. The look_at vector tells POV-Ray to pan and tilt the camera until it
is looking at the specified x, y, z coordinates. By default the camera looks
at a point one unit in the z-direction from the location.

The look_at specification should almost always be the last item in the camera
statement. If other camera items are placed after the look_at vector then the
camera may not continue to look at the specified point.

7.4.4.2          The Sky Vector

Normally POV-Ray pans left or right by rotating about the y-axis until it
lines up with the look_at point and then tilts straight up or down until the
point is met exactly. However you may want to slant the camera sideways like
an airplane making a banked turn. You may change the tilt of the camera using
the sky vector. For example:

  camera {
    location <3,5,-10>
    sky      <1,1,0>
    look_at  <0,2,1>
  }


This tells POV-Ray to roll the camera until the top of the camera is in line
with the sky vector. Imagine that the sky vector is an antenna pointing out
of the top of the camera. Then it uses the sky vector as the axis of rotation
left or right and then to tilt up or down in line with the sky vector. In
effect you're telling POV-Ray to assume that the sky isn't straight up. Note
that the sky vector must appear before the look_at vector.

The sky vector does nothing on its own. It only modifies the way the look_at
vector turns the camera. The default value for sky is <0, 1, 0>.

7.4.4.3          The Direction Vector

The direction vector tells POV-Ray the initial direction to point the camera
before moving it with look_at or rotate vectors (the default is direction <0,
0, 1>). It may also be used to control the (horizontal) field of view with
some types of projection. This should be done using the easier to use angle
keyword though.

If you are using the ultra wide angle, panoramic or cylindrical projection
you should use a unit length direction vector to avoid strange results.

The length of the direction vector doesn't matter if one of the following
projection types is used: orthographic, fisheye or omnimax.

7.4.4.4          Angle

The angle keyword specifies the (horizontal) viewing angle in degrees of the
camera used. Even though it is possible to use the direction vector to
determine the viewing angle for the perspective camera it is much easier to
use the angle keyword.

The necessary calculations to convert from one method to the other are
described below. These calculations are used to determine the length of the
direction vector whenever the angle keyword is encountered.

The viewing angle is converted to a direction vector length and vice versa
using the formula The viewing angle is given by the formula

  angle = 2 * arctan(0.5 * right_length / direction_length)


where right_length and direction_length are the lengths of the right and
direction vector respectively and arctan is the inverse tangens function.

From this the length of the direction vector can be calculated for a given
viewing angle and right vector.

From this the length of the direction vector can be calculated for a given
viewing angle and right vector.

  direction_length = 0.5 * right_length / tan(angle / 2)


7.4.4.5          Up and Right Vectors

The direction of the up and right vectors (together with the direction
vector) determine the orientation of the camera in the scene. They are set
implicitly by their default values of

  right 4/3*x
  up y


or the look_at parameter (in combination with location). The directions of an
explicitly specified right and up vector will be overridden by any following
look_at parameter.

While some camera types ignore the length of these vectors others use it to
extract valuable information about the camera settings. The following list
will explain the meaning of the right and up vector for each camera type.
Since the direction the vectors is always used to describe the orientation of
the camera it will not be explained again.

Perspective projection: The lengths of the up and right vectors are used to
set the size of the viewing window and the aspect ratio as described in
detail in section "Aspect Ratio". Since the field of view depends on the
length of the direction vector (implicitly set by the angle keyword or
explicitly set by the direction keyword) and the lengths of the right and up
vectors you should carefully choose them in order to get the desired results.


Orthographic projection: The lengths of the right and up vector set the size
of the viewing window regardless of the direction vector length, which is not
used by the orthographic camera. Again the relation of the lengths is used to
set the aspect ratio.

Fisheye projection: The right and up vectors are used to set the aspect
ratio.

Ultra wide angle projection: The up and right vectors work in a similar way
as for the perspective camera.

Omnimax projection: The omnimax projection is a 180 degrees fisheye that has
a reduced viewing angle in the vertical direction. In reality this projection
is used to make movies that can be viewed in the dome-like Omnimax theaters.
The image will look somewhat elliptical. The angle keyword isn't used with
this projection.

Panoramic projection: The up and right vectors work in a similar way as for
the perspective camera.

Cylindrical projection: In cylinder type 1 and 3 the axis of the cylinder
lies along the up vector and the width is determined by the length of right
vector or it may be overridden with the angle vector. In type 3 the up vector
determines how many units high the image is. For example if you have up 4*y
on a camera at the origin. Only points from y=2 to y=-2 are visible. All
viewing rays are perpendicular to the y-axis. For type 2 and 4, the cylinder
lies along the right vector. Viewing rays for type 4 are perpendicular to the
right vector.

Note that the up, right and direction vectors should always remain
perpendicular to each other or the image will be distorted. If this is not
the case a warning message will be printed. The vista buffer will not work
for non-perpendicular camera vectors.

7.4.4.5.1        Aspect Ratio

Together the right and up vectors define the aspect ratio (height to width
ratio) of the resulting image. The default values up  <0, 1, 0> and right
<1.33, 0,  0> result in an aspect ratio of 4 to 3. This is the aspect ratio
of a typical computer monitor. If you wanted a tall skinny image or a short
wide panoramic image or a perfectly square image you should adjust the up and
right vectors to the appropriate proportions.

Most computer video modes and graphics printers use perfectly square pixels.
For example Macintosh displays and IBM SVGA modes 640x480, 800x600 and
1024x768 all use square pixels. When your intended viewing method uses square
pixels then the width and height you set with the +W and +H switches should
also have the same ratio as the right and up vectors. Note that 640/480 = 4/3
so the ratio is proper for this square pixel mode.

Not all display modes use square pixels however. For example IBM VGA mode
320x200 and Amiga 320x400 modes do not use square pixels. These two modes
still produce a 4/3 aspect ratio image. Therefore images intended to be
viewed on such hardware should still use 4/3 ratio on their up and right
vectors but the +W and +H settings will not be 4/3.

For example:

  camera {
    location <3,5,-10>
    up       <0,1,0>
    right    <1,0,0>
    look_at  <0,2,1>
  }


This specifies a perfectly square image. On a square pixel display like SVGA
you would use +W and +H settings such as +W480 +H480 or +W600 +H600. However
on the non-square pixel Amiga 320x400 mode you would want to use values of
+W240 +H400 to render a square image.

7.4.4.5.2        Handedness

The right vector also describes the direction to the right of the camera. It
tells POV-Ray where the right side of your screen is. The sign of the right
vector can be used to determine the handedness of the coordinate system in
use. The default right statement is:

  right <1.33, 0, 0>


This means that the +x-direction is to the right. It is called a left-handed
system because you can use your left hand to keep track of the axes. Hold out
your left hand with your palm facing to your right. Stick your thumb up.
Point straight ahead with your index finger. Point your other fingers to the
right. Your bent fingers are pointing to the +x-direction. Your thumb now
points into +y-direction. Your index finger points into the +z-direction.

To use a right-handed coordinate system, as is popular in some CAD programs
and other ray-tracers, make the same shape using your right hand. Your thumb
still points up in the +y-direction and your index finger still points
forward in the +z-direction but your other fingers now say the +x-direction
is to the left. That means that the right side of your screen is now in the
-x-direction. To tell POV-Ray to act like this you can use a negative x value
in the right vector like this:

  right <-1.33, 0, 0>


Since x increasing to the left doesn't make much sense on a 2D screen you now
rotate the whole thing 180 degrees around by using a positive z value in your
camera's location. You end up with something like this.

  camera {
    location <0,0,10>
    up       <0,1,0>
    right    <-1.33,0,0>
    look_at  <0,0,0>
  }


Now when you do your ray-tracer's aerobics, as explained in the section
"Understanding POV-Ray's Coordinate System", you use your right hand to
determine the direction of rotations.

In a two dimensional grid, x is always to the right and y is up. The two
versions of handedness arise from the question of whether z points into the
screen or out of it and which axis in your computer model relates to up in
the real world.

Architectural CAD systems, like AutoCAD, tend to use the God's  Eye
orientation that the z-axis is the elevation and is the model's up direction.
This approach makes sense if you're an architect looking at a building
blueprint on a computer screen. z means up, and it increases towards you,
with x and y still across and up the screen. This is the basic right handed
system.

Stand alone rendering systems, like POV-Ray, tend to consider you as a
participant. You're looking at the screen as if you were a photographer
standing in the scene. Up in the model is now y, the same as up in the real
world and x is still to the right, so z must be depth, which increases away
from you into the screen. This is the basic left handed system.

7.4.4.6          Transforming the Camera

The translate and rotate commands can re-position the camera once you've
defined it. For example:

  camera {
    location  < 0,  0,  0>
    direction < 0,  0,  1>
    up        < 0,  1,  0>
    right     < 1,  0,  0>
    rotate    <30, 60, 30>
    translate < 5,  3,  4>
  }


In this example, the camera is created, then rotated by 30 degrees about the
x-axis, 60 degrees about the y-axis and 30 degrees about the z-axis, then
translated to another point in space.

7.4.5            Camera Identifiers

You may declare several camera identifiers if you wish. This makes it easy to
quickly change cameras. For example:

  #declare Long_Lens =
    camera {
      location -z*100
      angle 3
    }

  #declare Short_Lens =
    camera {
      location -z*50
      angle 15
    }

  camera {
    Long_Lens    // edit this line to change lenses
    look_at Here
  }


7.5              Objects

Objects are the building blocks of your scene. There are a lot of different
types of objects supported by POV-Ray: finite solid primitives, finite patch
primitives, infinite solid polynomial primitives and light sources.
Constructive Solid Geometry (CSG) is also supported.

The basic syntax of an object is a keyword describing its type, some floats,
vectors or other parameters which further define its location and/or shape
and some optional object modifiers such as texture, pigment, normal, finish,
bounding, clipping or transformations.

The texture describes what the object looks like, i. e. its material.
Textures are combinations of pigments, normals, finishes and halos. Pigment
is the color or pattern of colors inherent in the material. Normal is a
method of simulating various patterns of bumps, dents, ripples or waves by
modifying the surface normal vector. Finish describes the reflective and
refractive properties of a material. The halo is used to describe the
interior of the object.

Bounding shapes are finite, invisible shapes which wrap around complex, slow
rendering shapes in order to speed up rendering time. Clipping shapes are
used to cut away parts of shapes to expose a hollow interior. Transformations
tell the ray-tracer how to move, size or rotate the shape and/or the texture
in the scene.

7.5.1            Empty and Solid Objects

It is very important that you know the basic concept behind empty and solid
objects in POV-Ray to fully understand how features like halos and
translucency are used.

Objects in POV-Ray can either be solid, empty or filled with (small)
particles.

A solid object is made from the material specified by its pigment and finish
statements (and to some degree its normal statement). By default all objects
are assumed to be solid. If you assign a stone texture to a sphere you'll get
a ball made completely of stone. It's like you had cut this ball from a block
of stone. A glass ball is a massive sphere made of glass.

You should be aware that solid objects are conceptual things. If you e. g.
clip away parts of the sphere you'll see that the sphere is empty, i. e.
you'll clearly see that the interior is empty and it just has a very thin
surface.

This is not contrary to the concept of a solid object used in POV-Ray. It is
assumed that all space inside the sphere is covered by the sphere's material.
Thus there is no room for any other particles like those used by fog or
halos.

Empty objects are created by adding the hollow keyword (see "Hollow") to the
object statement. An empty (or hollow) object is assumed to be made of a very
thin surface which is of the material specified by the pigment, finish and
normal statements. The object's interior is empty, i. e. it normally contains
air molecules.

An empty object can be filled with particles by adding fog or atmosphere to
the scene or by adding a halo to the object. It is very important to
understand that in order to fill an object with any kind of particles it
first has to be made hollow.

7.5.1.1          Halo Pitfall

There is a pitfall in the current empty/solid object implementation that you
have to be aware of.

In order to be able to put solid objects inside a halo (this also holds for
fog and atmosphere) a test has to be made for every ray that passes through
the halo. If this ray travels through a solid object the halo will not be
calculated. This is what anyone will expect.

The problem arises when the camera ray is inside any non-hollow object. In
this case the ray is already traveling through a solid object and even if the
halo's container object is hit and it is hollow, the halo will not be
calculated. There is no way of telling between these two cases.

POV-Ray has to determine whether the camera is inside any object prior to
tracing a camera ray in order to be able to correctly render halos when the
camera is inside the container object. There's no way around doing this.

The solution to this problem (that will often happen with infinite objects
like planes) is to make those objects hollow too. Thus the ray will travel
through a hollow object, will hit the container object and the halo will be
calculated.


7.5.1.2          Refraction Pitfall

There is a pitfall in the way refractive (and non-refractive translucent)
objects are handled.

Imagine you want to create an object that's partially made of glass and
stone. You'd use something like the following merge because you don't want to
see any inside surfaces.

  merge {
    sphere { <-1,0,0>, 2 texture { Stone } }
    sphere { <+1,0,0>, 2 texture { Glass } }
  }


What's wrong with this, you may ask? The problem is that there is no way of
telling what the interior of the actual object will look like. This is not a
problem of POV-Ray, it's a general problem. You can't define the interior of
any object in a surface based model. You would have to create some (complex)
rules to decide what the interior will look like. Is it made of stone? Is it
made of glass? Is it made of some bizarre mixture between glass and stone? Is
it half stone and half glass? Where is the boundary between the two materials
and what does it look like?

You will not be able to answer any of the above questions by just looking at
the above object. You need more information.

If you wanted to create an object made half of stone and half of glass you
would have used the following statements.

  union {
    intersection {
      sphere { <-1,0,0>, 2 }
      plane { x, 0 }
      texture { Stone }
    }
    intersection {
      sphere { <+1,0,0>, 2 }
      plane { x, 0 inverse }
      texture { Glass }
    }
  }


This example is correct because there is one object made only of stone and
one made only of glass.

You should never use objects whose interior is not well defined, i. e. there
must not be different textures for the object having different refractive
(and translucent) properties. You should be aware that this holds only for
the lowest layer if you use layered textures.


7.5.2            Finite Solid Primitives

There are twelve different solid finite primitive shapes: blob, box, cone,
cylinder, fractal, height field, lathe, sphere, superellipsoid, surface of
revolution, text object and torus. These have a well-defined inside and can
be used in CSG (see section "Constructive Solid Geometry"). They are finite
and respond to automatic bounding. As with all shapes they can be translated,
rotated and scaled.

7.5.2.1          Blob

Blobs are an interesting and flexible object type. Mathematically they are
iso-surfaces of scalar fields, i. e. their surface is defined by the strength
of the field in each point. If this strength is equal to a threshold value
you're on the surface otherwise you're not.

Picture each blob component as an object floating in space. This object is
filled with a field that has its maximum at the center of the object and
drops off to zero at the object's surface. The field strength of all those
components are added together to form the field of the blob. Now POV-Ray
looks for points where this field has a given value, the threshold value. All
these points form the surface of the blob object. Points with a greater field
value than the threshold value are considered to be inside while points with
a smaller field value are outside.

There's another, simpler way of looking at blobs. They can be seen as a union
of flexible components that attract or repel each other to form a blobby
organic looking shape. The components' surfaces actually stretch out smoothly
and connect as if they were made of honey or something like that.

A blob is made up of spherical and cylindrical components and is defined as
follows:

  blob {
    threshold THRESHOLD_VALUE
    cylinder { <END1>, <END2>, RADIUS, [ strength ] STRENGTH }
    sphere { <CENTER>, RADIUS, [ strength ] STRENGTH }
    [ component STRENGTH, RADIUS, <CENTER> ]
    [ hierarchy FLAG ]
    [ sturm ]
  }


The threshold keyword determines the total field strength value that POV-Ray
is looking for. By following the ray out into space and looking at how each
blob component affects the ray, POV-Ray will find the points in space where
the field strength is equal to the threshold value. The following list shows
some things you should know about the threshold value.

  2)A component disappears if the threshold value is greater than its
  3)As the threshold value gets larger the surface you see gets closer to the
  4)As the threshold value gets smaller, the surface you see gets closer to
    the surface of the components.


Cylindrical components are specified by the keyword cylinder giving a
cylinder formed by the base <END1>, the apex <END2> and the radius. The
cylinder has hemispherical caps at the base and apex. Spherical components
are specified by the keyword sphere forming a sphere at <CENTER> with the
given radius. Each component can be individually translated, rotated, scaled
and textured. The complete syntax for the cylindrical and spherical
components is:

  sphere { <CENTER>, RADIUS, [strength] STRENGTH
    [ translate <VECTOR> ]
    [ rotate <VECTOR> ]
    [ scale <VECTOR> ]
    TEXTURE_MODIFIERS
  }

  cylinder { <END1>, <END2>, RADIUS, [strength] STRENGTH
    [ translate <VECTOR> ]
    [ rotate <VECTOR> ]
    [ scale <VECTOR> ]
    TEXTURE_MODIFIERS
  }


By unevenly scaling a spherical component you can create ellipsoidal
components. The component keyword gives a spherical component and is only
used for compatibility with earlier POV-Ray versions.

The strength parameter is a float value specifying the field strength at the
center of the object. The strength may be positive or negative. A positive
value will make that component attract other components while a negative
value will make it repel other components. Components in different, separate
blob shapes do not affect each other.

You should keep the following things in mind.

  1)The strength value may be positive or negative. Zero is a bad value, as
    the net result is that no field was added --- you might just as well have
  2)If strength is positive, then POV-Ray will add the component's field to
    the space around the center of the component. If this adds enough field
  3)If the strength value is negative, then POV-Ray will subtract thesurface.
    component's field from the space around the center of the component. This
    will only do something if there happen to be positive components nearby.
    What happens is that the surface around any nearby positive components
    will be dented away from the center of the negative component.


The components of each blob object are internally bounded by a spherical
bounding hierarchy to speed up blob intersection tests and other operations.
By using the optional keyword hierarchy you can switch this hierarchy off.

An example of a three component blob is:

  blob {
    threshold 0.6
    sphere { <.75, 0, 0>, 1, 1 }
    sphere { <-.375, .64952, 0>, 1, 1 }
    sphere { <-.375, -.64952, 0>, 1, 1 }
    scale 2
  }


If you have a single blob component then the surface you see will just look
like the object used, i. e. a sphere or a cylinder, with the surface being
somewhere inside the surface specified for the component. The exact surface
location can be determined from the blob equation listed below (you will
probably never need to know this, blobs are more for visual appeal than for
exact modeling).

For the more mathematically minded, here's the formula used internally by
POV-Ray to create blobs. You don't need to understand this to use blobs. The
formula used for a single blob component is:

  density = strength * (1 - radius^2)^2


This formula has the nice property that it is exactly equal to the strength
parameter at the center of the component and drops off to exactly 0 at a
distance from the center of the component that is equal to the radius value.
The density formula for more than one blob component is just the sum of the
individual component densities:


  density = density1 + density2 + ...


The calculations for blobs must be very accurate. If this shape renders
improperly you may add the keyword sturm after the last component to use
POV-Ray's slower-yet-more-accurate Sturmian root solver.

7.5.2.2          Box

A simple box can be defined by listing two corners of the box like this:

  box { <CORNER1>, <CORNER2> }


The geometry of a box.

Where <CORNER1> and <CORNER2> are vectors defining the x, y, z coordinates of
the opposite corners of the box.

Note that all boxes are defined with their faces parallel to the coordinate
axes. They may later be rotated to any orientation using the rotate keyword.

Each element of <CORNER1> should always be less than the corresponding
element in <CORNER2>. If any elements of <CORNER1> are larger than <CORNER2>
the box will not appear in the scene.

Boxes are calculated efficiently and make good bounding shapes (if manually
bounding seems to be necessary).

7.5.2.3          Cone

A finite length cone or a frustum (a cone with the point cut off) may be
defined by.

  cone {
    <BASE_POINT>, BASE_RADIUS, <CAP_POINT>, CAP_RADIUS
    [ open ]
  }


The geometry of a cone.

Where <BASE_POINT> and < CAP_POINT> are vectors defining the x, y, z
coordinates of the center of the cone's base and cap and BASE_RADIUS and
CAP_RADIUS are float values for the corresponding radii.

Normally the ends of a cone are closed by flat planes which are parallel to
each other and perpendicular to the length of the cone. Adding the optional
keyword open after CAP_RADIUS will remove the end caps and results in a
tapered hollow tube like a megaphone or funnel.

7.5.2.4          Cylinder

A finite length cylinder with parallel end caps may be defined by.

  cylinder {
    <BASE_POINT>, <CAP_POINT>, RADIUS
    [ open ]
  }


The geometry of a cylinder.

Where <BASE_POINT> and < CAP_POINT> are vectors defining the x, y, z
coordinates of the cylinder's base and cap and RADIUS is a float value for
the radius.

Normally the ends of a cylinder are closed by flat planes which are parallel
to each other and perpendicular to the length of the cylinder. Adding the
optional keyword open after the radius will remove the end caps and results
in a hollow tube.

7.5.2.5          Height Field

Height fields are fast, efficient objects that are generally used to create
mountains or other raised surfaces out of hundreds of triangles in a mesh.
The height field syntax is:

  height_field {
    FILE_TYPE "FILENAME"
    [ hierarchy BOOL ]
    [ smooth BOOL ]
    [ water_level FLOAT ]
  }


A height field is essentially a one unit wide by one unit long square with a
mountainous surface on top. The height of the mountain at each point is taken
from the color number or palette index of the pixels in a graphic image file.
The maximum height is one, which corresponds to the maximum possible color or
palette index value in the image file.

        ________  <---- image index 255 (or 65535 for 16-bit images)
      /        /|
+1y  ---------- |
     |        | |
     |        | |+1z <- Image upper-right
     |        | /
0,0,0---------- +1x
     ^
     |____ Image lower-left
The size and orientation of an un-scaled height field.

The mesh of triangles corresponds directly to the pixels in the image file.
Each square formed by four neighboring pixels is divided into two triangles.
An image with a resolution of N*M pixels has (N-1)*(M-1) squares that are
divided into 2*(N-1)*(M-1) triangles.

Four pixels of an image and the resulting heights and triangles in the height
field.

The resolution of the height field is influenced by two factors: the
resolution of the image and the resolution of the color/index values. The
size of the image determines the resolution in the x- and z-direction. A
larger image uses more triangles and looks smoother. The resolution of the
color/index value determines the resolution along the y-axis. A height field
made from an 8 bit image can have 256 different height levels while one made
from a 16 bit image can have up to 65536 different height levels. Thus the
second height field will look much smoother in the y-direction if the height
field is created appropriately.

The size/resolution of the image does not affect the size of the height
field. The un-scaled height field size will always be 1* 1. Higher resolution
image files will create smaller triangles, not larger height fields.

There are six or possibly seven types of files which can define a
heightfield, as follows:

  height_field { gif "filename.gif" }
  height_field { pgm "filename.pgm" }
  height_field { png "filename.png" }
  height_field { pot "filename.pot" }
  height_field { ppm "filename.ppm" }
  height_field { sys "filename.???" }
  height_field { tga "filename.tga" }


The image file used to create a height field can be a GIF, TGA, POT, PNG,
PGM, PPM and possibly a system specific (e. g. Windows BMP or Macintosh Pict)
format file. The GIF, PNG, PGM and possibly system format files are the only
ones that can be created using a standard paint program. Though there are
paint programs for creating TGA image files they won't be of much use for
creating the special 16 bit TGA files used by POV-Ray (see below and
"HF_Gray_16" for more details).

In an image file like GIF that uses a color palette the color number is the
palette index at a given pixel. Use a paint program to look at the palette of
a GIF image. The first color is palette index zero, the second is index one,
the third is index two and so on. The last palette entry is index 255.
Portions of the image that use low palette entries will result in lower parts
of the height field. Portions of the image that use higher palette entries
will result in higher parts of the height field.

Height fields created from GIF files can only have 256 different height
levels because the maximum number of colors in a GIF file is 256.

The color of the palette entry does not affect the height of the pixel. Color
entry 0 could be red, blue, black or orange but the height of any pixel that
uses color entry 0 will always be 0. Color entry 255 could be indigo, hot
pink, white or sky blue but the height of any pixel that uses color entry 255
will always be 1.

You can create height field GIF images with a paint program or a fractal
program like Fractint. You can usually get Fractint from most of the same
sources as POV-Ray.

A POT file is essentially a GIF file with a 16 bit palette. The maximum
number of colors in a POT file is 65536. This means a POT height field can
have up to 65536 possible height values. This makes it possible to have much
smoother height fields. Note that the maximum height of the field is still 1
even though more intermediate values are possible.

At the time of this writing the only program that created POT files was a
freeware IBM-PC program called Fractint. POT files generated with this
fractal program create fantastic landscapes.

The TGA and PPM file formats may be used as a storage device for 16 bit
numbers rather than an image file. These formats use the red and green bytes
of each pixel to store the high and low bytes of a height value. These files
are as smooth as POT files but they must be generated with special
custom-made programs. Several programs can create TGA heightfields in the
format POV uses, such as gforge and Terrain Maker.

PNG format heightfields are usually stored in the form of a grayscale image
with black corresponding to lower and white to higher parts of the height
field. Because PNG files can store up to 16 bits in grayscale images they
will be as smooth as TGA and PPM images. Since they are grayscale images you
will be able to view them with a regular image viewer. gforge can create
16-bit heightfields in PNG format. Color PNG images will be used in the same
way as TGA and PPM images.

SYS format is a platform specific file format. See your platform specific
documentation for details.

An optional water_level parameter may be added after the file name. It
consists of the keyword water_level followed by a float value telling the
program to ignore parts of the height field below that value. The default
value is zero and legal values are between zero and one. For example
water_level .5 tells POV-Ray to only render the top half of the height field.
The
other half is below the water and couldn't be seen anyway. This term comes
from the popular use of height fields to render landscapes. A height field
would be used to create islands and another shape would be used to simulate
water around the islands. A large portion of the height field would be
obscured by the water so the water_level parameter was introduced to allow
the ray-tracer to ignore the unseen parts of the height field. water_level is
also used to cut away unwanted lower values in a height field. For example if
you have an image of a fractal on a solid colored background, where the
background color is palette entry 0, you can remove the background in the
height field by specifying, water_level .001.

Normally height fields have a rough, jagged look because they are made of
lots of flat triangles. Adding the keyword smooth causes POV-Ray to modify
the surface normal vectors of the triangles in such a way that the lighting
and shading of the triangles will give a smooth look. This may allow you to
use a lower resolution file for your height field than would otherwise be
needed. However, smooth triangles will take longer to render.

In order to speed up the intersection tests an one-level bounding hierarchy
is available. By default it is always used but it can be switched off to
eventually improve the rendering speed for small height fields (i. e. low
resolution images).

7.5.2.6          Julia Fractal

A julia fractal object is a 3-D slice of a 4-D object created by generalizing
the process used to create the classic Julia sets. You can make a wide
variety of strange objects using julia_fractal, including some that look like
bizarre blobs of twisted taffy.

The julia_fractal syntax (with default values listed in comments) is:

  julia_fractal {
    4DJULIA_PARAMETER                 // default is <1,0,0,0>
    [ quaternion | hypercomplex ]     // default is quaternion
    [ sqr | cube | exp |
      reciprocal | sin | asin |
      sinh | asinh | cos | acos |
      cosh | acosh | tan | atan |
      tanh | atanh | log | pwr(X,Y) ] // default is sqr
    [ max_iteration MAX_ITERATION ]   // default value 20
    [ precision PRECISION ]           // default value 20
    [ slice 4DNORMAL, DISTANCE ]      // default <0,0,0,1>,0
  }


The 4-D vector 4DJULIA_PARAMETER is the classic Julia parameter p in the
iterated formula f(h) + p.

The julia fractal object is calculated by using an algorithm that determines
whether an arbitrary point h(0) in 4-D space is inside or outside the object.
The algorithm requires generating the sequence of vectors h(0), h(1), ... by
iterating the formula

  h(n+1) = f(h(n)) + p (n = 0, 1, ..., max_iteration-1)


where p is the fixed 4-D vector parameter of the julia fractal and f() is one
of the functions sqr, cube, ... specified by the presence of the
corresponding keyword. The point h(0) that begins the sequence is considered
inside the julia fractal object if none of the vectors in the sequence
escapes a hypersphere of radius 4 about the origin before the iteration
number reaches the max_iteration value. As you increase max_iteration, some
points escape that did not previously escape, forming the julia fractal.
Depending on the JULIA_PARAMETER, the julia fractal object is not necessarily
connected; it may be scattered fractal dust. Using a low max_iteration can
fuse together the dust to make a solid object. A high max_iteration is more
accurate but slows rendering. Even though it is not accurate, the solid
shapes you get with a low_maximum iteration value can be quite interesting.

Since the mathematical object described by this algorithm is four-dimensional
and POV-Ray renders three dimensional objects, there must be a way to reduce
the number of dimensions of the object from four dimensions to three. This is
accomplished by intersecting the 4-D fractal with a 3-D plane defined by the
slice field and then projecting the intersection to 3-D space. The slice
plane is the 3-D space that is perpendicular to NORMAL4D and is DISTANCE
units from the origin. Zero length NORMAL4D vectors or a NORMAL4D vector with
a zero fourth component are illegal.

You can get a good feel for the four dimensional nature of a julia fractal by
using POV-Ray's animation feature to vary a slice's DISTANCE parameter. You
can make the julia fractal appear from nothing, grow, then shrink to nothing
as DISTANCE changes, much as the cross section of a 3-D object changes as it
passes through a plane.

The precision parameter is a tolerance used in the determination of whether
points are inside or outside the fractal object. Larger values give more
accurate results but slower rendering. Use as low a value as you can without
visibly degrading the fractal object's appearance.

The presence of the keywords quaternion or hypercomplex determine which 4-D
algebra is used to calculate the fractal. Both are 4-D generalizations of the
complex numbers but neither satisfies all the field properties (all the
properties of real and complex numbers that many of us slept through in high
school). Quaternions have non-commutative multiplication and hypercomplex
numbers can fail to have a multiplicative inverse for some non-zero elements
(it has been proved that you cannot successfully generalize complex numbers
to four dimensions with all the field properties intact, so something has to
break). Both of these algebras were discovered in the 19th century. Of the
two, the quaternions are much better known, but one can argue that
hypercomplex numbers are more useful for our purposes, since complex valued
functions such as sin, cos, etc. can be generalized to work for hypercomplex
numbers in a uniform way.

For the mathematically curious, the algebraic properties of these two
algebras can be derived from the multiplication properties of the unit basis
vectors 1 = <1,0,0,0>, i=< 0,1,0,0>, j=<0,0,1,0> and k=< 0,0,0,1>. In both
algebras 1 x = x 1 = x for any x (1 is the multiplicative identity). The
basis vectors 1 and i behave exactly like the familiar complex numbers 1 and
i in both algebras.

Quaternion basis vector multiplication rules:

  ij = k;            jk  = i;   ki = j
  ji = -k;           kj  = -i;  ik = -j
  ii = jj = kk = -1; ijk = -1;


Hypercomplex basis vector multiplication rules:

  ij = k;            jk = -i;   ki = -j
  ji = k;            kj = -i;   ik = -j
  ii = jj = kk = -1; ijk = 1;


A distance estimation calculation is used with the quaternion calculations to
speed them up. The proof that this distance estimation formula works does not
generalize from two to four dimensions but the formula seems to work well
anyway, the absence of proof notwithstanding!

The presence of one of the function keywords sqr, cube, etc. determines which
function is used for f(h) in the iteration formula h(n+1) = f(h(n)) + p. Most
of the function keywords work only if the hypercomplex keyword is present.
Only sqr and cube work with quaternions. The functions are all familiar
complex functions generalized to four dimensions.

  Function Keyword    Maps 4-D value h to:
================================================
  sqr                 h*h
  cube                h*h*h
  exp                 e raised to the power h
  reciprocal          1/h
  sin                 sine of h
  asin                arcsine of h
  sinh                hyperbolic sine of h
  asinh               inverse hyperbolic sine of h
  cos                 cosine of h
  acos                arccosine of h
  cosh                hyperbolic cos of h
  acosh               inverse hyperbolic cosine of h

  tan                 tangent of h
  atan                arctangent of h
  tanh                hyperbolic tangent of h
  atanh               inverse hyperbolic tangent of h
  log                 natural logarithm of h
  pwr(x,y)            h raised to the complex power x+iy


A simple example of a julia fractal object is:

  julia_fractal {
    <-0.083,0.0,-0.83,-0.025>
    quaternion
    sqr
    max_iteration 8
    precision 15
  }


The first renderings of julia fractals using quaternions were done by Alan
Norton and later by John Hart in the '80's. This new POV-Ray implementation
follows Fractint in pushing beyond what is known in the literature by using
hypercomplex numbers and by generalizing the iterating formula to use a
variety of transcendental functions instead of just the classic Mandelbrot
z^2 + c formula. With an extra two dimensions and eighteen functions to work
with, intrepid explorers should be able to locate some new fractal beasties
in hyperspace, so have at it!

7.5.2.7          Lathe

The lathe is an object generated from rotating a two-dimensional curve about
an axis. This curve is defined by a set of points which are connected by
linear, quadratic or cubic spline curves. The syntax is:

  lathe {
    [ linear_spline | quadratic_spline | cubic_spline ]
    NUMBER_OF_POINTS,
    <POINT_1>, <POINT_2>, ..., <POINT_n>
    [ sturm ]
  }


The parameter NUMBER_OF_POINTS determines how many two-dimensional points are
forming the curve. These points are connected by linear, quadratic or cubic
splines as specified by an optional keyword (the default is linear_spline).
Since the curve is not automatically closed, i. e. the first and last points
are not automatically connected, you'll have to do this by your own if you
want a closed curve. The curve thus defined is rotated about the y-axis to
form the lathe object which is centered at the origin.

The following examples creates a simple lathe object that looks like a thick
cylinder, i. e. a cylinder with a thick wall:

  lathe {
    linear_spline
    5,
    <2, 0>, <3, 0>, <3, 5>, <2, 5>, <2, 0>
    pigment {Red}
  }


The cylinder has an inner radius of 2 and an outer radius of 3, giving a wall
width of 1. It's height is 5 and it's located at the origin pointing up, i.
e. the rotation axis is the y-axis. Note that the first and last point are
equal to get a closed curve.

The splines that are used by the lathe and prism objects are a little bit
difficult to understand. The basic concept of splines is to draw a curve
through a given set of points in a determined way. The linear spline is the
simplest spline because it's nothing more than connecting consecutive points
with a line. This means that the curve that is drawn between two points only
depends on those two points. No additional information is taken into account.
Quadratic and cubic splines are different in that they do not only take other
points into account when connecting two points but they also look smoother
and - in the case of the cubic spline - produce smoother transitions at each
point.

Quadratic splines are made of quadratic curves. Each of them connects two
consecutive points. Since those two points (call them second and third point)
are not sufficient to describe a quadratic curve the predecessor of the
second point is taken into account when the curve is drawn. Mathematically
the relationship (their location on the 2-D plane) between the first and
second point determines the slope of the curve at the second point. The slope
of the curve at the third point is out of control. Thus quadratic splines
look much smoother than linear splines but the transitions at each point are
generally not smooth because the slopes on both sides of the point are
different.

Cubic splines overcome the transition problem of quadratic splines because
they also take the fourth point into account when drawing the curve between
the second and third point. The slope at the fourth point is under control
now and allows a smooth transition at each point. Thus cubic splines produce
the most flexible and smooth curves.

You should note that the number of spline segments, i. e. curves between two
points, depends on the spline type used. For linear splines you get n-1
segments connecting the points P[i], i=1,...,n. A quadratic spline gives you
n-2 segments because the last point is only used for determining the slope as
explained above (thus you'll need at least three points to define a quadratic
spline). The same holds for cubic splines where you get n-3 segments with the
first and last point used only for slope calculations (thus needing at least
four points).

If you want to get a closed quadratic and cubic spline with smooth
transitions at the end points you have to make sure that in the cubic case
P[n-1] = P[2] (to get a closed curve), P[n] = P[3] and P[n-2] = P[1] (to
smooth the transition). In the quadratic case P[n-1] = P[1] (to close the
curve) and P[n] = P[2].

The slower but more accurate Sturmian root solver may be used with the
quadratic spline lathe if the shape does not render properly. Since a
quadratic polynomial has to be solved for the linear spline lathe the
Sturmian root solver is not needed. In case of cubic splines the Sturmian
root solver is always used because a 6th order polynomial has to be solved.

7.5.2.8          Prism

The prism is an object generated from sweeping one or more two-dimensional,
closed curves along an axis. These curves are defined by a set of points
which are connected by linear, quadratic or cubic splines.

The syntax for the prism is:

  prism {
    [ linear_sweep | conic_sweep ]
    [ linear_spline | quadratic_spline | cubic_spline ]
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <POINT_1>, <POINT_2>, ..., <POINT_n>
    [ open ]
    [ sturm ]
  }


The prism object allows you to use any number of sub-prisms inside one prism
statement (they are of the same spline and sweep type). Wherever an even
number of sub-prisms overlaps a hole appears.

The syntax of the prism object depends on the type of spline curve used.
Below the syntax of the linear spline prism is given.

  prism {
    linear_spline
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <A_1>, <A_2>, ..., <A_na>, <A_1>,
    <B_1>, <B_2>, ..., <B_nb>, <B_1>,
    <C_1>, <C_2>, ..., <C_nc>, <C_1>,
    ...
  }


Each of the sub-prisms has to be closed by repeating the first point of a
sub-prism at the end of the sub-prism's point sequence. If this is not the
case a warning is issued and the prism is ignored (with linear splines
automatic closing is used). This implies that all points of a prism are
different (except the first and last of course). This applies to all spline
types though the control points of the quadratic and cubic splines can be
arbitrarily chosen.

The last sub-prism of a linear spline prism is automatically closed - just
like the last sub-polygon in the polygon statement - if the first and last
point of the sub-polygon's point sequence are not the same. This make it very
easy to convert between polygons and prisms. Quadratic and cubic splines are
never automatically closed.

The syntax for quadratic spline prisms is:

  prism {
    quadratic_spline
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <CL_A>, <A_1>, <A_2>, ..., <A_na>, <A_1>,
    <CL_B>, <B_1>, <B_2>, ..., <B_nb>, <B_1>,
    <CL_C>, <C_1>, <C_2>, ..., <C_nc>, <C_1>,
    ...
  }


Quadratic spline sub-prisms need an additional control point at the beginning
of each sub-prisms' point sequence to determine the slope at the start of the
curve.

Last but not least the syntax for the cubic spline prism.

  prism {
    cubic_spline
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <CL_A1>, <A_1>, <A_2>, ..., <A_na>, <A_1>, <CL_A2>,
    <CL_B1>, <B_1>, <B_2>, ..., <B_nb>, <B_1>, <CL_B2>,
    <CL_C1>, <C_1>, <C_2>, ..., <C_nc>, <C_1>, <CL_C2>,
    ...
  }


In addition to the closed point sequence each cubic spline sub-prism needs
two control points to determine the slopes at the start and end of the curve.


The parameter TOTAL_NUMBER_OF_POINTS determines how many two-dimensional
points (lying in the x-z-plane) form the curves (this includes all control
points needed for quadratic and cubic splines). The curves are swept along
the y-axis from HEIGHT1 to HEIGHT2 to form the prism object. By default
linear sweeping is used to create the prism, i. e. the prism's walls are
perpendicular to the x-z-plane (the size of the curve does not change during
the sweep). You can also use conic sweeping (conic_sweep) that leads to a
prism with cone-like walls by scaling the curve down during the sweep.

Like cylinders the prism is normally closed. You can remove the caps on the
prism by using the open keyword. If you do so you shouldn't use it with CSG
because the results may get wrong.

The following example creates a simple prism object that looks like a piece
of cake:

  prism {
    linear_sweep
    linear_spline
    0, 1,
    4,
    <-1, 0>, <1, 0>, <0, 5>, <-1, 0>
    pigment {Red}
  }


For an explanation of the spline concept read the description of the lathe
object.

The slower but more accurate Sturmian root solver may be used with the cubic
spline prisms if the shape does not render properly. The linear and quadratic
spline prisms do not need the Sturmian root solver.

7.5.2.9          Sphere

The syntax of the sphere object is:

  sphere {
    <CENTER>, RADIUS
  }


The geometry of a sphere.

Where <CENTER> is a vector specifying the x, y, z coordinates of the center
of the sphere and RADIUS is a float value specifying the radius. Spheres may
be scaled unevenly giving an ellipsoid shape.

Because spheres are highly optimized they make good bounding shapes (if
manual bounding seems to be necessary).

7.5.2.10         Superquadric Ellipsoid

The superquadric ellipsoid is an extension of the quadric ellipsoid. It can
be used to create boxes and cylinders with round edges and other interesting
shapes. Mathematically it is given by the equation:

  f(x, y, z) = (|x|^(2/e) + |y|^(2/e)) ^ (e/n) + |z|^(2/n) - 1 = 0


The values of e and n, called the east-west and north-south exponent,
determine the shape of the superquadric ellipsoid. Both have to be greater
than zero. The sphere is e. g. given by e = 1 and n = 1.

The syntax of the superquadric ellipsoid, which is located at the origin, is:


  superellipsoid { <e, n> }


Two useful objects are the rounded box and the rounded cylinder. These are
declared in the following way.

  #declare Rounded_Box = superellipsoid { <r, r> }
  #declare Rounded_Cylinder = superellipsoid { <1, r> }


The roundedness r determines the roundedness of the edges and has to be
greater than zero and smaller than one. The smaller you choose the values of
r the smaller and sharper the edges will get.

Very small values of e and n might cause problems with the root solver (the
Sturmian root solver cannot be used).

7.5.2.11         Surface of Revolution

The surface of revolution (SOR) object is generated by rotating the graph of
a function about an axis. This function describes the dependence of the
radius from the position on the rotation axis. The syntax of the SOR object
is:

  sor {
    NUMBER_OF_POINTS,
    <POINT0>, <POINT1>, ..., <POINTn-1>
    [ open ]
    [ sturm ]
  }


The points <POINT0> through <POINTn-1> are two-dimensional vectors consisting
of the radius and the corresponding height, i. e. the position on the
rotation axis. These points are smoothly connected (the curve is passing
through the specified points) and rotated about the y-axis to form the SOR
object. The first and last points are only used to determine the slopes of
the function at the start and end point. The function used for the SOR object
is similar to the splines used for the lathe object. The difference is that
the SOR object is less flexible because it underlies the restrictions of any
mathematical function, i. e. to any given point y on the rotation axis
belongs at most one function value, i. e. one radius value. You can't rotate
closed curves with the SOR object.

The optional keyword open allows you to remove the caps on the SOR object. If
you do this you shouldn't use it with CSG anymore because the results may be
wrong.

The SOR object is useful for creating bottles, vases, and things like that. A
simple vase could look like this:

  #declare Vase = sor {
    7,
    <0.000000, 0.000000>
    <0.118143, 0.000000>
    <0.620253, 0.540084>
    <0.210970, 0.827004>
    <0.194093, 0.962025>
    <0.286920, 1.000000>
    <0.468354, 1.033755>
    open
  }


One might ask why there is any need for a SOR object if there is already a
lathe object which is much more flexible. The reason is quite simple. The
intersection test with a SOR object involves solving a cubic polynomial while
the test with a lathe object requires to solve of a 6th order polynomial (you
need a cubic spline for the same smoothness). Since most SOR and lathe
objects will have several segments this will make a great difference in
speed. The roots of the 3rd order polynomial will also be more accurate and
easier to find.

The slower but more accurate Sturmian root solver may be used with the
surface of revolution object if the shape does not render properly.

The following explanations are for the mathematically interested reader who
wants to know how the surface of revolution is calculated. Though it is not
necessary to read on it might help in understanding the SOR object.

The function that is rotated about the y-axis to get the final SOR object is
given by

  r^2 = f(h) = A*h^3 + B*h^2 + C*h + D


with radius r and height h. Since this is a cubic function in h it has enough
flexibility to allow smooth curves.

The curve itself is defined by a set of n points P(i), i=0...n-1, which are
interpolated using one function for every segment of the curve. A segment j,
j=1...n-3, goes from point P(j) to point P(j+1) and uses points P(j-1) and
P(j+2) to determine the slopes at the endpoints. If there are n points we
will have n-3 segments. This means that we need at least four points to get a
proper curve.

The coefficients A(j), B(j), C(j) and D(j) are calculated for every segment
using the equation

  b = M * x, with

      /                                        \
      | r(j)^2                                 |
      |                                        |
      | r(j+1)^2                               |
  b = |                                        |
      | 2*r(j)*(r(j+1)-r(j-1))/(h(j+1)-h(j-1)) |
      |                                        |
      | 2*r(j+1)*(r(j+2)-r(j))/(h(j+2)-h(j))   |
                                              /

      /                                 \
      |   h(j)^3    h(j)^2    h(j)    1 |
      |                                 |
      |   h(j+1)^3  h(j+1)^2  h(j+1)  1 |
  M = |                                 |
      | 3*h(j)^2    2*h(j)    1       0 |
      |                                 |
      | 3*h(j+1)^2  2*h(j+1)  1       0 |
                                       /

      /      \
      | A(j) |
      |      |
      | B(j) |
  x = |      |
      | C(j) |
      |      |
      | D(j) |
            /


where r(j) is the radius and h(j) is the height of point P(j).

The figure below shows the configuration of the points P(i), the location of
segment j, and the curve that is defined by this segment.

Segment j of n-3 segments in a point configuration of n points. The points
describe the curve of a surface of revolution.

7.5.2.12         Text

A text object creates 3-D text as an extruded block letter. Currently only
TrueType fonts are supported but the syntax allows for other font types to be
added in the future. The syntax is:

  text {
    ttf "FONTNAME.TTF",
    "STRING_OF_TEXT",
    THICKNESS_FLOAT, OFFSET_VECTOR
  }


Where fontname.ttf is the name of the TrueType font file. It is a quoted
string literal or string expression. The string expression which follows is
the actual text of the string object. It too may be a quoted string literal
or string expression. See section "Strings" for more on string expressions.

The text will start with the origin at the lower left, front of the first
character and will extend in the +x-direction. The baseline of the text
follows the x-axis and decenders drop into the -y-direction. The front of the
character sits in the x-y-plane and the text is extruded in the +z-direction.
The front-to-back thickness is specified by the required value
THICKNESS_FLOAT.

Characters are generally sized so that 1 unit of vertical spacing is correct.
The characters are about 0.5 to 0.75 units tall.

The horizontal spacing is handled by POV-Ray internally including any kerning
information stored in the font. The required vector OFFSET_VECTOR defines any
extra translation between each character. Normally you should specify a zero
for this value. Specifing 0.1*x would put additional 0.1 units of space
between each character.

Only printable characters are allowed in text objects. Characters such as
return, line feed, tabs, backspace etc. are not supported.

7.5.2.13         Torus

A torus is a 4th order quartic polynomial shape that looks like a donut or
inner tube. Because this shape is so useful and quartics are difficult to
define, POV-Ray lets you take a short-cut and define a torus by:

  torus {
    MAJOR, MINOR
    [ sturm ]
  }


where MAJOR is a float value giving the major radius and MINOR is a float
specifying the minor radius. The major radius extends from the center of the
hole to the mid-line of the rim while the minor radius is the radius of the
cross-section of the rim. The torus is centered at the origin and lies in the
x-z-plane with the y-axis sticking through the hole.

|---------------------------------------------------------------|
|                                                               |
|    ----------- - - - - - - - ----------              +Y       |
|   /                        /                        |       |
|  /                        /                         |       |
| |              |          |       |<-B-->|       -X---|---+X  |
|              /                        /             |       |
|   __________/_ _ _ _ _ _ _ __________/              |       |
|                     |<-----A----->|                  -Y       |
|                                                               |
|  A = Major Radius                                             |
|  B = Minor Radius                                             |
|                                                               |
|---------------------------------------------------------------|
Major and minor radius of a torus.

The torus is internally bounded by two cylinders and two rings forming a
thick cylinder. With this bounding cylinder the performance of the torus
intersection test is vastly increased. The test for a valid torus
intersection, i. e. solving a 4th order polynomial, is only performed if the
bounding cylinder is hit. Thus a lot of slow root solving calculations are
avoided.

Calculations for all higher order polynomials must be very accurate. If the
torus renders improperly you may add the keyword sturm after the MINOR value
to use POV-Ray's slower-yet-more-accurate Sturmian root solver.

7.5.3            Finite Patch Primitives

There are six totally thin, finite objects which have no well-defined inside.
They are bicubic patch, disc, smooth triangle, triangle, polygon and mesh.
They may be combined in CSG union but cannot be use in other types of CSG (or
inside a clipped_by statement). Because these types are finite POV-Ray can
use automatic bounding on them to speed up rendering time. As with all shapes
they can be translated, rotated and scaled.

7.5.3.1          Bicubic Patch

A bicubic patch is a 3D curved surface created from a mesh of triangles.
POV-Ray supports a type of bicubic patch called a Bezier patch. A bicubic
patch is defined as follows:

  bicubic_patch {
    type PATCH_TYPE
    flatness FLATNESS_VALUE
    u_steps NUM_U_STEPS
    v_steps NUM_V_STEPS
    <CP1>,  <CP2>,   <CP3>,   <CP4>,
    <CP5>,  <CP6>,   <CP7>,   <CP8>,
    <CP9>,  <CP10>,  <CP11>,  <CP12>,
    <CP13>, <CP14>,  <CP15>,  <CP16>
  }


The keyword type is followed by a float PATCH_TYPE which currently must be
either 0 or 1. For type 0 only the control points are retained within
POV-Ray. This means that a minimal amount of memory is needed but POV-Ray
will need to perform many extra calculations when trying to render the patch.
Type 1 preprocesses the patch into many subpatches. This results in a
significant speedup in rendering at the cost of memory.

The four parameters type, flatness, u_steps and v_steps may appear in any
order. They are followed by 16 vectors that define the x, y, z coordinates of
the 16 control points which define the patch. The patch touches the four
corner points <CP1>, <CP4>, < CP13> and <CP16> while the other 12 points pull
and stretch the patch into shape. The Bezier surface is enclosed by the
convex hull formed by the 16 control points, this is known as the convex hull
property.

The keywords u_steps and v_steps are each followed by float values which tell
how many rows and columns of triangles are the minimum to use to create the
surface. The maximum number of individual pieces of the patch that are tested
by POV-Ray can be calculated from the following:

  sub-pieces = 2^u_steps * 2^v_steps


This means that you really should keep u_steps and v_steps under 4. Most
patches look just fine with u_steps  3 and v_steps 3, which translates to 64
subpatches (128 smooth triangles).

As POV-Ray processes the Bezier patch it makes a test of the current piece of
the patch to see if it is flat enough to just pretend it is a rectangle. The
statement that controls this test is flatness. Typical flatness values range
from 0 to 1 (the lower the slower).

If the value for flatness is 0 POV-Ray will always subdivide the patch to the
extend specified by u_steps and v_steps. If flatness is greater than 0 then
every time the patch is split, POV-Ray will check to see if there is any need
to split further.

There are both advantages and disadvantages to using a non-zero flatness. The
advantages include:

  - If the patch isn't very curved, then this will be detected and POV-Ray
  - If the patch is only highly curved in a couple of places, POV-Ray will
    keep subdividing there and concentrate it's efforts on the hard part.


The biggest disadvantage is that if POV-Ray stops subdividing at a particular
level on one part of the patch and at a different level on an adjacent part
of the patch there is the potential for cracking. This is typically visible
as spots within the patch where you can see through. How bad this appears
depends very highly on the angle at which you are viewing the patch.

Like triangles, the bicubic patch is not meant to be generated by hand. These
shapes should be created by a special utility. You may be able to acquire
utilities to generate these shapes from the same source from which you
obtained POV-Ray.

  bicubic_patch {
    type 1
    flatness 0.01
    u_steps 4
    v_steps 4
    <0, 0, 2>, <1, 0, 0>, <2, 0, 0>, <3, 0,-2>,
    <0, 1  0>, <1, 1, 0>, <2, 1, 0>, <3, 1, 0>,
    <0, 2, 0>, <1, 2, 0>, <2, 2, 0>, <3, 2, 0>,
    <0, 3, 2>, <1, 3, 0>, <2, 3, 0>, <3, 3, -2>
  }


The triangles in a POV-Ray bicubic_patch are automatically smoothed using
normal interpolation but it is up to the user (or the user's utility program)
to create control points which smoothly stitch together groups of patches.

7.5.3.2          Disc

One other flat, finite object available with POV-Ray is the disc. The disc is
infinitely thin, it has no thickness. If you want a disc with true thickness
you should use a very short cylinder. A disc shape may be defined by:

  disc {
    <CENTER>, <NORMAL>, RADIUS [, HOLE_RADIUS ]
  }


The vector <CENTER> defines the x, y, z coordinates of the center of the
disc. The < NORMAL> vector describes its orientation by describing its
surface normal vector. This is followed by a float specifying the RADIUS.
This may be optionally followed by another float specifying the radius of a
hole to be cut from the center of the disc.

7.5.3.3          Mesh

The mesh object can be used to efficiently store large numbers of triangles.
Its syntax is:

  mesh {
    triangle {
      <CORNER1>, <CORNER2>, <CORNER3>
      [ texture { STRING } ]
    }
    smooth_triangle {
      <CORNER1>, <NORMAL1>,
      <CORNER2>, <NORMAL2>,
      <CORNER3>, <NORMAL3>
      [ texture { STRING } ]
    }
    [ hierarchy FLAG ]
  }


Any number of triangles and/or smooth triangles can be used and each of those
triangles can be individually textured by assigning a texture name to it. The
texture has to be declared before the mesh is parsed. It is not possible to
use texture definitions inside the triangle or smooth triangle statements.
This is a restriction that is necessary for an efficient storage of the
assigned textures.

The mesh's components are internally bounded by a bounding box hierarchy to
speed up intersection testing. The bounding hierarchy can be turned off with
the hierarchy keyword. This should only be done if memory is short or the
mesh consists of only a few triangles.

Copies of a mesh object refer to the same triangle data and thus consume very
little memory. You can easily trace hundred copies of an 10000 triangle mesh
without running out of memory (assuming the first mesh fits into memory).

The mesh object has two advantages over a union of triangles: it needs less
memory and it is transformed faster. The memory requirements are reduced by
efficiently storing the triangles vertices and normals. The parsing time for
transformed meshes is reduced because only the mesh object has to be
transformed and not every single triangle as it is necessary for unions.

The mesh object can currently only include triangle and smooth triangle
components. That restriction is liable to change, allowing polygonal
components, at some point in the future.

7.5.3.4          Polygon

Polygons are useful for creating rectangles, squares and other planar shapes
with more than three edges. Their syntax is:

  polygon {
    TOTAL_NUMBER_OF_POINTS,
    <A_1>, <A_2>, ..., <A_na>, <A_1>,
    <B_1>, <B_2>, ..., <B_nb>, <B_1>,
    <C_1>, <C_2>, ..., <C_nc>, <C_1>,
    ...
  }


The points <A_1> through <A_na> describe the first sub-polygon, the points
<B_1> through <B_nb> describe the second sub-polygon, and so on. A polygon
can contain any number of sub-polygons, either overlapping or not. In places
where an even number of polygons overlaps a hole appears. You only have to be
sure that each of these polygons is closed. This is insured by repeating the
first point of a sub-polygon at the end of the sub-polygon's point sequence.
This implies that all points of a sub-polygon are different.

If the (last) sub-polygon is not closed a warning is issued and the program
automatically closes the polygon. This is useful because polygons imported
from other programs may not be closed, i. e. their first and last point are
not the same.

All points of a polygon are three-dimensional vectors that have to lay on one
plane. If this is not the case an error occurs. You can also use
two-dimensional vectors to describe the polygon. POV-Ray assumes that the z
value is zero in this case.

A square polygon that matches the default planar imagemap is simply:

  polygon {
    4,
    <0, 0>, <0, 1>, <1, 1>, <1, 0>
    texture {
      finish { ambient 1 diffuse 0 }
      pigment { image_map { gif "test.gif"  } }
    }
    //scale and rotate as needed here
  }


The sub-polygon feature can be used to generate complex shapes like the
letter "P", where a hole is cut into another polygon:

  #declare P = polygon {
    12,
    <0, 0>, <0, 6>, <4, 6>, <4, 3>, <1, 3>, <1, 0>, <0, 0>,
    <1, 4>, <1, 5>, <3, 5>, <3, 4>, <1, 4>
  }


The first sub-polygon (on the first line) describes the outer shape of the
letter "P". The second sub-polygon (on the second line) describes the
rectangular hole that is cut in the top of the letter "P". Both rectangles
are closed, i. e. their first and last points are the same.

The feature of cutting holes into a polygon is based on the polygon
inside/outside test used. A point is considered to be inside a polygon if a
straight line drawn from this point in an arbitrary direction crosses an odd
number of edges (this is known as Jordan's curve  theorem).

Another very complex example showing one large triangle with three small
holes and three separate, small triangles is given below:

  polygon {
    28,
    <0, 0> <1, 0> <0, 1> <0, 0>          // large outer triangle
    <.3, .7> <.4, .7> <.3, .8> <.3, .7>  // small outer triangle #1
    <.5, .5> <.6, .5> <.5, .6> <.5, .5>  // small outer triangle #2
    <.7, .3> <.8, .3> <.7, .4> <.7, .3>  // small outer triangle #3
    <.5, .2> <.6, .2> <.5, .3> <.5, .2>  // inner triangle #1
    <.2, .5> <.3, .5> <.2, .6> <.2, .5>  // inner triangle #2
    <.1, .1> <.2, .1> <.1, .2> <.1, .1>  // inner triangle #3
  }


7.5.3.5          Triangle and Smooth Triangle

The triangle primitive is available in order to make more complex objects
than the built-in shapes will permit. Triangles are usually not created by
hand but are converted from other files or generated by utilities. A triangle
is defined by

  triangle {
    <CORNER1>, <CORNER2>, <CORNER3>
  }


where <CORNERn> is a vector defining the x, y, z coordinates of each corner
of the triangle.

Because triangles are perfectly flat surfaces it would require extremely
large numbers of very small triangles to approximate a smooth, curved
surface. However much of our perception of smooth surfaces is dependent upon
the way light and shading is done. By artificially modifying the surface
normals we can simulate as smooth surface and hide the sharp-edged seams
between individual triangles.

The smooth triangle primitive is used for just such purposes. The smooth
triangles use a formula called Phong normal interpolation to calculate the
surface normal for any point on the triangle based on normal vectors which
you define for the three corners. This makes the triangle appear to be a
smooth curved surface. A smooth triangle is defined by

  smooth_triangle {
    <CORNER1>, <NORMAL1>,
    <CORNER2>, <NORMAL2>,
    <CORNER3>, <NORMAL3>
  }


where the corners are defined as in regular triangles and < NORMALn> is a
vector describing the direction of the surface normal at each corner.

These normal vectors are prohibitively difficult to compute by hand.
Therefore smooth triangles are almost always generated by utility programs.
To achieve smooth results, any triangles which share a common vertex should
have the same normal vector at that vertex. Generally the smoothed normal
should be the average of all the actual normals of the triangles which share
that point.

7.5.4            Infinite Solid Primitives

There are five polynomial primitive shapes that are possibly infinite and do
not respond to automatic bounding. They are plane, cubic, poly, quadric and
quartic. They do have a well defined inside and may be used in CSG and inside
a clipped_by statement. As with all shapes they can be translated, rotated
and scaled..

7.5.4.1          Plane

The plane primitive is a simple way to define an infinite flat surface. The
plane is specified as follows:

  plane { <NORMAL>, DISTANCE }


The <NORMAL> vector defines the surface normal of the plane. A surface normal
is a vector which points up from the surface at a 90 degree angle. This is
followed by a float value that gives the distance along the normal that the
plane is from the origin (that is only true if the normal vector has unit
length; see below). For example:

  plane { <0, 1, 0>, 4 }


This is a plane where straight up is defined in the positive y-direction. The
plane is 4 units in that direction away from the origin. Because most planes
are defined with surface normals in the direction of an axis you will often
see planes defined using the x, y or z built-in vector identifiers. The
example above could be specified as:

  plane { y, 4 }


The plane extends infinitely in the x- and z-directions. It effectively
divides the world into two pieces. By definition the normal vector points to
the outside of the plane while any points away from the vector are defined as
inside. This inside/outside distinction is only important when using planes
in CSG and clipped_by.

A plane is called a polynomial shape because it is defined by a first order
polynomial equation. Given a plane:

  plane { <A, B, C>, D }


it can be represented by the equation

  A*x + B*y + C*z - D*sqrt(A^2 + B^2 + C^2) = 0.


Therefore our example plane { y,4 } is actually the polynomial equation y=4.
You can think of this as a set of all x, y, z points where all have y values
equal to 4, regardless of the x or z values.

This equation is a first order polynomial because each term contains only
single powers of x, y or z. A second order equation has terms like x^2, y^2,
z^2, xy, xz and yz. Another name for a 2nd order equation is a quadric
equation. Third order polys are called cubics. A 4th order equation is a
quartic. Such shapes are described in the sections below.

7.5.4.2          Poly, Cubic and Quartic

Higher order polynomial surfaces may be defined by the use of a poly shape.
The syntax is

  poly { ORDER, <T1, T2, T3, .... Tm> }


where ORDER is an integer number from 2 to 7 inclusively that specifies the
order of the equation. T1, T2, ... Tm are float values for the coefficients
of the equation. There are m such terms where

  m = ((ORDER+1)*(ORDER+2)*(ORDER+3))/6.


An alternate way to specify 3rd order polys is:

  cubic { <T1, T2,... T20> }


Also 4th order equations may be specified with:

  quartic { <T1, T2,... T35> }


Here's a more mathematical description of quartics for those who are
interested. Quartic surfaces are 4th order surfaces and can be used to
describe a large class of shapes including the torus, the lemniscate, etc.
The general equation for a quartic equation in three variables is (hold onto
your hat):

  a00 x^4 + a01 x^3 y + a02 x^3 z+ a03 x^3 + a04 x^2 y^2+
  a05 x^2 y z+ a06 x^2 y + a07 x^2 z^2+a08 x^2 z+a09 x^2+
  a10 x y^3+a11 x y^2 z+ a12 x y^2+a13 x y z^2+a14 x y z+
  a15 x y + a16 x z^3 + a17 x z^2 + a18 x z + a19 x+
  a20 y^4 + a21 y^3 z + a22 y^3+ a23 y^2 z^2 +a24 y^2 z+
  a25 y^2 + a26 y z^3 + a27 y z^2 + a28 y z + a29 y+
  a30 z^4 + a31 z^3 + a32 z^2 + a33 z + a34 = 0


To declare a quartic surface requires that each of the coefficients (a0 ...
a34) be placed in order into a single long vector of 35 terms.

As an example let's define a torus the hard way. A Torus can be represented
by the equation:

 x^4 + y^4 + z^4 + 2 x^2 y^2 + 2 x^2 z^2 + 2 y^2 z^2 -
 2 (r_0^2 + r_1^2) x^2 + 2 (r_0^2 - r_1^2) y^2 -
 2 (r_0^2 + r_1^2) z^2 + (r_0^2 - r_1^2)^2 = 0


Where r_0 is the major radius of the torus, the distance from the hole of the
donut to the middle of the ring of the donut, and r_1 is the minor radius of
the torus, the distance from the middle of the ring of the donut to the outer
surface. The following object declaration is for a torus having major radius
6.3 minor radius 3.5 (Making the maximum width just under 20).

  // Torus having major radius sqrt(40), minor radius sqrt(12)

  quartic {
    < 1,   0,   0,   0,   2,   0,   0,   2,   0,
   -104,   0,   0,   0,   0,   0,   0,   0,   0,
      0,   0,   1,   0,   0,   2,   0,  56,   0,
      0,   0,   0,   1,   0, -104,  0, 784 >
    sturm
    bounded_by { // bounded_by speeds up the render,
                 // see bounded_by
                 // explanation later
                 // in docs for more info.
     sphere { <0, 0, 0>, 10 }
    }
  }


Poly, cubic and quartics are just like quadrics in that you don't have to
understand what one is to use one. The file shapesq.inc has plenty of
pre-defined quartics for you to play with. The syntax for using a pre-defined
quartic is:

  object { Quartic_Name }


Polys use highly complex computations and will not always render perfectly.
If the surface is not smooth, has dropouts, or extra random pixels, try using
the optional keyword sturm in the definition. This will cause a slower but
more accurate calculation method to be used. Usually, but not always, this
will solve the problem. If sturm doesn't work, try rotating or translating
the shape by some small amount. See the sub-directory math in the scene files
directory for examples of polys in scenes.

There are really so many different quartic shapes, we can't even begin to
list or describe them all. If you are interested and mathematically inclined,
an excellent reference book for curves and surfaces where you'll find more
quartic shape formulas is:

  "The CRC Handbook of Mathematical Curves and Surfaces"
  David von Seggern
  CRC Press, 1990


7.5.4.3          Quadric

Quadric surfaces can produce shapes like ellipsoids, spheres, cones,
cylinders, paraboloids (dish shapes) and hyperboloids (saddle or hourglass
shapes). Note that you do not confuse quaDRic with quaRTic. A quadric is a
2nd order polynomial while a quartic is 4th order. Quadrics render much
faster and are less error-prone.

A quadric is defined in POV-Ray by

  quadric { <A,B,C>, <D,E,F>, <G,H,I>, J }


where A through J are float expressions that define a surface of x, y, z
points which satisfy the equation

  A x^2   + B y^2   + C z^2 +
  D xy    + E xz    + F yz +
  G x     + H y     + I z    + J = 0


Different values of A, B, C, ... J will give different shapes. If you take
any three dimensional point and use its x, y and z coordinates in the above
equation the answer will be 0 if the point is on the surface of the object.
The answer will be negative if the point is inside the object and positive if
the point is outside the object. Here are some examples:

  X^2 + Y^2 + Z^2 - 1 = 0  Sphere
  X^2 + Y^2 - 1 = 0        Infinite cylinder along the Z axis
  X^2 + Y^2 - Z^2 = 0      Infinite cone along the Z axis


The easiest way to use these shapes is to include the standard file
shapes.inc into your program. It contains several pre-defined quadrics and
you can transform these pre-defined shapes (using translate, rotate and
scale) into the ones you want. You can invoke them by using the syntax:

  object { Quadric_Name }


The pre-defined quadrics are centered about the origin < 0,0,0> and have a
radius of 1. Don't confuse radius with width. The radius is half the diameter
or width making the standard quadrics 2 units wide.

Some of the pre-defined quadrics are,

  Ellipsoid
  Cylinder_X, Cylinder_Y, Cylinder_Z
  QCone_X, QCone_Y, QCone_Z
  Paraboloid_X, Paraboloid_Y, Paraboloid_Z


7.5.5            Constructive Solid Geometry

POV-Ray supports Constructive Solid Geometry (CSG) with five different
operations: difference, intersection, merge, union and negation (inversion).
While the first four operations represent binary operators, i. e. they need
two arguments, the negation is a unary operator, it takes only one argument.

7.5.5.1          About CSG

Constructive Solid Geometry is a technique for combining two or more objects
to create a new object using the three boolean set operators union,
intersection, and negation. It only works with solid objects, i. e. objects
that have a well-defined interior. This is the case for all objects described
in the sections "Finite Solid Primitives" and "Infinite Solid Primitives".

CSG shapes may be used anywhere a standard shape can be used, even inside
other CSG shapes. They can be translated, rotated or scaled in the same way
as any other shape. The shapes making up the CSG shape may be individually
translated, rotated and scaled as well.

7.5.5.2          Inside and Outside

Most shape primitives, like spheres, boxes and blobs divide the world into
two regions. One region is inside the object and one is outside.

Given any point in space you can say it's either inside or outside any
particular primitive object. Well, it could be exactly on the surface but
this case is rather hard to determine due to numerical problems.

Even planes have an inside and an outside. By definition, the surface normal
of the plane points towards the outside of the plane. You should note that
triangles and triangle-based shapes cannot be used as solid objects in CSG
since they have no well defined inside and outside.

CSG uses the concepts of inside and outside to combine shapes together as
explained in the following sections.

Imagine you have to objects that partially overlap like shown in the figure
below. Four different areas of points can be distinguished: points that are
neither in object A nor in object B, points that are in object A but not in
object B, points that are not in object A but in object B and last not least
points that are in object A and object B.

* = Object A
% = Object B

         *
        * *    %
       *   *  % %
      *     *%   %
     *      %*    %
    *      %  *    %
   *      %    *    %
  *******%*******    %
        %             %
       %%%%%%%%%%%%%%%%%
Two overlapping objects.

Keeping this in mind it will be quite easy to understand how the CSG
operations work.

7.5.5.3          Inverse

When using CSG it is often useful to invert an object so that it'll be
inside-out. The appearance of the object is not changed, just the way that
POV-Ray perceives it. When the inverse keyword is used the inside of the
shape is flipped to become the outside and vice versa.

Note that the difference operation is performed by intersecting the first
object with the negation of the second object.

7.5.5.4          Union

         *
        * *    %
       *   *  % %
      *     *%   %
     *      %*    %
    *      %  *    %
   *      %    *    %
  *******%*******    %
        %             %
       %%%%%%%%%%%%%%%%%
The union of two objects.

Unions are simply glue used to bind two or more shapes into a single entity
that can be manipulated as a single object. The image above shows the union
of A and B. The new object created by the union operation can be scaled,
translated and rotated as a single shape. The entire union can share a single
texture but each object contained in the union may also have its own texture,
which will override any matching texture statements in the parent object.

You should be aware that the surfaces inside the union will not be removed.
As you can see from the figure this may be a problem for transparent unions.
If you want those surfaces to be removed you'll have to use the merge
operations explained in a later section.

The following union will contain a box and a sphere.

  union {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }


Earlier versions of POV-Ray placed restrictions on unions so you often had to
combine objects with composite statements. Those earlier restrictions have
been lifted so composite is no longer needed. Composite is still supported
for backwards compatibility but it is recommended that union is now used in
it's place since future support for the composite keyword is not guaranteed.

7.5.5.5          Intersection

A point is inside an intersection if it is inside both objects, A and B, as
show in the figure below.

          %*
         %  *
        %    *
       %*******
The intersection of two objects.

For example:

  intersection {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }


7.5.5.6          Difference

The CSG difference operation takes the intersection between the first object
and the negation of the second object. Thus only points inside object A and
outside object B belong to the difference of both objects.

The results is a subtraction of the 2nd shape from the first shape as shown
in the figure below.

       *
      * *
     *   *
    *     *
   *  1   %
  *      %
 *      %
*******%
The difference between two objects.

For example:

  difference {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }


7.5.5.7          Merge

The union operation just glues objects together, it does not remove the
objects' surfaces inside the union. If a transparent union is used those
surface will get visible.

The merge operations can be used to avoid this problem. It works just like
union but it eliminates the inner surfaces like shown in the figure below.

         *
        * *    %
       *   *  % %
      *     *%   %
     *            %
    *              %
   *                %
  *******%           %
        %             %
       %%%%%%%%%%%%%%%%%
Merge removes inner surfaces.

7.5.6            Light Sources

The last object covered is the light source. Light sources have no visible
shape of their own. They are just points or areas which emit light. Their
full syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    [ spotlight ]
    [ point_at <POINT_AT> ]
    [ radius RADIUS ]
    [ falloff FALLOFF ]
    [ tightness TIGHTNESS ]
    [ area_light <AXIS1>, <AXIS2>, SIZE1, SIZE2 ]
    [ adaptive ADAPTIVE ]
    [ jitter JITTER ]
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


The different types of light sources and the optional modifiers are described
in the following sections.

7.5.6.1          Point Lights

A point light source sends light of the specified color uniformly in all
directions. Its location is described by the location keyword and its color
is given by the color keyword. The complete syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


7.5.6.2          Spotlights

A spotlight is a point light source where the rays of light are constrained
by a cone. The light is bright in the center of this cone and falls off or
darkens at the edges of the cone. The syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    spotlight
    point_at <POINT_AT>
    radius RADIUS
    falloff FALLOFF
    tightness TIGHTNESS
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


The spotlight is identified by the spotlight keyword. It is located at
LOCATION and points at POINT_AT. The following illustration will be helpful
in understanding how these values relate to each other.

     (+) location
     / \
    /   \
   /     \
  /       \
 /         \
/           \
+-----*-----+
      ^ point_at
The geometry of a spotlight.

The spotlight's other parameters are radius, falloff and tightness.

Think of a spotlight as two nested cones as shown in the figure. The inner
cone is specified by the radius parameter and is fully lit. The outer cone is
the falloff cone beyond which there is no light. The values for these two
parameters are half the opening angles of the corresponding cones, both
angles have to be smaller than 90 degrees. The light smoothly falls off
between the radius and the falloff angle like shown in the figures below (as
long as the radius angle is not negative).

Intensity multiplier curve with a fixed falloff angle of 45 degrees.

Intensity multiplier curve with a fixed radius angle of 45 degrees.

The tightness value specifies how quickly the light dims, or falls off, from
the spotlight's center line to the falloff cone (full darkness outside). The
default value for tightness is 10. Lower tightness values will make the
spotlight brighter, making the spot wider and the edges sharper. Higher
values will dim the spotlight, making the spot tighter and the edges softer.
Values from 1 to 100 are acceptable.

Intensity multiplier curve with fixed angle and falloff angles of 30 and 60
degrees respectively and different tightness values.

You should note from the figures that the radius and falloff angles interact
with the tightness parameter. Only negative radius angles will give the
tightness value full control over the spotlight's appearance as you can see
from the figure below. In that case the falloff angle has no effect and the
lit area is only determined by the tightness parameter.

Intensity multiplier curve with a negative radius angle and different
tightness values.

Spotlights may be used anyplace that a normal light source is used. Like any
light sources, they are invisible. They are treated as shapes and may be
included in CSG shapes. They may also be used in conjunction with area
lights.

7.5.6.3          Cylindrical Lights

Cylindrical light sources work pretty much like spotlights except that the
light rays are constraint by a cylinder and not a cone. The syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    cylinder
    point_at <POINT_AT>
    radius RADIUS
    falloff FALLOFF
    tightness TIGHTNESS
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


The radius, falloff and tightness keywords control the same features as with
the spotlight.

You should keep in mind that the cylindrical light source is still a point
light source. The rays are emitted from one point and are only constraint by
a cylinder. The light rays are not parallel.

7.5.6.4          Area Lights

Area light sources occupy a finite, one- or two-dimensional area of space.
They can cast soft shadows because they can partially block light.

The area lights used in POV-Ray are rectangular in shape, sort of like a flat
panel light. Rather than performing the complex calculations that would be
required to model a true area light, it is approximated as an array of point
light sources spread out over the area occupied by the light. The intensity
of each individual point light in the array is dimmed so that the total
amount of light emitted by the light is equal to the light color specified in
the declaration. The syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    area_light <AXIS1>, <AXIS2>, SIZE1, SIZE2
    adaptive ADAPTIVE
    jitter JITTER
    [ spotlight ]
    [ point_at <POINT_AT> ]
    [ radius RADIUS ]
    [ falloff FALLOFF ]
    [ tightness TIGHTNESS ]
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmosphere BOOL ]
    [ atmospheric_attenuation BOOL ]
  }


The light's location and color are specified in the same way as a for a
regular light source.

The area_light command defines the size and orientation of the area light as
well as the number of lights in the light source array. The vectors AXIS1 and
AXIS2 specify the lengths and directions of the edges of the light. Since the
area lights are rectangular in shape these vectors should be perpendicular to
each other. The larger the size of the light the thicker the soft part of
shadows will be. The numbers SIZE1 and SIZE2 specify the dimensions of the
array of point lights. The more lights you use the smoother your shadows will
be but the longer they will take to render.

The jitter command is optional. When used it causes the positions of the
point lights in the array to be randomly jittered to eliminate any shadow
banding that may occur. The jittering is completely random from render to
render and should not be used when generating animations.

Note that it is possible to specify spotlight parameters along with the area
light parameters to create area spotlights. Using area spotlights is a good
way to speed up scenes that use area lights since you can confine the lengthy
soft shadow calculations to only the parts of your scene that need them.

An interesting effect can be created using a linear light source. Rather than
having a rectangular shape, a linear light stretches along a line sort of
like a thin fluorescent tube. To create a linear light just create an area
light with one of the array dimensions set to 1.

The adaptive command is used to enable adaptive sampling of the light source.
By default POV-Ray calculates the amount of light that reaches a surface from
an area light by shooting a test ray at every point light within the array.
As you can imagine this is very slow. Adaptive sampling on the other hand
attempts to approximate the same calculation by using a minimum number of
test rays. The number specified after the keyword controls how much adaptive
sampling is used. The higher the number the more accurate your shadows will
be but the longer they will take to render. If you're not sure what value to
use a good starting point is adaptive 1. The adaptive keyword only accepts
integer values and cannot be set lower than 0.

When performing adaptive sampling POV-Ray starts by shooting a test ray at
each of the four corners of the area light. If the amount of light received
from all four corners is approximately the same then the area light is
assumed to be either fully in view or fully blocked. The light intensity is
then calculated as the average intensity of the light received from the four
corners. However, if the light intensity from the four corners differs
significantly then the area light is partially blocked. The area light is
split into four quarters and each section is sampled as described above. This
allows POV-Ray to rapidly approximate how much of the area light is in view
without having to shoot a test ray at every light in the array. Visually the
sampling goes like shown below.

 level       0            1           2         3
 rays        4            9           25        81
         * . . . *    x . * . x   x * x * x
         . . . . .    . . . . .   * * * * *
         . . . . .    * . * . *   x * x * x    etc...
         . . . . .    . . . . .   * * * * *
         * . . . *    x . * . x   x * x * x

 * new samples
 x reused samples from previous level
Area light adaptive samples.

While the adaptive sampling method is fast (relatively speaking) it can
sometimes produces inaccurate shadows. The solution is to reduce the amount
of adaptive sampling without completely turning it off. The number after the
adaptive keyword adjusts the number of times that the area light will be
split before the adaptive phase begins. For example if you use adaptive 0 a
minimum of 4 rays will be shot at the light. If you use adaptive 1 a minimum
of 9 rays will be shot (adaptive 2 gives 25 rays, adaptive 3 gives 81 rays,
etc). Obviously the more shadow rays you shoot the slower the rendering will
be so you should use the lowest value that gives acceptable results.

The number of rays never exceeds the values you specify for rows and columns
of points. For example area_light x,y,4,4 specifies a 4 by 4 array of lights.
If you specify adaptive 3 it would mean that you should start with a 9 by 9
array. In this case no adaptive sampling is done. The 4 by 4 array is used.

7.5.6.5          Shadowless Lights

Using the shadowless keyword you can stop a light source from casting
shadows.

7.5.6.6          Looks_like

Normally the light source itself has no visible shape. The light simply
radiates from an invisible point or area. You may give a light source any
shape by adding a looks_like { OBJECT } statement.

There is an implied no_shadow attached to the looks_like object so that light
is not blocked by the object. Without the automatic no_shadow the light
inside the object would not escape. The object would, in effect, cast a
shadow over everything.

If you want the attached object to block light then you should attach it with
a union and not a looks_like as follows:

  union {
    light_source { <100, 200, -300> color White }
    object { My_Lamp_Shape }
  }


7.5.6.7          Light Fading

By default POV-Ray does not diminish light from any light source as it
travels through space. In order to get a more realistic effect fade_distance
and fade_power can be used to model the distance based falloff in light
intensity.

The fade_distance keyword is used to specify the distance at which the full
light intensity arrives, i. e. the intensity which was given by the color
keyword. The actual attenuation is described by the fade_power keyword, which
determines the falloff rate. E. g. linear or quadratic falloff can be used by
setting FADE_POWER to 1 or 2 respectively. The complete formula to calculate
the factor by which the light is attenuated is

                                 2
  attenuation = --------------------------------------
                 1 + (d / FADE_DISTANCE) ^ FADE_POWER


with d being the distance the light has traveled.

Light fading functions for different fading powers.

You should note two important facts: First, for FADE_DISTANCEs larger than
one the light intensity at distances smaller than FADE_DISTANCE actually
increases. This is necessary to get the light source color if the distance
traveled equals the FADE_DISTANCE. Second, only light coming directly from
light sources is attenuated. Reflected or refracted light is not attenuated
by distance.

7.5.6.8          Atmosphere Interaction

By default light sources will interact with an atmosphere added to the scene.
This behaviour can be switched off by using the atmosphere keyword inside the
light source statement.

  light_source {
    ...
    atmosphere off
  }


7.5.6.9          Atmospheric Attenuation

Normally light coming from light sources is not influenced by fog or
atmosphere. This can be changed by turning the atmospheric attenuation for a
given light source on. All light coming from this light source will now be
diminished as it travels through the fog or atmosphere. This results in an
distance-based, exponential intensity falloff ruled by the used fog or
atmosphere. If there is no fog or atmosphere no change will be seen.

7.5.7            Object Modifiers

A variety of modifiers may be attached to objects. Transformations such as
translate, rotate and scale have already been discussed. Textures are in a
section of their own below. Here are three other important modifiers:
clipped_by, bounded_by and no_shadow. Although the examples below use object
statements and object identifiers, these modifiers may be used on any type of
object such as sphere, box etc.

7.5.7.1          Clipped_By

The clipped_by statement is technically an object modifier but it provides a
type of CSG similar to CSG intersection. You attach a clipping object like
this:

  object {
    My_Thing
    clipped_by{plane{y,0}}
  }


Every part of the object My_Thing that is inside the plane is retained while
the remaining part is clipped off and discarded. In an intersection object
the hole is closed off. With clipped_by it leaves an opening. For example the
following figure shows object A being clipped by object B.

   *       *
  *         *
 *           *
***************
An object clipped by another object.

clipped_by may be used to slice off portions of any shape. In many cases it
will also result in faster rendering times than other methods of altering a
shape.

Often you will want to use the clipped_by and bounded_by options with the
same object. The following shortcut saves typing and uses less memory.

  object {
    My_Thing
    bounded_by { box { <0,0,0>, <1,1,1> } }
    clipped_by { bounded_by }
  }


7.5.7.2          Bounded_By

The calculations necessary to test if a ray hits an object can be quite time
consuming. Each ray has to be tested against every object in the scene.
POV-Ray attempts so speed up the process by building a set of invisible
boxes, called bounding boxes, which cluster the objects together. This way a
ray that travels in one part of the scene doesn't have to be tested against
objects in another, far away part of the scene. When large a number of
objects are present the boxes are nested inside each other. POV-Ray can use
bounding boxes on any finite object and even some clipped or bounded
quadrics. However infinite objects (such as a planes, quartic, cubic and
poly) cannot be automatically bound. CSG objects are automatically bound if
they contain finite (and in some cases even infinite) objects. This works by
applying the CSG set operations to the bounding boxes of all objects used
inside the CSG object. For difference and intersection operations this will
hardly ever lead to an optimal bounding box. It's sometimes better (depending
on the complexity of the CSG object) to use a bounded_by statement with such
shapes.

Normally bounding shapes are not necessary but there are cases where they can
be used to speed up the rendering of complex objects. Bounding shapes tell
the ray-tracer that the object is totally enclosed by a simple shape. When
tracing rays, the ray is first tested against the simple bounding shape. If
it strikes the bounding shape the ray is further tested against the more
complicated object inside. Otherwise the entire complex shape is skipped,
which greatly speeds rendering.

To use bounding shapes, simply include the following lines in the declaration
of your object:

  bounded_by {
    object { ... }
  }


An example of a bounding shape:

  intersection {
    sphere { <0,0,0>, 2 }
    plane  { <0,1,0>, 0 }
    plane  { <1,0,0>, 0 }
    bounded_by { sphere { <0,0,0>, 2 } }
  }


The best bounding shape is a sphere or a box since these shapes are highly
optimized, although, any shape may be used. If the bounding shape is itself a
finite shape which responds to bounding slabs then the object which it
encloses will also be used in the slab system.

CSG shapes can benefit from bounding slabs without a bounded_by statement
however they may do so inefficiently in intersection, difference and merge.
In these three CSG types the automatic bound used covers all of the component
objects in their entirety. However the result of these intersections may
result in a smaller object. Compare the sizes of the illustrations for union
and intersection in the CSG section above. It is possible to draw a much
smaller box around the intersection of A and B than the union of A and B yet
the automatic bounds are the size of the union of A and B regardless of the
kind of CSG specified.

While it is almost always a good idea to manually add a bounded_by to
intersection, difference and merge, it is often best to not bound a union. If
a union has no bounded_by and no clipped_by POV-Ray can internally split
apart the components of a union and apply automatic bounding slabs to any of
its finite parts. Note that some utilities such as raw2pov may be able to
generate bounds more efficiently than POV-Ray's current system. However most
unions you create yourself can be easily bounded by the automatic system. For
technical reasons POV-Ray cannot split a merge object. It is probably best to
hand bound a merge, especially if it is very complex.

Note that if bounding shape is too small or positioned incorrectly it may
clip the object in undefined ways or the object may not appear at all. To do
true clipping, use clipped_by as explained above. Often you will want to use
the clipped_by and bounded_by options with the same object. The following
shortcut saves typing and uses less memory.

  object {
    My_Thing
    clipped_by{ box { <0,0,0>,<1,1,1 > }}
    bounded_by{ clipped_by }
  }


7.5.7.3          Hollow

POV-Ray by default assumes that objects are made of a solid material that
completely fills the interior of an object. By adding the hollow keyword to
the object you can make it hollow. That is very useful if you want
atmospheric effects to exist inside an object. It is even required for
objects containing a halo (see "Halo" for details).

In order to get a hollow CSG object you just have to make the top level
object hollow. All children will assume the same hollow state except their
state is explicitly set. The following example will set both spheres inside
the union hollow

  union {
    sphere { -0.5*x, 1 }
    sphere {  0.5*x, 1 }
    hollow
  }


while the next example will only set the second sphere hollow because the
first sphere was explicitly set to be not hollow.

  union {
    sphere { -0.5*x, 1 hollow off }
    sphere {  0.5*x, 1 }
    hollow
  }


7.5.7.4          No_Shadow

You may specify the no_shadow keyword in an object to make that object cast
no shadow. This is useful for special effects and for creating the illusion
that a light source actually is visible. This keyword was necessary in
earlier versions of POV-Ray which did not have the looks_like statement. Now
it is useful for creating things like laser beams or other unreal effects.

Simply attach the keyword as follows:

  object {
    My_Thing
    no_shadow
  }


7.5.7.5          Sturm

Some of POV-Ray's objects allow you to choose between a fast but sometimes
inaccurate root solver and a slower but more accurate one. This is the case
for all objects that involve the solution of a cubic or quartic polynomial.
There are analytic mathematical solutions for those polynomials that can be
used.

Lower order polynomials are trivial to solve while higher order polynomials
require iterative algorithms to solve them. One of those algorithms is the
Sturmian root solver.

The following list shows all objects for which the Sturmian root solver can
be used.

  blob
  cubic
  lathe    (only with quadratic splines)
  poly
  prism    (only with cubic splines)
  quartic
  sor


7.6              Textures

The texture describes what the object looks like, i. e. its material.
Textures are combinations of pigments, normals, finishes and halos. Pigment
is the color or pattern of colors inherent in the material. Normal is a
method of simulating various patterns of bumps, dents, ripples or waves by
modifying the surface normal vector. Finish describes the reflective and
refractive properties of a material. Halo simulates effects like clouds, fog,
fire etc. by using a density field defined inside the object.

A plain texture consists of a single pigment, an optional normal, a single
finish and optionally one or more halos. A special  texture combines two or
more textures using a pattern or blending function. Special textures may be
made quite complex by nesting patterns within patterns. At the innermost
levels however, they are made up from plain textures. Note that although we
call a plain texture plain it may be a very complex texture. The term plain
only means that it has a single pigment, normal, finish and halo.

The most complete form for defining a plain texture is as follows:

  texture {
    TEXTURE_IDENTIFIER
    pigment {...}
    normal {...}
    finish {...}
    halo {...}
    TRANSFORMATIONS
  }


Each of the items in a texture are optional but if they are present the
identifier must be first and the transformations must be last. The pigment,
normal and finish parameters modify any pigment, normal and finish already
specified in the TEXTURE_IDENTIFIER. Any halos are added to the already
existing halos. If no texture identifier is specified the pigment, normal and
finish statements modify the current default values and any halo is added to
the default halo, if any. TRANSFORMATIONs are translate, rotate, scale and
matrix statements. They should be specified last.

The sections below describe all of the options available in pigments,
normals, finishes and halos. Special textures are covered later.

7.6.1            Pigment

The color or pattern of colors for an object is defined by a pigment
statement. All plain textures must have a pigment. If you do not specify one
the default pigment is used. A pigment statement is part of a texture
specification. However it can be tedious to use a texture statement just to
add a color to an object. Therefore you may attach a pigment directly to an
object without explicitly specifying that it as part of a texture. For
example:

  //this...                //can be shortened to this...

  object {                 object {
    My_Object                My_Object
    texture {                pigment {color Red}
      pigment {color Red}  }
    }
  }


The color you define is the way you want the object to look if fully
illuminated. You pick the basic color inherent in the object and POV-Ray
brightens or darkens it depending on the lighting in the scene. The parameter
is called pigment because we are defining the basic color the object actually
is rather than how it looks.

The most complete form for defining a pigment is as follows:

  pigment {
    PIGMENT_IDENTIFIER
    PATTERN_TYPE
    PIGMENT_MODIFIERS...
  }


Each of the items in a pigment are optional but if they are present, they
should be in the order shown above to insure that the results are as
expected. Any items after the PIGMENT_IDENTIFIER modify or override settings
given in the identifier. If no identifier is specified then the items modify
the pigment values in the current default texture. Valid PIGMENT_MODIFIERS
are color_map, pigment_map, image_map and quick_color statements as well as
any of the generic PATTERN_MODIFIERS such as translate, rotate, scale,
turbulence, wave shape and warp statements. Such modifiers apply only to the
pigment and not to other parts of the texture. Modifiers should be specified
last.

The various pattern types fall into roughly four categories. Each category is
discussed below. They are solid color, color list patterns, color mapped
patterns and image maps.

7.6.1.1          Solid Color Pigments

The simplest type of pigment is a solid color. To specify a solid color you
simply put a color specification inside a pigment. For example:

  pigment {color Orange}


A color specification consists of the option keyword color followed by a
color identifier or by a specification of the amount of red, green, blue,
filtered and unfiltered transparency in the surface. See section "Specifying
Colors" for more details about colors. Any pattern modifiers used with a
solid color are ignored because there is no pattern to modify.

7.6.1.2          Color List Pigments

There are three color list patterns: checker, hexagon and brick. The result
is a pattern of solid colors with distinct edges rather than a blending of
colors as with color mapped patterns. Each of these patterns is covered in
more detail in a later section. The syntax for each is:

  pigment { brick COLOR1, COLOR2 MODIFIERS ... }
  pigment { checker COLOR1, COLOR2 MODIFIERS ... }
  pigment { hexagon COLOR1, COLOR2, COLOR3 MODIFIERS ... }


Each COLORn is any valid color specification. There should be a comma between
each color or the color keyword should be used as a separator so that POV-Ray
can determine where each color specification starts and ends.

7.6.1.3          Color Maps

Most of the color patterns do not use abrupt color changes of just two or
three colors like those in the brick, checker or hexagon patterns. They
instead use smooth transitions of many colors that gradually change from one
point to the next. The colors are defined in a pigment modifier called a
color map that describes how the pattern blends from one color to the next.

Each of the various pattern types available is in fact a mathematical
function that takes any x, y, z location and turns it into a number between
0.0 and 1.0 inclusive. That number is used to specify what mix of colors to
use from the color map.

A color map is specified by...

  pigment{
    PATTERN_TYPE
    color_map {
      [ NUM_1 COLOR_1]
      [ NUM_2 COLOR_2]
      [ NUM_3 COLOR_3]
       ...
    }
    PIGMENT_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive.
COLOR_1, COLOR_2, ... are color specifications. Note that the [] brackets are
part of the actual statement. They are not notational symbols denoting
optional parts. The brackets surround each entry in the color map. There may
be from 2 to 256 entries in the map. The alternate spelling colour_map may be
used.

For example

  sphere {
    <0,1,2>, 2
    pigment {
      gradient x       //this is the PATTERN_TYPE
      color_map {
        [0.1  color Red]
        [0.3  color Yellow]
        [0.6  color Blue]
        [0.6  color Green]
        [0.8  color Cyan]
      }
    }
  }


The pattern function is evaluated and the result is a value from 0.0 to 1.0.
If the value is less than the first entry (in this case 0.1) then the first
color (red) is used. Values from 0.1 to 0.3 use a blend of red and yellow
using linear interpolation of the two colors. Similarly values from 0.3 to
0.6 blend from yellow to blue. Note that the 3rd and 4th entries both have
values of 0.6. This causes an immediate abrupt shift of color from blue to
green. Specifically a value that is less than 0.6 will be blue but exactly
equal to 0.6 will be green. Moving along, values from 0.6 to 0.8 will be a
blend of green and cyan. Finally any value greater than or equal to 0.8 will
be cyan.

If you want areas of unchanging color you simply specify the same color for
two adjacent entries. For example:

  color_map {
    [0.1  color Red]
    [0.3  color Yellow]
    [0.6  color Yellow]
    [0.8  color Green]
  }


In this case any value from 0.3 to 0.6 will be pure yellow.

The color_map keyword may be used with any pattern except brick, checker,
hexagon and image_map. You may declare and use color_map identifiers. For
example:

  #declare Rainbow_Colors=
    color_map {
      [0.0   color Magenta]
      [0.33  color Yellow]
      [0.67  color Cyan]
      [1.0   color Magenta]
    }

  object{My_Object
    pigment{
      gradient x
      color_map{Rainbow_Colors}
    }
  }


7.6.1.4          Pigment Maps

In addition to specifying blended colors with a color map you may create a
blend of pigments using a pigment map. The syntax for a pigment map is
identical to a color map except you specify a pigment in each map entry (and
not a color).

A pigment map is specified by...

  pigment{
    PATTERN_TYPE
    pigment_map {
      [ NUM_1 PIGMENT_BODY_1]
      [ NUM_2 PIGMENT_BODY_2]
      [ NUM_3 PIGMENT_BODY_3]
       ...
    }
    PIGMENT_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive. A
PIGMENT_BODY is anything that would normally appear inside a pigment
statement but the pigment keyword and {} braces are not needed. Note that the
[] brackets are part of the actual statement. They are not notational symbols
denoting optional parts. The brackets surround each entry in the map. There
may be from 2 to 256 entries in the map.

For example

  sphere {
    <0,1,2>, 2
    pigment {
      gradient x       //this is the PATTERN_TYPE
      pigment_map {
        [0.3 wood scale 0.2]
        [0.3 Jade]    //this is a pigment identifier
        [0.6 Jade]
        [0.9 marble turbulence 1]
      }
    }
  }


When the gradient x function returns values from 0.0 to 0.3 the scaled wood
pigment is used. From 0.3 to 0.6 the pigment identifier Jade is used. From
0.6 up to 0.9 a blend of Jade and a turbulent marble is used. From 0.9 on up
only the turbulent marble is used.

Pigment maps may be nested to any level of complexity you desire. The
pigments in a map may have color maps or pigment maps or any type of pigment
you want. Any entry of a pigment map may be a solid color however if all
entries are solid colors you should use a color map which will render
slightly faster.

Entire pigments may also be used with the block patterns such as checker,
hexagon and brick. For example...

  pigment {
    checker
    pigment { Jade scale .8 }
    pigment { White_Marble scale .5 }
  }


Note that in the case of block patterns the pigment wrapping is required
around the pigment information.

A pigment map is also used with the average pigment type. See "Average" for
details.

You may not use pigment_map or individual pigments with an image_map. See
section "Texture Maps" for an alternative way to do this.

7.6.1.5          Image Maps

When all else fails and none of the above pigment pattern types meets your
needs you can use an image map to wrap a 2-D bit-mapped image around your 3-D
objects.

7.6.1.5.1        Specifying an Image Map

The syntax for an image map is...

  pigment {
    image_map {
      FILE_TYPE "filename"
      MODIFIERS...
    }
  }


Where FILE_TYPE is one of the following keywords gif, tga, iff, ppm, pgm, png
or sys. This is followed by the name of the file in quotes. Several optional
modifiers may follow the file specification. The modifiers are described
below. Note that earlier versions of POV-Ray allowed some modifiers before
the FILE_TYPE but that syntax is being phased out in favor of the syntax
described here.

Filenames specified in the image_map statements will be searched for in the
home (current) directory first and, if not found, will then be searched for
in directories specified by any -L (library path) options active. This would
facilitate keeping all your image maps files in a separate subdirectory and
giving an -L option on the command line to where your library of image maps
are.

By default, the image is mapped onto the x-y-plane. The image is projected
onto the object as though there were a slide projector somewhere in the
-z-direction. The image exactly fills the square area from (x,y) coordinates
(0,0) to (1,1) regardless of the image's original size in pixels. If you
would like to change this default you may translate, rotate or scale the
pigment or texture to map it onto the object's surface as desired.

In section "Checker" the checker pigment pattern is explained. The checks are
described as solid cubes of colored clay from which objects are carved. With
image maps you should imagine that each pixel is a long, thin, square,
colored rod that extends parallel to the z-axis. The image is made from rows
and columns of these rods bundled together and the object is then carved from
the bundle.

If you would like to change this default orientation you may translate,
rotate or scale the pigment or texture to map it onto the object's surface as
desired.

7.6.1.5.2        The map_type Option

The default projection of the image onto the x-y-plane is called a planar map
type. This option may be changed by adding the map_type keyword followed by a
number specifying the way to wrap the image around the object.

A map_type 0 gives the default planar mapping already described.

A map_type 1 gives a spherical mapping. It assumes that the object is a
sphere of any size sitting at the origin. The y-axis is the north/south pole
of the spherical mapping. The top and bottom edges of the image just touch
the pole regardless of any scaling. The left edge of the image begins at the
positive x-axis and wraps the image around the sphere from west to east in a
-y-rotation. The image covers the sphere exactly once. The once keyword has
no meaning for this mapping type.

With map_type 2 you get a cylindrical mapping. It assumes that a cylinder of
any diameter lies along the y-axis. The image wraps around the cylinder just
like the spherical map but the image remains one unit tall from y=0 to y=1.
This band of color is repeated at all heights unless the once keyword is
applied.

Finally map_type 5 is a torus or donut shaped mapping. It assumes that a
torus of major radius one sits at the origin in the x-z-plane. The image is
wrapped around similar to spherical or cylindrical maps. However the top and
bottom edges of the map wrap over and under the torus where they meet each
other on the inner rim.

Types 3 and 4 are still under development.

Note that the map_type option may also be applied to bump_map and
material_map statements.

7.6.1.5.3        The Filter and Transmit Bitmap Modifiers

To make all or part of an image map transparent you can specify filter and/or
transmit values for the color palette/registers of PNG, GIF or IFF pictures
(at least for the modes that use palettes). You can do this by adding the
keyword filter or transmit following the filename. The keyword is followed by
two numbers. The first number is the palette number value and the second is
the amount of transparency. The values should be separated by a comma. For
example:

  image_map {
    gif "mypic.gif"
    filter   0, 0.5 // Make color 0 50% filtered transparent
    filter   5, 1.0 // Make color 5 100% filtered transparent
    transmit 8, 0.3 // Make color 8 30% non-filtered transparent
  }


You can give the entire image a filter or transmit value using filter all
VALUE or transmit all VALUE. For example:

  image_map {
    gif "stnglass.gif"
    filter all 0.9
  }


Note that early versions of POV-Ray used the keyword alpha to specify
filtered transparency however that word is often used to describe
non-filtered transparency. For this reason alpha is no longer used.

See section "Specifying Colors" for details on the differences between
filtered and non-filtered transparency.

7.6.1.5.4        Using the Alpha Channel

Another way to specify non-filtered transmit transparency in an image map is
by using the alpha channel.

PNG allows you to store a different transparency for each color index in the
PNG file, if desired. If your paint programs support this feature of PNG you
can do the transparency editing within your paint program rather than
specifying transmit values for each color in the POV file. Since PNG and TGA
image formats can also store full alpha channel (transparency) information
you can generate image maps that have transparency which isn't dependent on
the color of a pixel but rather its location in the image.

Although POV uses transmit 0.0 to specify no transparency and 1.0 to specify
full transparency, the alpha data ranges from 0 to 255 in the opposite
direction. Alpha data 0 means the same as transmit 1.0 and alpha data 255
produces transmit 0.0.

7.6.1.6          Quick Color

When developing POV-Ray scenes its often useful to do low quality test runs
that render faster. The +Q command line switch can be used to turn off some
time consuming color pattern and lighting calculations to speed things up.
However all settings of +Q5 or lower turns off pigment calculations and
creates gray objects.

By adding a quick_color to a pigment you tell POV-Ray what solid color to use
for quick renders instead of a patterned pigment. For example:

  pigment {
    gradient x
    color_map{
      [0.0 color Yellow]
      [0.3 color Cyan]
      [0.6 color Magenta]
      [1.0 color Cyan]
    }
    turbulence 0.5
    lambda 1.5
    omega 0.75
    octaves 8
    quick_color Neon_Pink
  }


This tells POV-Ray to use solid Neon_Pink for test runs at quality +Q5 or
lower but to use the turbulent gradient pattern for rendering at +Q6 and
higher.

Note that solid color pigments such as

  pigment {color Magenta}


automatically set the quick_color to that value. You may override this if you
want. Suppose you have 10 spheres on the screen and all are yellow. If you
want to identify them individually you could give each a different
quick_color like this:

  sphere {
    <1,2,3>,4
    pigment { color Yellow  quick_color Red }
  }

  sphere {
    <-1,-2,-3>,4
    pigment { color Yellow  quick_color Blue }
  }


and so on. At +Q6 or higher they will all be yellow but at +Q5 or lower each
would be different colors so you could identify them.

7.6.2            Normal

Ray-tracing is known for the dramatic way it depicts reflection, refraction
and lighting effects. Much of our perception depends on the reflective
properties of an object. Ray tracing can exploit this by playing tricks on
our perception to make us see complex details that aren't really there.

Suppose you wanted a very bumpy surface on the object. It would be very
difficult to mathematically model lots of bumps. We can however simulate the
way bumps look by altering the way light reflects off of the surface.
Reflection calculations depend on a vector called a surface normal vector.
This is a vector which points away from the surface and is perpendicular to
it. By artificially modifying (or perturbing) this normal vector you can
simulate bumps.

The normal statement is the part of a texture which defines the pattern of
normal perturbations to be applied to an object. Like the pigment statement,
you can omit the surrounding texture block to save typing. Do not forget
however that there is a texture implied. For example...

  //this...                    //can be shortened to this...

  object {                     object {
    My_Object                    My_Object
    texture {                    pigment {color Purple}
      pigment {color Purple}     normal {bumps 0.3}
      normal {bumps 0.3}       }
    }
  }


Note that attaching a normal pattern does not really modify the surface. It
only affects the way light reflects or refracts at the surface so that it
looks bumpy.

The most complete form for defining a normal is as follows:

  normal {
    NORMAL_IDENTIFIER
    PATTERN_TYPE FloatValue
    NORMAL_MODIFIERS
    TRANSFORMATIONS...
  }


Each of the items in a normal are optional but if they are present they
should be in the order shown above to insure that the results are as
expected. Any items after the NORMAL_IDENTIFIER modify or override settings
given in the identifier. If no identifier is specified then the items modify
the normal values in the current default texture. The PATTERN_TYPE may
optionally be followed by a float value that controls the apparent depth of
the bumps. Typical values range from 0.0 to 1.0 but any value may be used.
Negative values invert the pattern. The default value if none is specified is
0.5.

Valid NORMAL_MODIFIERS are slope_map, normal_map, bump_map and bump_size
statements as well as any of the generic PATTERN_MODIFIERS such as translate,
rotate, scale, turbulence, wave shape and warp statements. Such modifiers
apply only to the normal and not to other parts of the texture. Modifiers
should be specified last.

There are three basic types of NORMAL_PATTERN_TYPEs. They are pattern
normals, specialized normals and bump maps. They differ in the types of
modifiers you may use with them. Originally POV-Ray had some patterns which
were exclusively used for pigments while others were exclusively used for
normals. Since POV-Ray 3.0 you can use any pattern for either pigments or
normals. For example it is now valid to use ripples as a pigment or wood as a
normal type. The patterns bumps, dents, ripples, waves, wrinkles and bump_map
were once exclusively normal patterns which could not be used as pigments.
Because these six types use specialized normal modification calculations they
cannot have slope_map, normal_map or wave shape modifiers. All other normal
pattern types may use them.

7.6.2.1          Slope Maps

A slope map is a normal pattern modifier which gives the user a great deal of
control over the exact shape of the bumpy features. It is best illustrated
with a gradient normal pattern. Suppose you have...

  plane{ z, 0
    pigment{ White }
    normal { gradient x }
  }


This gives a ramp wave pattern that looks like small linear ramps that climb
from the points at x=0 to x=1 and then abruptly drops to 0 again to repeat
the ramp from x=1 to x=2. A slope map turns this simple linear ramp into
almost any wave shape you want. The syntax is as follows...

  normal{
    PATTERN_TYPE Value
    slope_map {
      [ NUM_1 POINT_SLOPE_1]
      [ NUM_2 POINT_SLOPE_2]
      [ NUM_3 POINT_SLOPE_3]
       ...
    }
    NORMAL_MODIFIERS...
  }


Note that the [] brackets are part of the actual statement. They are not
notational symbols denoting optional parts. The brackets surround each entry
in the slope map. There may be from 2 to 256 entries in the map.

The NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive.
POINT_SLOPE_1, POINT_SLOPE_2, ... are 2 component vectors such as <0,1> where
the first value represents the apparent height of the wave and the second
value represents the slope of the wave at that point. The height should range
between 0.0 and 1.0 but any value could be used.

The slope value is the change in height per unit of distance. For example a
slope of zero means flat, a slope of 1.0 means slope upwards at a 45 degree
angle and a slope of -1 means slope down at 45 degrees. Theoretically a slope
straight up would have infinite slope. In practice, slope values should be
kept in the range -3.0 to +3.0. Keep in mind that this is only the visually
apparent slope. A normal does not actually change the surface.

For example here is how to make the ramp slope up for the first half and back
down on the second half creating a triangle wave with a sharp peak in the
center.

  normal {
    gradient x       // this is the PATTERN_TYPE
    slope_map {
      [0   <0, 1>]   // start at bottom and slope up
      [0.5 <1, 1>]   // halfway through reach top still climbing
      [0.5 <1,-1>]   // abruptly slope down
      [1   <0,-1>]   // finish on down slope at bottom
    }
  }


The pattern function is evaluated and the result is a value from 0.0 to 1.0.
The first entry says that at x=0 the apparent height is 0 and the slope is 1.
At x=0.5 we are at height 1 and slope is still up at 1. The third entry also
specifies that at x=0.5 (actually at some tiny fraction above 0.5) we have
height 1 but slope -1 which is downwards. Finally at x=1 we are at height 0
again and still sloping down with slope -1.

Although this example connects the points using straight lines the shape is
actually a cubic spline. This example creates a smooth sine wave.

  normal {
    gradient x          // this is the PATTERN_TYPE
    slope_map {
      [0    <0.5, 1>]   // start in middle and slope up
      [0.25 <1.0, 0>]   // flat slope at top of wave
      [0.5  <0.5,-1>]   // slope down at mid point
      [0.75 <0.0, 0>]   // flat slope at bottom
      [1    <0.5, 1>]   // finish in middle and slope up
    }
  }


This example starts at height 0.5 sloping up at slope 1. At a fourth of the
way through we are at the top of the curve at height 1 with slope 0 which is
flat. The space between these two is a gentle curve because the start and end
slopes are different. At half way we are at half height sloping down to
bottom out at 3/4ths. By the end we are climbing at slope 1 again to complete
the cycle. There are more examples in slopemap.pov in the sample scenes.

A slope_map may be used with any pattern except brick, checker, hexagon,
bumps, dents, ripples, waves, wrinkles and bump_map.

You may declare and use slope map identifiers. For example:

  #declare Fancy_Wave =
    slope_map {       // Now let's get fancy
      [0.0  <0, 1>]   // Do tiny triangle here
      [0.2  <1, 1>]   //  down
      [0.2  <1,-1>]   //     to
      [0.4  <0,-1>]   //       here.
      [0.4  <0, 0>]   // Flat area
      [0.5  <0, 0>]   //   through here.
      [0.5  <1, 0>]   // Square wave leading edge
      [0.6  <1, 0>]   //   trailing edge
      [0.6  <0, 0>]   // Flat again
      [0.7  <0, 0>]   //   through here.
      [0.7  <0, 3>]   // Start scallop
      [0.8  <1, 0>]   //   flat on top
      [0.9  <0,-3>]   //     finish here.
      [0.9  <0, 0>]   // Flat remaining through 1.0
    }

  object{ My_Object
    pigment { White }
    normal {
      wood
      slope_map { Fancy_Wave }
    }
  }


7.6.2.2          Normal Maps

Most of the time you will apply single normal pattern to an entire surface
but you may also create a pattern or blend of normals using a normal map. The
syntax for a normal map is identical to a pigment map except you specify a
normal in each map entry.

A normal map is specified by...

  normal{
    PATTERN_TYPE
    normal_map {
      [ NUM_1 NORMAL_BODY_1]
      [ NUM_2 NORMAL_BODY_2]
      [ NUM_3 NORMAL_BODY_3]
       ...
    }
    NORMAL_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive. A
NORMAL_BODY is anything that would normally appear inside a normal statement
but the normal keyword and {} braces are not needed. Note that the []
brackets are part of the actual statement. They are not notational symbols
denoting optional parts. The brackets surround each entry in the map. There
may be from 2 to 256 entries in the map.

For example

  normal {
    gradient x       //this is the PATTERN_TYPE
    normal_map {
      [0.3  bumps scale 2]
      [0.3  dents]
      [0.6  dents]
      [0.9  marble turbulence 1]
    }
  }


When the gradient x function returns values from 0.0 to 0.3 then the scaled
bumps normal is used. From 0.3 to 0.6 dents are From 0.6 up to 0.9 a blend of
dents and a turbulent marble is used. From 0.9 on up only the turbulent
marble is used.

Normal maps may be nested to any level of complexity you desire. The normals
in a map may have slope maps or normal maps or any type of normal you want.

A normal map is also used with the average normal type. See "Average" for
details.

Entire normals may also be used with the block patterns such as checker,
hexagon and brick. For example...

  normal {
    checker
      normal { gradient x scale .2 }
      normal { gradient y scale .2 }
    }
  }


Note that in the case of block patterns the normal wrapping is required
around the normal information.

You may not use normal_map or individual normals with a bump_map. See section
"Texture Maps" for an alternative way to do this.

7.6.2.3          Bump Maps

When all else fails and none of the above normal pattern types meets your
needs you can use a bump map to wrap a 2-D bit-mapped bump pattern around
your 3-D objects.

Instead of placing the color of the image on the shape like an image map a
bump map perturbs the surface normal based on the color of the image at that
point. The result looks like the image has been embossed into the surface. By
default, a bump map uses the brightness of the actual color of the pixel.
Colors are converted to gray scale internally before calculating height.
Black is a low spot, white is a high spot. The image's index values may be
used instead (see section "Use_Index and Use_Color" below).

7.6.2.3.1        Specifying a Bump Map

The syntax for bump_map is...

  normal {
    bump_map {
      FILE_TYPE "filename"
      BITMAP_MODIFIERS...
    }
    NORMAL_MODIFIERS...
  }


Where FILE_TYPE is one of the following keywords gif, tga, iff, ppm, pgm, png
or sys. This is followed by the name of the file using any valid string
expression. Several optional modifiers may follow the file specification. The
modifiers are described below. Note that earlier versions of POV-Ray allowed
some modifiers before the FILE_TYPE but that syntax is being phased out in
favor of the syntax described here.

Filenames specified in the bump_map statement will be searched for in the
home (current) directory first and, if not found, will then be searched for
in directories specified by any +L switches or Library_Path options. This
would facilitate keeping all your bump maps files in a separate subdirectory,
and specifying a library path to them. Note that any operating system default
paths are not searched unless you also specify them as a Library_Path.

By default, the bump pattern is mapped onto the x-y-plane. The bumps are
projected onto the object as though there were a slide projector somewhere in
the -z-direction. The bump pattern exactly fills the square area from (x,y)
coordinates (0,0) to (1,1) regardless of the bitmap's original size in
pixels. If you would like to change this default, you may translate, rotate
or scale the normal or texture to map it onto the object's surface as
desired.

The file name is optionally followed by one or more BITMAP_MODIFIERS. The
bump_size, use_color and use_index modifiers are specific to bump maps and
are discussed in the following sections. See section "Bitmap Modifiers" for
other general bitmap modifiers.

After a bump_map statement but still inside the normal statement you may
apply any legal normal modifiers except slope_map and pattern wave forms.

7.6.2.3.2        Bump_Size

The relative bump size can be scaled using the bump_size modifier. The bump
size number can be any number other than 0 but typical values are from about
0.1 to as high as 4.0 or 5.0.

  normal {
    bump_map {
      gif "stuff.gif"
      bump_size 5.0
    }
  }


Originally bump_size could only be used inside a bump map but it can now be
used with any normal. Typically it is used to override a previously defined
size. For example:

  normal {
    My_Normal   //this is a previously defined normal identifier
    bump_size 2.0
  }


7.6.2.3.3        Use_Index and Use_Color

Usually the bump map converts the color of the pixel in the map to a gray
scale intensity value in the range 0.0 to 1.0 and calculates the bumps based
on that value. If you specify use_index, the bump map uses the color's
palette number to compute as the height of the bump at that point. So, color
number 0 would be low and color number 255 would be high (if the image has
256 palette entries). The actual color of the pixels doesn't matter when
using the index. This option is only available on palette based formats. The
use_color keyword may be specified to explicitly note that the color methods
should be used instead. The alternate spelling use_colour is also valid.
These modifiers may only be used inside the bump_map statement.

7.6.3            Finish

The finish properties of a surface can greatly affect its appearance. How
does light reflect? What happens when light passes through? What kind of
highlights are visible. To answer these questions you need a finish
statement.

The finish statement is the part of a texture which defines the various
finish properties to be applied to an object. Like the pigment or normal
statement you can omit the surrounding texture block to save typing. Do not
forget however that there is a texture implied. For example...

  this...                            can be shortened to this...

  object {                           object {
    My_Object                          My_Object
    texture {                          pigment {color Purple}
      pigment {color Purple}           finish {phong 0.3}
      finish {phong 0.3}             }
    }
  }


The most complete form for defining a finish is as follows:

  finish {
    FINISH_IDENTIFIER
    [ ambient COLOR ]
    [ diffuse FLOAT ]
    [ brilliance FLOAT ]
    [ phong FLOAT ]
    [ phong_size FLOAT ]
    [ specular FLOAT ]
    [ roughness FLOAT ]
    [ metallic [ FLOAT ] ]
    [ reflection COLOR ]
    [ refraction FLOAT ]
    [ ior FLOAT ]
    [ caustics FLOAT ]
    [ fade_distance FLOAT ]
    [ fade_power FLOAT ]
    [ irid { thickness FLOAT turbulence VECTOR } ]
    [ crand FLOAT ]
  }


The FINISH_IDENTIFIER is optional but should proceed all other items. Any
items after the FINISH_IDENTIFIER modify or override settings given in the
IDENTIFIER. If no identifier is specified then the items modify the finish
values in the current default texture. Note that transformations are not
allowed inside a finish because finish items cover the entire surface
uniformly.

7.6.3.1          Ambient

The light you see in dark shadowed areas comes from diffuse reflection off of
other objects. This light cannot be directly modeled using ray-tracing.
However we can use a trick called ambient lighting to simulate the light
inside a shadowed area.

Ambient light is light that is scattered everywhere in the room. It bounces
all over the place and manages to light objects up a bit even where no light
is directly shining. Computing real ambient light would take far too much
time, so we simulate ambient light by adding a small amount of white light to
each texture whether or not a light is actually shining on that texture.

This means that the portions of a shape that are completely in shadow will
still have a little bit of their surface color. It's almost as if the texture
glows, though the ambient light in a texture only affects the shape it is
used on.

Usually a single float value is specified even though the syntax calls for a
color. For example a float value of 0.3 gets promoted to the full color
vector <0.3,0.3,0.3,0.3,0.3> which is acceptable because only the red, green
and blue parts are used.

The default value is very little ambient light (0.1). The value can range
from 0.0 to 1.0. Ambient light affects both shadowed and non-shadowed areas
so if you turn up the ambient value you may want to turn down the diffuse
value.

Note that this method doesn't account for the color of surrounding objects.
If you walk into a room that has red walls, floor and ceiling then your white
clothing will look pink from the reflected light. POV-Ray's ambient shortcut
doesn't account for this. There is also no way to model specular reflected
indirect illumination such as the flashlight shining in a mirror.

You may color the ambient light using one of two methods. You may specify a
color rather than a float after the ambient keyword in each finish statement.
For example

   finish { ambient rgb <0.3,0.1,0.1> } //a pink ambient


You may also specify the overall ambient light source used when calculating
the ambient lighting of an object using the global ambient_light setting. The
formula is given by

   AMBIENT = FINISH_AMBIENT * GLOBAL_AMBIENT_LIGHT_SOURCE


7.6.3.2          Diffuse Reflection Items

When light reflects off of a surface the laws of physics say that it should
leave the surface at the exact same angle it came in. This is similar to the
way a billiard ball bounces off a bumper of a pool table. This perfect
reflection is called specular reflection. However only very smooth polished
surfaces reflect light in this way. Most of the time, light reflects and is
scattered in all directions by the roughness of the surface. This scattering
is called diffuse reflection because the light diffuses or spreads in a
variety of directions. It accounts for the majority of the reflected light we
see.

POV-Ray and most other ray-tracers can only simulate directly one of these
three types of illumination. That is the light which comes directly from
actual light sources. Light coming from other objects such as mirrors via
specular reflection (shine a flashlight onto a mirror for example). And last
not least light coming from other objects via diffuse reflections (look at
some dark area under a desk or in a corner: even though a lamp may not
directly illuminate that spot you can still see a little bit because light
comes from diffuse reflection off of nearby objects).

7.6.3.2.1        Diffuse

The keyword diffuse is used in a finish statement to control how much of the
light coming directly from any light sources is reflected via diffuse
reflection. For example

  finish {diffuse 0.7}


means that 70% of the light seen comes from direct illumination from light
sources. The default value is diffuse 0.6.

7.6.3.2.2        Brilliance

The amount of direct light that diffuses from an object depends upon the
angle at which it hits the surface. When light hits at a shallow angle it
illuminates less. When it is directly above a surface it illuminates more.
The brilliance keyword can be used in a finish statement to vary the way
light falls off depending upon the angle of incidence. This controls the
tightness of the basic diffuse illumination on objects and slightly adjusts
the appearance of surface shininess. Objects may appear more metallic by
increasing their brilliance. The default value is 1.0. Higher values from to
about 10.0 cause the light to fall off less at medium to low angles. There
are no limits to the brilliance value. Experiment to see what works best for
a particular situation. This is best used in concert with highlighting.

7.6.3.2.3        Crand Graininess

Very rough surfaces, such as concrete or sand, exhibit a dark graininess in
their apparent color. This is caused by the shadows of the pits or holes in
the surface. The crand keyword can be added to cause a minor random darkening
in the diffuse reflection of direct illumination. Typical values range from
crand 0.01 to crand 0.5 or higher. The default value is 0. For example:

  finish { crand 0.05 }


The grain or noise introduced by this feature is applied on a pixel-by-pixel
basis. This means that it will look the same on far away objects as on close
objects. The effect also looks different depending upon the resolution you
are using for the rendering. For these reasons it is not a very accurate way
to model the rough surface effect but some objects still look better with a
little crand thrown in.

Note that this should not be used when rendering animations. This is the one
of a few truly random features in POV-Ray and will produce an annoying
flicker of flying pixels on any textures animated with a crand value.

7.6.3.3          Highlights

Highlights are the bright spots that appear when a light source reflects off
of a smooth object. They are a blend of specular reflection and diffuse
reflection. They are specular-like because they depend upon viewing angle and
illumination angle. However they are diffuse-like because some scattering
occurs. In order to exactly model a highlight you would have to calculate
specular reflection off of thousands of microscopic bumps called micro
facets. The more that micro facets are facing the viewer the shinier the
object appears and the tighter the highlights become. POV-Ray uses two
different models to simulate highlights without calculating micro facets.
They are the specular and Phong models.

Note that specular and Phong highlights are not mutually exclusive. It is
possible to specify both and they will both take effect. Normally, however,
you will only specify one or the other.

7.6.3.3.1        Phong Highlights

The phong keyword controls the amount of Phong highlighting on the object. It
causes bright shiny spots on the object that are the color of the light
source being reflected.

The Phong method measures the average of the facets facing in the mirror
direction from the light sources to the viewer.

Phong's value is typically from 0.0 to 1.0, where 1.0 causes complete
saturation to the light source's color at the brightest area (center) of the
highlight. The default phong 0.0 gives no highlight.

The size of the highlight spot is defined by the phong_size value. The larger
the phong size the tighter, or smaller, the highlight and the shinier the
appearance. The smaller the phong size the looser, or larger, the highlight
and the less glossy the appearance.

Typical values range from 1.0 (very dull) to 250 (highly polished) though any
values may be used. Default phong size is 40 (plastic) if phong_size is not
specified. For example:

  finish { phong 0.9 phong_size 60 }


7.6.3.3.2        Specular Highlight

A specular highlight is very similar to Phong highlighting but it uses
slightly different model. The specular model more closely resembles real
specular reflection and provides a more credible spreading of the highlights
occurring near the object horizons.

The specular value is typically from 0.0 to 1.0, where 1.0 causes complete
saturation to the light source's color at the brightest area (center) of the
highlight. The default specular 0.0 gives no highlight.

The size of the spot is defined by the value given for roughness. Typical
values range from 1.0 (very rough - large highlight) to 0.0005 (very smooth -
small highlight). The default value, if roughness is not specified, is 0.05
(plastic).

It is possible to specify wrong values for roughness that will generate an
error when you try to render the file. Don't use 0 and if you get errors
check to see if you are using a very, very small roughness value that may be
causing the error. For example:

  finish {specular 0.9  roughness 0.02}


7.6.3.3.3        Metallic Highlight Modifier

The keyword metallic may be used with Phong or specular highlights. This
keyword indicates that the color of the highlights will be calculated by an
empirical function that models the reflectivity of metallic surfaces.

White light reflected specularly from a metallic surface takes the color of
the surface, except then the incidence angle approaches 90 degrees, where it
becomes white again.

The metallic keyword may be follow by a numeric value to specify the
influence the above effect has (the default value is one). For example:

  finish {
    phong 0.9
    phong_size 60
    metallic
  }


7.6.3.4          Specular Reflection

When light does not diffuse and it does reflect at the same angle as it hits
an object, it is called specular reflection. Such mirror-like reflection is
controlled by the reflection keyword in a finish statement. For example:

  finish { reflection 1.0 ambient 0 diffuse 0 }


This gives the object a mirrored finish. It will reflect all other elements
in the scene. Usually a single float value is specified after the keyword
even though the syntax calls for a color. For example a float value of 0.3
gets promoted to the full color vector < 0.3,0.3,0.3,0.3,0.3> which is
acceptable because only the red, green and blue parts are used.

The value can range from 0.0 to 1.0. By default there is no reflection.

Adding reflection to a texture makes it take longer to render because an
additional ray must be traced. The reflected light may be tinted by
specifying a color rather than a float. For example

   finish { reflection rgb <1,0,0> }


gives a real red mirror that only reflects red light.

Note that although such reflection is called specular it is not controlled by
the specular keyword. That keyword controls a specular highlight.

7.6.3.5          Refraction

When light passes through a surface either into or out of a dense medium the
path of the ray of light is bent. Such bending is called refraction. Normally
transparent or semi-transparent surfaces in POV-Ray do not refract light.
Adding refraction 1.0 to the finish statement turns on refraction.

Note that it is recommended that you only use refraction 0 or refraction 1
(or even better refraction off and refraction on). Values in between will
darken the refracted light in ways that do not correspond to any physical
property. Many POV-Ray scenes were created with intermediate refraction
values before this bug was discovered so the feature has been maintained. A
more appropriate way to reduce the brightness of refracted light is to change
the filter or transmit value in the colors specified in the pigment
statement. Note also that refraction does not cause the object to be
transparent. Transparency only occurs if there is a non-zero filter or
transmit value in the color.

The amount of bending or refracting of light depends upon the density of the
material. Air, water, crystal and diamonds all have different densities and
thus refract differently. The index of  refraction or ior value is used by
scientists to describe the relative density of substances. The ior keyword is
used in POV-Ray to specify the value. For example:

  texture {
    pigment { White filter 0.9 }
    finish {
      refraction 1
      ior 1.5
    }
  }


The default ior value of 1.0 will give no refraction. The index of refraction
for air is 1.0, water is 1.33, glass is 1.5 and diamond is 2.4. The file
consts.inc pre-defines several useful values for ior.

Note that if a texture has a filter component and no value for refraction and
ior are supplied the renderer will simply transmit the ray through the
surface with no bending. In layered textures, the refraction and ior keywords
must be in the last texture, otherwise they will not take effect.

7.6.3.5.1        Light Attenuation

Light attenuation is used to model the decrease in light intensity as the
light travels through a translucent object. Its syntax is:

  finish {
    fade_distance FADE_DISTANCE
    fade_power FADE_POWER
  }


The fade_distance keyword determines the distance the light has to travel to
reach half intensity while the fade_power keyword describes how fast the
light will fall off. For realistic effects a fade power of 1 to 2 should be
used.

The attenuation is calculated by a formula similar to that used for light
source attenuation.

                                 1
  attenuation = --------------------------------------
                 1 + (d / FADE_DISTANCE) ^ FADE_POWER


7.6.3.5.2        Faked Caustics

Caustics are light effects that occur if light is reflected or refrected by
specular reflective or refractive surfaces. Imagine a glass of water standing
on a table. If sunlight falls onto the glass you will see spots of light on
the table. Some of the spots are caused by light being reflected by the glass
while some of them are caused by light being refratced by the water in the
glass.

Since it is a very difficult and time-consuming process to actually calculate
those effects (though it is not impossible) POV-Ray uses a quite simple
method to simulate caustics caused by refraction. This caustic effect is
limited to areas that are shaded by the translucent object. You'll get no
caustic effects from reflective surfaces nor in parts that are not shaded by
the object.

The syntax is:

  finish {
    caustics POWER
  }


7.6.3.6          Iridescence

Iridescence, or Newton's thin film interference, simulates the effect of
light on surfaces with a microscopic transparent film overlay. The effect is
like an oil slick on a puddle of water or the rainbow hues of a soap bubble
(see also "Irid_Wavelength").

The syntax is:

  finish {
    irid {
      AMOUNT
      thickness FLOAT
      turbulence VECTOR
    }
  }


This finish modifies the surface color as a function of the angle between the
light source and the surface. Since the effect works in conjunction with the
position and angle of the light sources to the surface it does not behave in
the same ways as a procedural pigment pattern.

The AMOUNT parameter is the contribution of the iridescence effect to the
overall surface color. As a rule of thumb keep to around 0.25 (25%
contribution) or less, but experiment. If the surface is coming out too
white, try lowering the diffuse and possibly the ambient values of the
surface.

The thickness keyword represents the film's thickness. This is an awkward
parameter to set, since the thickness value has no relationship to the
object's scale. Changing it affects the scale or busy-ness of the effect. A
very thin film will have a high frequency of color changes while a thick film
will have large areas of color.

The thickness of the film can be varied with the turbulence keyword. You can
only specify the amount of turbulence with iridescence. The octaves, lambda,
and omega values are internally set and are not adjustable by the user at
this time.

In addition, perturbing the object's surface normal through the use of bump
patterns will affect iridescence.

For the curious, thin film interference occurs because, when the ray hits the
surface of the film, part of the light is reflected from that surface, while
a portion is transmitted into the film. This subsurface ray travels through
the film and eventually reflects off the opaque substrate. The light emerges
from the film slightly out of phase with the ray that was reflected from the
surface.

This phase shift creates interference, which varies with the wavelength of
the component colors, resulting in some wavelengths being reinforced, while
others are cancelled out. When these components are recombined, the result is
iridescence.

The concept used for this feature came from the book Fundamentals  of
Three-Dimensional Computer Graphics by Alan Watt (Addison-Wesley).

7.6.4            Halo

Important notice: The halo feature in POV-Ray 3.0 are somewhat experimental.
There is a high probability that the design and implementation of these
features will be changed in future versions. We cannot guarantee that scenes
using these features in 3.0 will render identically in future releases or
that full backwards compatibility of language syntax can be maintained.

A halo is used to simulate some of the atmospheric effects that occur when
small particles interact with light or radiate on their own. Those effects
include clouds, fogs, fire, etc.

Halos are attached to an object, the so called container object, which they
completely fill. If the object is partially or completely translucent and the
object is specified to be hollow (see section "Hollow" for more details) the
halo will be visible. Thus the halo effects are limited to the space that the
object covers. This should always be kept in mind.

What the halo actually will look like depends on a lot of parameters. First
of all you have to specify which kind of effect you want to simulate. After
this you need to define the distribution of the particles. This is basically
done in two steps: a mapping function is selected and a density function is
chosen. The first function maps world coordinates onto a one-dimensional
interval while the later describes how this linear interval is mapped onto
the final density values.

The properties of the particles, such as their color and their translucency,
are given by a color map. The density values calculated by the mapping
processes are used to determine the appropriate color using this color map.

A ray marching process is used to volume sample the halo and to accumulate
the intensities and opacity of each interval.

The following sections will describe all of the halo parameters in more
detail. The complete halo syntax is given by:

  halo {
    attenuating | emitting | glowing | dust
    [ constant | linear | cubic | poly ]
    [ planar_mapping | spherical_mapping |
      cylindrical_mapping | box_mapping ]
    [ dust_type DUST_TYPE ]
    [ eccentricity ECCENTRICITY ]
    [ max_value MAX_VALUE ]
    [ exponent EXPONENT ]
    [ samples SAMPLES ]
    [ aa_level AA_LEVEL ]
    [ aa_threshold AA_THRESHOLD ]
    [ jitter JITTER ]
    [ turbulence <TURBULENCE> ]
    [ octaves OCTAVES ]
    [ omega OMEGA ]
    [ lambda LAMBDA ]
    [ colour_map COLOUR_MAP ]
    [ frequency FREQUENCY ]
    [ phase PHASE ]
    [ scale <VECTOR> ]
    [ rotate <VECTOR> ]
    [ translate <VECTOR> ]
  }


7.6.4.1          Halo Mapping

As described above the actual particle distribution and halo appearance is
influenced by a lot of parameters. The steps that are performed during the
halo calculation will be explained below. It will also be noted where the
different halo keywords will have an effect on the calculations.

  1.Depending on the current sampling position along the ray, point P
    (coordinates x, y, z) inside the halo container object is calculated. The
    actual location is influenced by the jitter keyword, the number of
  2.Point P is transformed into point Q using the (current) halo'sd).
    transformation. Here all local halo transformations come into play, i.e.
  3.Turbulence is added to point Q. The amount of turbulence is given by the
    urbulence keyword. The turbulence calculation is influenced by the
  4.Radius r is calculated depending on the specified density mapping
    (planar_mapping, spherical_mapping, cylindrical_mapping, box_mapping).
  5.The density d is calculated from the radius r using the specified density
    function (constant, linear, cubic, poly) and the maximum value given by
  6.The density d is first multiplied by the frequency value, added to the
    phase value and clipped to the range from 0 to 1 before it is used to get
    the color from the color_map . If an attenuating halo is used the color
    will be determined by the total density along the ray and not by the sum
    of the colors for each sample.


All steps are repeated for each sample point along the ray that is inside the
halo container object. Steps 2 through 6 are repeated for all halos attached
to the halo container object.

It should be noted that in order to get a finite particle distribution, i. e.
a particle distribution that vanishes outside a finite area, a finite density
mapping and a finite density function has to be used.

A finite density mapping gives the constant value one for all points outside
a finite area. The box and spherical mappings are the only finite mapping
types.

A finite density function vanishes for all parameter values above one (there
are no negative parameter values). The only infinite density function is the
constant function.

Finite particle distributions are especially useful because they can always
be transformed to stay inside the halo container object. If particles leave
the container object they become invisible and the surface of the container
will be visible due to the density discontinuity at the surface.

7.6.4.2          Multiple Halos

It is possible to put more than one halo inside a container object. This is
simply done by putting more than one halo statement inside the container
object statement like:

  sphere { 0, 1
    pigment { Clear }
    halo { here comes halo nr. 1 }
    halo { here comes halo nr. 2 }
    halo { here comes halo nr. 3 }
    ...
  }


The effects of the different halos are added. This is in fact similar to the
CSG union operation.

You should note that currently multiple attenuating halos will use the color
map of the last halo only. It is not possible to use different color maps for
multiple attenuating halos.

7.6.4.3          Halo Type

The type of the halo is defined by one of the following mutually exclusive
keywords (if more than one is specified the last will be used). The default
is attenuating.

  halo {
    attenuating | emitting | glowing | dust
  }


The halo type determines how the light will interact with the particles
inside the container object. There are two basic categories of light
interaction: self-illuminated and illuminated. The first type includes the
attenuating, emitting and glowing effects while the dust effect is of the
second type.


7.6.4.3.1        Attenuating

The attenuating halo that only absorbs light passing through it is rendered
by accumulating the particle density along a ray. The total halo color is
determined from the total, accumulated density and the specified color map
(see section "Halo Color Map" for details about the color map). The
background light, i. e. the light passing through the halo, is attenuated by
the total density and added to the total halo color to get the final color of
the halo.

This model is suited to render particle distributions with a high albedo
because the final color does not depend on the transparency of single volume
elements but only on the total transparency along the ray. The albedo of a
particle is given by the amount of light scattered by this particle in all
directions in relation to the amount of incoming light. If the particle
doesn't absorb any light the albedo is one.

Clouds and steams are two of the effects that can be rendered quite realistic
by adding enough turbulence.

7.6.4.3.2        Dust

The dust halo consists of particles that do not emit any light. They only
reflect and absorb incoming light. Its syntax is:

  halo {
    dust
    [ dust_type DUST_TYPE ]
    [ eccentricity ECCENTRICITY ]
  }


As the ray marches through the dust all light coming from any light sources
is accumulated and scattered according to the dust type and the current dust
density. Since this light accumulation includes a test for occlusion, other
objects may cast shadows into the dust.

The same scattering types that are used with the atmosphere in section
"Atmosphere" can be used with the dust (the default type is isotropic
scattering). They are:

  #declare ISOTROPIC_SCATTERING         = 1
  #declare MIE_HAZY_SCATTERING          = 2
  #declare MIE_MURKY_SCATTERING         = 3
  #declare RAYLEIGH_SCATTERING          = 4
  #declare HENYEY_GREENSTEIN_SCATTERING = 5


The Henyey-Greenstein function needs the additional parameter eccentricity
that is described in the section about atmosphere. This keyword only applies
to dust type 5, the Henyey-Greenstein scattering.

7.6.4.3.3        Emitting

Emitting halos only emit light. Every particle is a small light source that
emits some light. This light is not attenuated by the other particles because
they are assumed to be very small.

As the ray travels through the density field of an emitting halo the color of
the particles in each volume element and their differential transparency is
determined from the color map. These intensities are accumulated to get the
total color of the density field. This total intensity is added to the light
passing through the halo. The background light is attenuated by the total
density of the halo.

Since the emitted light is not attenuated it can be used to model effects
like fire, explosions, light beams, etc. By choosing a well suited color map
those effects can be rendered with a high degree of realism.

Fire is best modeled using planar mapping. Spherical mapping and high
turbulence values can be used to create explosions (it's best to use a
periodic color map and frequencies larger than one).

Emitting halos do not cast any light on other objects like light sources do,
even though they are made up of small, light-emitting particles. In order to
make them actually emit light hundreds or thousands of small light sources
would have to be used. This would slow down tracing by a degree that would
make it useless.

7.6.4.3.4        Glowing

The glowing halo is similar to the emitting halo. The difference is that the
light emitted by the particles is attenuated by the other particles. This can
be seen as a combination of the attenuating and the emitting model.

7.6.4.4          Density Mapping

The density mapping is used to map points in space onto a linear,
one-dimensional interval between 0.0 and 1.0, thus describing the appearance
of the three-dimensional particle distribution. The different mapping types
are specified by:

  halo {
    planar_mapping | spherical_mapping |
    cylindrical_mapping | box_mapping
  }


The default mapping type is planar mapping.

Since the mapping takes place in relation to the origin of the world
coordinate system the following rule must always be kept in mind: Halo
container objects ought to be unit sized objects centered at the origin. They
can be transformed later to suit the individuals needs.

The different mapping types are explained in more detail in the following
sections.

7.6.4.4.1        Box Mapping

The box mapping can be used to create a box-shaped particle distribution. The
mapping is calculated by getting the maximum of the absolute values of each
coordinate as given by the formula:

  r(x, y, z) = max(abs(x), abs(y), abs(z))


7.6.4.4.2        Cylindrical Mapping

The distance r(x,y,z) from the y-axis given by

  r(x, y, z) = sqrt(x*x + z*z)


is used to get the interval values. Values larger than one are clipped to
one.

7.6.4.4.3        Planar Mapping

The distance r(x,y,z) from the x-z-plane given by

  r(x, y, z) = abs(y)


is used to get the interval values. Values larger than one are clipped to
one.

7.6.4.4.4        Spherical Mapping

The distance r(x,y,z) from the origin given by

  r(x, y, z) = sqrt(x*x + y*y + z*z)


is used to get the interval values. Values larger than one are clipped to
one.

7.6.4.5          Density Function

The density function determines how the actual density values are calculated
from the linear, one-dimensional interval that resulted from the density
mapping.

The density function is specified by the following keywords:

  halo {
    [ constant | linear | cubic | poly ]
    [ max_value MAX_VALUE ]
    [ exponent EXPONENT ]
  }


The exponent keyword is only used together with the poly density function.

The individual functions f(r) are described in the following sections. They
all map the value r(x,y,z) calculated by the density mapping onto a suitable
density range between 0 and MAX_VALUE (specified with the keyword max_value).

7.6.4.5.1        Constant

The constant function gives the constant value MAX_VALUE regardless of the
interval value and the type of density mapping. It is calculated by the
trivial formula   f(r) = MAX_VALUE.


The constant density function.

The constant density function can be used to create a constant particle
distribution that is only constrained by the container object.

7.6.4.5.2        Linear

A linear falloff from MAX_VALUE at r=0 to zero at r=1 is created with the
linear density function. It is given by:

  f(r) = MAX_VALUE * (1 - r)


7.6.4.5.3        Cubic

The cubic function gives a smooth blend between the maximum value MAX_VALUE
at r=0 and 0 at r=1. It is given by:

  f(r) = MAX_VALUE * (2 * r  - 3) * r * r + 1


The cubic density function.


7.6.4.5.4        Poly

A polynomial function can be used to get a large variety of density
functions. All have the maximum value MAX_VALUE at r=0 and the minimum value
0 at r=1. It is given by:

  f(r) = MAX_VALUE * (1 - r) ^ EXPONENT


The polynomial density function for different exponent values.

The exponent is given by the exponent keyword. In case of EXPONENT=0 you'll
get a linear falloff.

7.6.4.6          Halo Color Map

The density f(r), which ranges from 0 to MAX_VALUE, is mapped onto the color
map to get the color and differential translucency for each volume element as
the ray marches through the density field (the final color of attenuating
halos is calculated from the total density; see section "Halo Mapping" and
section "Attenuating"). The differential translucency determines for each
value of f(r) how much the total opacity has to be increased (or decreased).

The color map is specified by:

  halo {
    [ colour_map COLOUR_MAP ]
  }


The differential translucency is stored in the transmittance channel of the
map's color entries. A simple example is given by

  colour_map {
    [0 rgbt<1, 1, 1, 1>]
    [1 rgbt<1, 1, 1, 0>]
  }


In this example areas with a low density (small f(r)) will be translucent
(large differential translucency of 1=100%) and areas with a high density
(large f(r)) will be opaque (small differential translucency of 0=0%). You
should note that negative transmittance values can be used to create very
dense fields.

In the case of the dust halo the filter channels of the colors in the color
map are used to specify the amount of light that will be filtered by the
corresponding color map entry. For all other halo types the filter value is
ignored.


7.6.4.7          Halo Sampling

The halo effects are calculated by marching through the density field along a
ray. At discrete steps samples are taken from the density field and evaluated
according to the color map and all other parameters. The effects of all
volume elements are accumulated to get the total effect.

The following parameters are used to tune the sampling process:

  halo {
    [ samples SAMPLES ]
    [ aa_level AA_LEVEL ]
    [ aa_threshold AA_THRESHOLD ]
    [ jitter JITTER ]
  }


7.6.4.7.1        Number of Samples

The number of samples that are taken along the ray inside the halo container
object is specified by the samples keyword. The greater the number of samples
the more denser the density field is sampled and the more accurate but slower
the result will be.

The default number of samples is 10. This is sufficient for simple density
fields that don't use turbulence.

High turbulence values and dust halos normally need a large number of samples
to avoid aliasing artifacts.

7.6.4.7.2        Super-Sampling

The sampling is prone to alias (like the atmosphere sampling in section
"Atmosphere"). One way to reduce possible aliasing artifacts is to use
super-sampling. If two neighboring samples differ too much an additional
sampling is taken in-between. This process recurses until the values of the
samples are close too each other or the maximum recursion level given by
aa_level is reached. The threshold to kick super-sampling in is given by
aa_threshold.

By default super-sampling is not used. The default values for aa_threshold
and aa_level are 0.3 and 3 respectively.

7.6.4.7.3        Jitter

Jitter can be used to introduce some noise to the sampling locations. This
may help to reduce aliasing artifacts at the cost of an increased noise level
in the image. Since the human visual system is much more forgiving to noise
than it is to regular patterns this is not much of a problem.

By default jittering is not used. The values should be smaller than 1.0.


7.6.4.8          Halo Modifiers

This section covers all general halo modifiers. They are:

  halo {
    [ turbulence <TURBULENCE> ]
    [ octaves OCTAVES ]
    [ omega OMEGA ]
    [ lambda LAMBDA ]
    [ frequency FREQUENCY ]
    [ phase PHASE ]
    [ scale <VECTOR> ]
    [ rotate <VECTOR> ]
    [ translate <VECTOR> ]
  }


7.6.4.8.1        Frequency Modifier

The frequency parameter adjusts the number of times the density interval is
mapped onto itself, i. e. the range from 0.0 to 1.0, before it is mapped onto
the color map. The formula doing this is:

  f_new(r) = (f(r) * FREQUENCY + PHASE) modulo 1.0


7.6.4.8.2        Phase Modifier

The phase parameter determines the offset at which the mapping of the density
field onto itself starts. See the formula in the previous section for how the
pahse is used.


7.6.4.8.3        Transformation Modifiers

Halos can be transformed using the rotate, scale and translate keywords. You
have to be careful that you don't move the density field out of the container
object though.

7.6.5            Special Textures

Special textures are complex textures made up of multiple textures. The
component textures may be plain textures or may be made up of special
textures. A plain texture has just one pigment, normal and finish statement
(and maby some halo statements). Even a pigment with a pigment map is still
one pigment and thus considered a plain texture as are normals with normal
map statements.

Special textures use either a texture_map keyword to specify a blend or
pattern of textures or they use a bitmap similar to an image map called a
material map (specified with the material_map keyword).

There are restrictions on using special textures. A special texture may not
be used as a default texture (see section "Default Directive"). A special
texture cannot be used as a layer in a layered texture however you may use
layered textures as any of the textures contained within a special texture.

7.6.5.1          Texture Maps

In addition to specifying blended color with a color map or a pigment map you
may create a blend of textures using texture_map. The syntax for a texture
map is identical to the pigment map except you specify a texture in each map
entry.

A texture map is specified by...

  texture{
    PATTERN_TYPE
    texture_map {
      [ NUM_1 TEXTURE_BODY_1]
      [ NUM_2 TEXTURE_BODY_2]
      [ NUM_3 TEXTURE_BODY_3]
       ...
    }
    TEXTURE_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive. A
TEXTURE_BODY is anything that would normally appear inside a texture
statement but the texture keyword and {} braces are not needed. Note that the
[] brackets are part of the actual statement. They are not notational symbols
denoting optional parts. The brackets surround each entry in the map. There
may be from 2 to 256 entries in the map.

For example:

  texture {
    gradient x       //this is the PATTERN_TYPE
    texture_map {
      [0.3  pigment{Red} finish{phong 1}]
      [0.3  T_Wood11]    //this is a texture identifier
      [0.6  T_Wood11]
      [0.9  pigment{DMFWood4} finish{Shiny}]
    }
  }


When the gradient x function returns values from 0.0 to 0.3 the red
highlighted texture is used. From 0.3 to 0.6 the texture identifier T_Wood11
is used. From 0.6 up to 0.9 a blend of T_Wood11 and a shiny DMFWood4 is used.
From 0.9 on up only the shiny wood is used.

Texture maps may be nested to any level of complexity you desire. The
textures in a map may have color maps or texture maps or any type of texture
you want.

The blended area of a texture map works by fully calculating both
contributing textures in their entirety and then linearly interpolating the
apparent colors. This means that reflection, refraction and lighting
calculations are done twice for every point. This is in contrast to using a
pigment map and a normal map in a plain texture, where the pigment is
computed, then the normal, then reflection, refraction and lighting are
calculated once for that point.

Entire textures may also be used with the block patterns such as checker,
hexagon and brick. For example...

  texture {
    checker
      texture { T_Wood12 scale .8 }
      texture {
        pigment { White_Marble }
        finish { Shiny }
        scale .5
      }
    }
  }


Note that in the case of block patterns the texture wrapping is required
around the texture information. Also note that this syntax prohibits the use
of a layered texture however you can work around this by declaring a texture
identifier for the layered texture and referencing the identifier.

A texture map is also used with the average pattern type. See "Average" for
details.

7.6.5.2          Tiles

Earlier versions of POV-Ray had a special texture called tiles texture that
created a checkered pattern of textures. Although it is still supported for
backwards computability you should use a checker block texture pattern
described in section "Texture Maps" rather than tiles textures.

7.6.5.3          Material Maps

The material map special texture extends the concept of image maps to apply
to entire textures rather than solid colors. A material map allows you to
wrap a 2-D bit-mapped texture pattern around your 3-D objects.

Instead of placing a solid color of the image on the shape like an image map,
an entire texture is specified based on the index or color of the image at
that point. You must specify a list of textures to be used like a texture
palette rather than the usual color palette.

When used with mapped file types such as GIF, and some PNG and TGA images,
the index of the pixel is used as an index into the list of textures you
supply. For unmapped file types such as some PNG and TGA images the 8 bit
value of the red component in the range 0-255 is used as an index.

If the index of a pixel is greater than the number of textures in your list
then the index is taken modulo N where N is the length of your list of
textures.

7.6.5.3.1        Specifying a Material Map

The syntax of a material map is...

  texture {
    material_map {
      FILE_TYPE "filename"
      BITMAP_MODIFIERS...
      texture {...} // First used for index 0
      texture {...} // Second texture used for index 1
      texture {...} // Third texture used for index 2
      texture {...} // Fourth texture used for index 3
                    // and so on for however many used.
    }
    TRANSFORMATION...
  }


Where FILE_TYPE is one of the following keywords gif, tga, iff, ppm, pgm, png
or sys. This is followed by the name of the file using any valid string
expression. Several optional modifiers may follow the file specification. The
modifiers are described below. Note that earlier versions of POV-Ray allowed
some modifiers before the FILE_TYPE but that syntax is being phased out in
favor of the syntax described here.

Filenames specified in the material_map statements will be searched for in
the home (current) directory first and, if not found, will then be searched
for in directories specified by any +L switches or Library_Path options. This
would facilitate keeping all your material map files in a separate
subdirectory and specifying a library path to them. Note that any operating
system default paths are not searched unless you also specify them as a
Library_Path.

By default, the material is mapped onto the x-y-plane. The material is
projected onto the object as though there were a slide projector somewhere in
the -z-direction. The material exactly fills the square area from (x,y)
coordinates (0,0) to (1,1) regardless of the bitmap's original size in
pixels. If you would like to change this default you may translate, rotate or
scale the texture to map it onto the object's surface as desired.

The file name is optionally followed by one or more BITMAP_MODIFIERS. See
section "Bitmap Modifiers" for other details.

After a material_map statement but still inside the texture statement you may
apply any legal texture modifiers. Note that no other pigment, normal, finish
or halo statements may be added to the texture outside the material map. The
following is illegal:

  texture {
    material_map {
      gif "matmap.gif"
      texture {T1}
      texture {T2}
      texture {T3}
    }
    finish {phong 1.0}
  }


The finish must be individually added to each texture.

Note that earlier versions of POV-Ray allowed such specifications but they
were ignored. The above restrictions on syntax were necessary for various bug
fixes. This means some POV-Ray 1.0 scenes using material maps many need minor
modifications that cannot be done automatically with the version
compatibility mode.

If particular index values are not used in an image then it may be necessary
to supply dummy textures. It may be necessary to use a paint program or other
utility to examine the map file's palette to determine how to arrange the
texture list.

The textures within a material map texture may be layered but material map
textures do not work as part of a layered texture. To use a layered texture
inside a material map you must declare it as a texture identifier and invoke
it in the texture list.

7.6.6            Layered Textures

It is possible to create a variety of special effects using layered textures.
A layered texture consists of several textures that are partially transparent
and are laid one on top of the other to create a more complex texture. The
different texture layers show through the transparent portions to create the
appearance of one texture that is a combination of several textures.

You create layered textures by listing two or more textures one right after
the other. The last texture listed will be the top layer, the first one
listed will be the bottom layer. All textures in a layered texture other than
the bottom layer should have some transparency. For example:

  object {
    My_Object
    texture {T1}  // the bottom layer
    texture {T2}  // a semi-transparent layer
    texture {T3}  // the top semi-transparent layer
  }


In this example T2 shows only where T3 is transparent and T1 shows only where
T2 and T3 are transparent.

The color of underlying layers is filtered by upper layers but the results do
not look exactly like a series of transparent surfaces. If you had a stack of
surfaces with the textures applied to each, the light would be filtered
twice: once on the way in as the lower layers are illuminated by filtered
light and once on the way out. Layered textures do not filter the
illumination on the way in. Other parts of the lighting calculations work
differently as well. The results look great and allow for fantastic looking
textures but they are simply different from multiple surfaces. See stones.inc
in the standard include files directory for some magnificent layered
textures.

Note layered textures must use the texture wrapped around any pigment, normal
or finish statements. Do not use multiple pigment, normal or finish
statements without putting them inside the texture statement.

Layered textures may be declared. For example

  #declare Layered_Examp =
    texture {T1}
    texture {T2}
    texture {T3}


may be invoked as follows:

  object {
    My_Object
    texture {
      Layer_Examp
      // Any pigment, normal or finish here
      // modifies the bottom layer only.
    }
  }


If you wish to use a layered texture in a block pattern, such as checker,
hexagon, or brick, or in a material map, you must declare it first and then
reference it inside a single texture statement. A special texture cannot be
used as a layer in a layered texture however you may use layered textures as
any of the textures contained within a special texture.

7.6.7            Patterns

POV-Ray uses a method called three-dimensional solid texturing to define the
color, bumpiness and other properties of a surface. You specify the way that
the texture varies over a surface by specifying a pattern. Patterns are used
in pigments, normals and texture maps.

All patterns in POV-Ray are three dimensional. For every point in space, each
pattern has a unique value. Patterns do not wrap around a surface like
putting wallpaper on an object. The patterns exist in 3d and the objects are
carved from them like carving an object from a solid block of wood or stone.

Consider a block of wood. It contains light and dark bands that are
concentric cylinders being the growth rings of the wood. On the end of the
block you see these concentric circles. Along its length you see lines that
are the veins. However the pattern exists throughout the entire block. If you
cut or carve the wood it reveals the pattern inside. Similarly an onion
consists of concentric spheres that are visible only when you slice it.
Marble stone consists of wavy layers of colored sediments that harden into
rock.

These solid patterns can be simulated using mathematical functions. Other
random patterns such as granite or bumps and dents can be generated using a
random number system and a noise function.

In each case, the x, y, z coordinate of a point on a surface is used to
compute some mathematical function that returns a float value. When used with
color maps or pigment maps, that value looks up the color of the pigment to
be used. In normal statements the pattern function result modifies or
perturbs the surface normal vector to give a bumpy appearance. Used with a
texture map, the function result determines which combinations of entire
textures to be used.

The following sections describe each pattern. See the sections "Pigment" and
"Normal" for more details on how to use patterns.

7.6.7.1          Agate

The agate pattern is a banded pattern similar to marble but it uses a
specialized built-in turbulence function that is different from the
traditional turbulence. The traditional turbulence can be used as well but it
is generally not necessary because agate is already very turbulent. You may
control the amount of the built-in turbulence by adding the agate_turb
keyword followed by a float value. For example:   pigment {
    agate
    agate_turb 0.5
    color_map {
      ...
    }
  }


The agate pattern uses the ramp_wave wave type by default but may use any
wave type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.2          Average

Technically average is not a pattern type but it is listed here because the
syntax is similar to other patterns. Typically a pattern type specifies how
colors or normals are chosen from a pigment map or normal map, however
average tells POV-Ray to average together all of the patterns you specify.
Average was originally designed to be used in a normal statement with a
normal map as a method of specifying more than one normal pattern on the same
surface. However average may be used in a pigment statement with a pigment
map or in a texture statement with a texture map to average colors too.

When used with pigments, the syntax is:

  pigment {
    average
    pigment_map
    {
      [WEIGHT_1 PIGMENT_BODY_1]
      [WEIGHT_2 PIGMENT_BODY_2]
      ...
      [WEIGHT_n PIGMENT_BODY_n]
    }
    PIGMENT_MODIFIER
  }


Similarly you may use a texture map in a texture statement. All textures are
fully computed. The resulting colors are then weighted and averaged.

When used with a normal map in a normal statement, multiple copies of the
original surface normal are created and are perturbed by each pattern. The
perturbed normals are then weighted, added and normalized.

See the sections "Pigment Maps", "Normal Maps" and "Texture Maps" for more
information.

7.6.7.3          Bozo

The bozo pattern is a very smooth, random noise function that is
traditionally used with some turbulence to create clouds. The spotted pattern
is identical to bozo but in early versions of POV-Ray spotted did not allow
turbulence to be added. Turbulence can now be added to any pattern so these
are redundant but both are retained for backwards compatibility. The bumps
pattern is also identical to bozo when used anywhere except in a normal
statement. When used as a normal, bumps uses a slightly different method to
perturb the normal with a similar noise function.

The bozo noise function has the following properties:

  1.It's defined over 3D space i.e., it takes x, y, and z and returns the
  2.If two points are far apart, the noise values at those points are
  3.If two points are close together, the noise values at those points are
    close to each other.


You can visualize this as having a large room and a thermometer that ranges
from 0.0 to 1.0. Each point in the room has a temperature. Points that are
far apart have relatively random temperatures. Points that are close together
have close temperatures. The temperature changes smoothly but randomly as we
move through the room.

Now let's place an object into this room along with an artist. The artist
measures the temperature at each point on the object and paints that point a
different color depending on the temperature. What do we get? A POV-Ray bozo
texture!

The bozo pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.4          Brick

The brick pattern generates a pattern of bricks. The bricks are offset by
half a brick length on every other row in the x- and z-directions. A layer of
mortar surrounds each brick. The syntax is given by

  pigment {
    brick COLOR_1, COLOR_2
    brick_size VECTOR
    mortar FLOAT
  }


where COLOR_1 is the color of the mortar and COLOR_2 is the color of the
brick itself. If no colors are specified a default deep red and dark gray are
used. The default size of the brick and mortar together is <8, 3, 4.5> units.
The default thickness of the mortar is 0.5 units. These values may be changed
using the optional brick_size and mortar pattern modifiers. You may also use
pigment statements in place of the colors. For example:

  pigment {
    brick pigment{Jade}, pigment{Black_Marble}
  }


When used with normals, the syntax is   normal {
    brick BUMP_FLOAT
  }


Where BUMP_FLOAT is an optional bump size float value. You may also use full
normal statements. For example:

  normal {
    brick normal{bumps 0.2}, normal{granite 0.3}
  }


When used with textures, the syntax is

  texture {
    brick texture{T_Gold_1A}, texture{Stone12}
  }


This is a block pattern which cannot use wave types, color map, or slope map
modifiers.

7.6.7.5          Bumps

The bumps pattern was originally designed only to be used as a normal
pattern. It uses a very smooth, random noise function that creates the look
of rolling hills when scaled large or a bumpy orange peal when scaled small.
Usually the bumps are about 1 unit apart.

When used as a normal, bumps uses a specialized normal perturbation function.
This means that the bumps pattern cannot be used with normal map, slope map
or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the bumps pattern is
identical to bozo or spotted and is similar to normal bumps but is not
identical as are most normals when compared to pigments. When used as pigment
or texture statements the bumps pattern uses the ramp_wave wave type by
default but may use any wave type. The pattern may be used with color_map,
pigment_map, and texture_map.

7.6.7.6          Checker

The checker pattern produces a checkered pattern consisting of alternating
squares of COLOR_1 and COLOR_2. If no colors are specified then default blue
and green colors are used.

  pigment { checker COLOR_1, COLOR_2 }


The checker pattern is actually a series of cubes that are one unit in size.
Imagine a bunch of 1 inch cubes made from two different colors of modeling
clay. Now imagine arranging the cubes in an alternating check pattern and
stacking them in layer after layer so that the colors still alternate in
every direction. Eventually you would have a larger cube. The pattern of
checks on each side is what the POV-Ray checker pattern produces when applied
to a box object. Finally imagine cutting away at the cube until it is carved
into a smooth sphere or any other shape. This is what the checker pattern
would look like on an object of any kind.

You may also use pigment statements in place of the colors. For example:

  pigment { checker pigment{Jade}, pigment{Black_Marble} }


When used with normals, the syntax is

  normal { checker BUMP_FLOAT }


Where BUMP_FLOAT is an optional bump size float value. You may also use full
normal statements. For example:

  normal {
    checker normal{gradient x scale .2},
            normal{gradient y scale .2}
  }


When used with textures, the syntax is...

  texture { checker texture{T_Wood_3A},texture{Stone12} }


This use of checker as a texture pattern replaces the special tiles texture
in previous versions of POV-Ray. You may still use tiles but it may be phased
out in future versions so checker textures are best.

This is a block pattern which cannot use wave types, color map, or slope map
modifiers.

7.6.7.7          Crackle

The crackle pattern is a set of random tiled polygons. With a large scale and
no turbulence it makes a pretty good stone wall or floor. With a small scale
and no turbulence it makes a pretty good crackle ceramic glaze. Using high
turbulence it makes a good marble that avoids the problem of apparent
parallel layers in traditional marble.

Mathematically, the set crackle(p)=0 is a 3D Voronoi diagram of a field of
semi random points and crackle(p) < 0 is the distance from the set along the
shortest path (a Voronoi diagram is the locus of points equidistant from
their two nearest neighbors from a set of disjoint points, like the membranes
in suds are to the centers of the bubbles).

The crackle pattern uses the ramp_wave wave type by default but may use any
wave type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.8          Dents

The dents pattern was originally designed only to be used as a normal
pattern. It is especially interesting when used with metallic textures. It
gives impressions into the metal surface that look like dents have been
beaten into the surface with a hammer. Usually the dents are about 1 unit
apart.

When used as a normal pattern, dents uses a specialized normal perturbation
function. This means that the dents pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the dents pattern is
similar to normal dents but is not identical as are most normals when
compared to pigments. When used in pigment or texture statements the dents
pattern uses the ramp_wave wave type by default but may use any wave type.
The pattern may be used with color_map, pigment_map and texture_map.

7.6.7.9          Gradient

One of the simplest patterns is the gradient pattern. It is specified as

  pigment {gradient VECTOR}


where VECTOR is a vector pointing in the direction that the colors blend. For
example    pigment { gradient x } // bands of color vary as you move
                          // along the "x" direction.


produces a series of smooth bands of color that look like layers of colors
next to each other. Points at x=0 are the first color in the color map. As
the x location increases it smoothly turns to the last color at x=1. Then it
starts over with the first again and gradually turns into the last color at
x=2. The pattern reverses for negative values of x. Using gradient y or
gradient z makes the colors blend along the y- or z-axis. Any vector may be
used but x, y and z are most common.

As a normal pattern, gradient generates a saw-tooth or ramped wave
appearance. The syntax is

   normal { gradient VECTOR, BUMP_FLOAT}


where the VECTOR giving the orientation is a required parameter but the
BUMP_FLOAT bump size which follows is optional.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.10         Granite

This pattern uses a simple 1/f fractal noise function to give a good granite
pattern. This pattern is used with creative color maps in stones.inc to
create some gorgeous layered stone textures.

As a normal pattern it creates an extremely bumpy surface that looks like a
gravel driveway or rough stone.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.11         Hexagon

The hexagon pattern is a block pattern that generates a repeating pattern of
hexagons in the x-y-plane. In this instance imagine tall rods that are
hexagonal in shape and are parallel to the y-axis and grouped in bundles like
shown in the example image. Three separate colors should be specified as
follows:

  pigment { hexagon COLOR_1, COLOR_2, COLOR_3 }


     _____
    /     \
   /   C2  _____
  |       /     \
  | _____/   C3  \
  | /            /|
   /   C1  _____/ |
  |       /|    | |
  | _____/ |    | |
  | |     | |    | |
  | |     | |    | |
  | |     | |    | |
  | |     | |    | |
  | |     | |    |
  | |     | |    |
    |     |
    |     |
The hexagon pattern.

The three colors will repeat the hexagonal pattern with hexagon COLOR_1
centered at the origin, COLOR_2 in the +z-direction and COLOR_3 to either
side. Each side of the hexagon is one unit long. The hexagonal rods of color
extend infinitely in the +y- and -y-directions. If no colors are specified
then default blue, green and red colors are used.

You may also use pigment statements in place of the colors. For example:

  pigment {
    hexagon pigment { Jade },
            pigment { White_Marble },
            pigment { Black_Marble }
  }


When used with normals, the syntax is

  normal { hexagon BUMP_FLOAT }


Where BUMP_FLOAT is an optional bump size float value. You may also use full
normal statements. For example:

  normal {
    hexagon
      normal { gradient x scale .2 },
      normal { gradient y scale .2 },
      normal { bumps scale .2 }
  }


When used with textures, the syntax is...

  texture {
    hexagon
      texture { T_Gold_3A },
      texture { T_Wood_3A },
      texture { Stone12 }
  }


This is a block pattern which cannot use wave types, color map, or slope map
modifiers.

7.6.7.12         Leopard

Leopard creates regular geometric pattern of circular spots.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.13         Mandel

The mandel pattern computes the standard Mandelbrot fractal pattern and
projects it onto the x-y-plane. It uses the x and y coordinates to compute
the Mandelbrot set. The pattern is specified with the keyword mandel followed
by an integer number. This number is the maximum number of iterations to be
used to compute the set. Typical values range from 10 up to 256 but any
positive integer may be used. For example:

  pigment {
    mandel 25
    color_map {
      [0.0  color Cyan]
      [0.3  color Yellow]
      [0.6  color Magenta]
      [1.0  color Cyan]
    }
    scale .5
  }


The value passed to the color map is computed by the formula:

  value = number_of_iterations / max_iterations


When used as a normal pattern, the syntax is...

  normal {
    mandel ITER, BUMP_AMOUNT
  }


where the required integer ITER value is optionally followed by a float bump
size.

The pattern extends infinitely in the z-direction similar to a planar image
map. The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.14         Marble

The marble pattern is very similar to the gradient x pattern. The gradient
pattern uses a default ramp_wave wave type which means it uses colors from
the color map from 0.0 up to 1.0 at location x=1 but then jumps back to the
first color for x > 1 and repeats the pattern again and again. However the
marble pattern uses the triangle_wave wave type in which it uses the color
map from 0 to 1 but then it reverses the map and blends from 1 back to zero.
For example:

  pigment {
    gradient x
    color_map {
      [0.0  color Yellow]
      [1.0  color Cyan]
    }
  }


This blends from yellow to cyan and then it abruptly changes back to yellow
and repeats. However replacing gradient x with marble smoothly blends from
yellow to cyan as the x coordinate goes from 0.0 to 0.5 and then smoothly
blends back from cyan to yellow by x=1.0.

Earlier versions of POV-Ray did not allow you to change wave types. Now that
wave types can be changed for most any pattern, the distinction between
marble and gradient x is only a matter of default wave types.

When used with turbulence and an appropriate color map, this pattern looks
like veins of color of real marble, jade or other types of stone. By default,
marble has no turbulence.

The pattern may be used with color_map, pigment_map, normal_map, slope_map
and texture_map.

7.6.7.15         Onion

Onion is a pattern of concentric spheres like the layers of an onion. Each
layer is one unit thick.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.16         Quilted

The quilted pattern was originally designed only to be used as a normal
pattern. The quilted pattern is so named because it can create a pattern
somewhat like a quilt or a tiled surface. The squares are actually 3-D cubes
that are 1 unit in size.

When used as a normal pattern it uses a specialized normal perturbation
function. This means that the quilted pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the quilted pattern is
similar to normal quilted but is not identical as are most normals when
compared to pigments. When used in pigment or texture statements the quilted
pattern uses the ramp_wave wave type by default but may use any wave type.
The pattern may be used with color_map, pigment_map and texture_map.

The two parameters control0 and control1 are used to adjust the curvature of
the seam or gouge area between the quilts. The syntax is:

  normal {
    quilted AMOUNT
    control0 C0
    control1 C1
  }


The values should generally be kept to around the 0.0 to 1.0 range. The
default value is 1.0 if none is specified. Think of this gouge between the
tiles in cross-section as a sloped line.

Quilted pattern with c0=0 and different values for c1.

Quilted pattern with c0=0.33 and different values for c1.

Quilted pattern with c0=0.67 and different values for c1.

Quilted pattern with c0=1 and different values for c1.

This straight slope can be made to curve by adjusting the two control values.
The control values adjust the slope at the top and bottom of the curve. A
control values of 0 at both ends will give a linear slope, as shown above,
yielding a hard edge. A control value of 1 at both ends will give an "s"
shaped curve, resulting in a softer, more rounded edge.

7.6.7.17         Radial

The radial pattern is a radial blend that wraps around the +y-axis. The color
for value 0.0 starts at the +x-direction and wraps the color map around from
east to west with 0.25 in the -z-direction, 0.5 in -x, 0.75 at +z and back to
1.0 at +x. Typically the pattern is used with a frequency modifier to create
multiple bands that radiate from the y-axis.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.18         Ripples

The ripples pattern was originally designed only to be used as a normal
pattern. It makes the surface look like ripples of water. The ripples radiate
from 10 random locations inside the unit cube area <0,0,0> to <1,1,1>. Scale
the pattern to make the centers closer or farther apart.

Usually the ripples from any given center are about 1 unit apart. The
frequency keyword changes the spacing between ripples. The phase keyword can
be used to move the ripples outwards for realistic animation.

The number of ripple centers can be changed with the global parameter
global_settings { number_of_waves FLOAT } somewhere in the scene. This
affects the entire scene. You cannot change the number of wave centers on
individual patterns. See section "Number_Of_Waves" for details.

When used as a normal pattern, ripples uses a specialized normal perturbation
function. This means that the ripples pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used in pigment or texture statements the ripples pattern uses the
ramp_wave wave type by default but may use any wave type. The pattern may be
used with color_map, pigment_map and texture_map.

7.6.7.19         Spiral1

The spiral1 pattern creates a spiral that winds around the y-axis similar to
a screw. Its syntax is:

  pigment {
    spiral1 NUMBER_OF_ARMS
  }


The NUMBER_OF_ARMS value determines how may arms are winding around the
y-axis.

The pattern uses the triangle_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.20         Spiral2

The spiral2 pattern is a modification of the spiral1 pattern with an
extraordinary look.

The pattern uses the triangle_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.21         Spotted

The spotted pattern is identical to the bozo pattern. Early versions of
POV-Ray did not allow turbulence to be used with spotted. Now that any
pattern can use turbulence there is no difference between bozo and spotted.
See section "Bozo" for details.

7.6.7.22         Waves

The waves pattern was originally designed only to be used as a normal
pattern. The waves pattern looks similar to the ripples pattern except the
features are rounder and broader. The effect is to make waves that look more
like deep ocean waves. The waves radiate from ten random locations inside the
unit cube area <0,0,0> to <1,1,1>. Scale the pattern to make the centers
closer or farther apart.

Usually the waves from any given center are about 1 unit apart. The frequency
keyword changes the spacing between waves. The phase keyword can be used to
move the waves outwards for realistic animation.

The number of ripple centers can be changed with the global parameter
global_settings { number_of_waves FLOAT } somewhere in the scene. This
affects the entire scene. You cannot change the number of wave centers on
individual patterns. See section "Number_Of_Waves" for details.

When used as a normal pattern, waves uses a specialized normal perturbation
function. This means that the waves pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used in pigment or texture statements the waves pattern uses the
ramp_wave wave type by default but may use any wave type. The pattern may be
used with color_map, pigment_map and texture_map.

7.6.7.23         Wood

The wood pattern consists of concentric cylinders centered on the z-axis.
When appropriately colored, the bands look like the growth rings and veins in
real wood. Small amounts of turbulence should be added to make it look more
realistic. By default, wood has no turbulence.

Unlike most patterns, the wood pattern uses the triangle_wave wave type by
default. This means that like marble, wood uses color map values 0.0 to 1.0
then repeats the colors in reverse order from 1.0 to 0.0. However you may use
any wave type. The pattern may be used with color_map, pigment_map,
normal_map, slope_map and texture_map.

7.6.7.24         Wrinkles

The wrinkles pattern was originally designed only to be used as a normal
pattern. It uses a 1/f noise pattern similar to granite but the features in
wrinkles are sharper. The pattern can be used to simulate wrinkled cellophane
or foil. It also makes an excellent stucco texture.

When used as a normal pattern it uses a specialized normal perturbation
function. This means that the wrinkles pattern cannot be used with normal
map, slope map or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the wrinkles pattern is
similar to normal wrinkles but is not identical as are most normals when
compared to pigments. When used in pigment or texture statements the wrinkles
pattern uses the ramp_wave wave type by default but may use any wave type.
The pattern may be used with color_map, pigment_map and texture_map.

7.6.8            Pattern Modifiers

Pattern modifiers are statements or parameters which modify how a pattern is
evaluated or tells what to do with the pattern. The modifiers color_map and
pigment_map apply only to pigments. See section "Pigment". The modifiers
bump_size, slope_map and normal_map apply only to normals. See section
"Normal". The texture_map modifier can only be used with textures. See
section "Texture Maps".

The pattern modifiers in the following section can be used with pigment,
normal or texture patterns.

7.6.8.1          Transforming Patterns

The most common pattern modifiers are the transformation modifiers translate,
rotate, scale and matrix. For details on these commands see section
"Transformations".

These modifiers may be placed inside pigment, normal and texture statements
to change the position, size and orientation of the patterns.

In general the order of transformations relative to other pattern modifiers
such as turbulence, color_map and other maps is not important. For example
scaling before or after turbulence makes no difference. The turbulence is
done first, then the scaling regardless of which is specified first. However
the order in which transformations are performed relative to warp statements
is important. See "Warps" for details.

7.6.8.2          Frequency and Phase

The frequency and phase modifiers act as a type of scale and translate
modifiers for color_map, pigment_map, normal_map, slope_map and texture_map.
This discussion uses a color map as an example but the same principles apply
to pigment maps, normal maps, slope maps and texture maps.

The frequency keyword adjusts the number of times that a color map repeats
over one cycle of a pattern. For example gradient covers color map values 0
to 1 over the range from x=0 to x=1. By adding frequency 2.0 the color map
repeats twice over that same range. The same effect can be achieved using
scale 0.5*x so the frequency keyword isn't that useful for patterns like
gradient.

However the radial pattern wraps the color map around the +y-axis once. If
you wanted two copies of the map (or 3 or 10 or 100) you'd have to build a
bigger map. Adding frequency 2.0 causes the color map to be used twice per
revolution. Try this:

  pigment {
    radial
    color_map{[0.5 color Red][0.5 color White]}
    frequency 6
  }


The result is six sets of red and white radial stripes evenly spaced around
the object.

The float after frequency can be any value. Values greater than 1.0 causes
more than one copy of the map to be used. Values from 0.0 to 1.0 cause a
fraction of the map to be used. Negative values reverses the map.

The phase value causes the map entries to be shifted so that the map starts
and ends at a different place. In the example above if you render successive
frames at phase 0 then phase 0.1, phase 0.2 etc you could create an animation
that rotates the stripes. The same effect can be easily achieved by rotating
the radial pigment using rotate  y*Angle but there are other uses where phase
can be handy.

Sometimes you create a great looking gradient or wood color map but you want
the grain slightly adjusted in or out. You could re-order the color map
entries but that's a pain. A phase adjustment will shift everything but keep
the same scale. Try animating a mandel pigment for a color palette rotation
effect.

Frequency and phase have no effect on block patterns checker, brick and
hexagon nor do they effect image maps, bump maps or material maps. They also
have no effect in normal statements when used with bumps, dents, quilted or
wrinkles because these normal patterns cannot use normal_map or slope_map.

They can be used with normal patterns ripples and waves even though these two
patterns cannot use normal_map or slope_map either. When used with ripples or
waves, frequency adjusts the space between features and phase can be adjusted
from 0.0 to 1.0 to cause the ripple or waves to move relative to their center
for animating the features.

These values work by applying the following formula

  NEW_VALUE = fmod ( OLD_VALUE * FREQUENCY + PHASE, 1.0 ).


7.6.8.3          Waveform

Most patterns that take color_map, pigment_map, slope_map, normal_map or
texture_map use the entries in the map in order from 0.0 to 1.0. The wood and
marble patterns use the map from 0.0 to 1.0 and then reverses it and runs it
from 1.0 to 0.0. The difference can easily be seen when these patterns are
used as normal patterns with no maps.

Patterns such as gradient or onion generate a grove or slot that looks like a
ramp that drops off sharply. This is called a ramp_wave wave type. However
wood and marble slope upwards to a peak, then slope down again in a
triangle_wave. In previous versions of POV-Ray there was no way to change the
wave types. You could simulate a triangle wave on a ramp wave pattern by
duplicating the map entries in reverse, however there was no way to use a
ramp wave on wood or marble.

Now any pattern that takes a map can have the default wave type overridden.
For example:

  pigment { wood color_map { MyMap } ramp_wave }


Also available are sine_wave and scallop_wave types. These types are of most
use in normal patterns as a type of built-in slope map. The sine_wave takes
the zig-zag of a ramp wave and turns it into a gentle rolling wave with
smooth transitions. The scallop_wave uses the absolute value of the sine wave
which looks like corduroy when scaled small or like a stack of cylinders when
scaled larger.

Although any of these wave types can be used for pigments, normals or
textures, the sine_wave and scallop_wave types are not as noticeable on
pigments or textures as they are for normals.

Wave types have no effect on block patterns checker, brick and hexagon nor do
they effect image maps, bump maps or material maps. They also have no effect
in normal statements when used with bumps, dents, quilted or wrinkles because
these normal patterns cannot use normal_map or slope_map.

7.6.8.4          Turbulence

The keyword turbulence followed by a float or vector may be used to stir up
any pigment, normal, texture, irid or halo. A number of optional parameters
may be used with turbulence to control how it is computed. For example:

  pigment  {
    wood color_map { MyMap }
    turbulence TURB_VECTOR
    octaves FLOAT
    omega FLOAT
    lambda FLOAT
  }


Typical turbulence values range from the default 0.0, which is no turbulence,
to 1.0 or more, which is very turbulent. If a vector is specified different
amounts of turbulence are applied in the x-, y- and z-direction. For example

  turbulence <1.0, 0.6, 0.1>


has much turbulence in the x-direction, a moderate amount in the y-direction
and a small amount in the z-direction.

Turbulence uses a random noise function called DNoise. This is similar to the
noise used in the bozo pattern except that instead of giving a single value
it gives a direction. You can think of it as the direction that the wind is
blowing at that spot. Points close together generate almost the same value
but points far apart are randomly different.

In general the order of turbulence parameters relative to other pattern
modifiers such as transformations, color maps and other maps is not
important. For example scaling before or after turbulence makes no
difference. The turbulence is done first, then the scaling regardless of
which is specified first. See section "Warps" for a way to work around this
behavior.

Turbulence uses DNoise to push a point around in several steps called
octaves. We locate the point we want to evaluate, then push it around a bit
using turbulence to get to a different point then look up the color or
pattern of the new point.

It says in effect Don't give me the color at this spot... take a  few random
steps in different directions and give me that color. Each step is typically
half as long as the one before. For example:

  P ------------------------->
           First Move        /
                            /
                           /
                          /Second
                         /  Move
                        /
                 ______/
                 \
                  \
                   Q - Final point.
Turbulence random walk.

The magnitude of these steps is controlled by the turbulence value. There are
three additional parameters which control how turbulence is computed. They
are octaves, lambda and omega. Each is optional. Each is followed by a single
float value. Each has no effect when there is no turbulence.

7.6.8.5          Octaves

The octaves value controls the number of steps of turbulence that are
computed. Legal values range from 1 to 10. The default value of 6 is a fairly
high value; you won't see much change by setting it to a higher value because
the extra steps are too small. Float values are truncated to integer. Smaller
numbers of octaves give a gentler, wavy turbulence and computes faster.
Higher octaves create more jagged or fuzzy turbulence and takes longer to
compute.

7.6.8.6          Lambda

The lambda parameter controls how statistically different the random move of
an octave is compared to its previous octave. The default value is 2.0 which
is quite random. Values close to lambda 1.0 will straighten out the
randomness of the path in the diagram above. The zig-zag steps in the
calculation are in nearly the same direction. Higher values can look more
swirly under some circumstances.

7.6.8.7          Omega

The omega value controls how large each successive octave step is compared to
the previous value. Each successive octave of turbulence is multiplied by the
omega value. The default omega 0.5 means that each octave is 1/2 the size of
the previous one. Higher omega values mean that 2nd, 3rd, 4th and up octaves
contribute more turbulence giving a sharper, crinkly look while smaller
omegas give a fuzzy kind of turbulence that gets blurry in places.

7.6.8.8          Warps

The warp statement is a pattern modifier that is similar to turbulence.
Turbulence works by taking the pattern evaluation point and pushing it about
in a series of random steps. However warps push the point in very
well-defined, non-random, geometric ways. The warp statement also overcomes
some limitations of traditional turbulence and transformations by giving the
user more control over the order in which turbulence, transformation and warp
modifiers are applied to the pattern.

Currently there are three types of warps but the syntax was designed to allow
future expansion. The first two, the repeat warp and the black_hole warp are
new features for POV-Ray that modify the pattern in geometric ways. The other
warp provides an alternative way to specify turbulence.

The syntax for using a warp statement in a pigment is

  pigment {
    PATTERN_TYPE
    PIGMENT_MODIFIERS...
    warp { WARP_ITEMS...}
    OTHER_PIGMENT_MODIFIERS...
  }


Similarly warps may be used in normals and textures. You may have as many
separate warp statements as you like in each pattern. The placement of warp
statements relative to other modifiers such as color_map or turbulence is not
important. However placement of warp statements relative to each other and to
transformations is significant. Multiple warps and transformations are
evaluated in the order in which you specify them. For example if you
translate, then warp or warp, then translate, the results can be different.

7.6.8.8.1        Black Hole Warp

A black hole is so named because of its similarity to real black holes. Just
like the real thing, you cannot actually see a black hole. The only way to
detect its presence is by the effect it has on things that surround it.
Unlike the real thing, however, it won't swallow you up and compress your
entire body to a volume of, say, 2.0 10-10 microns in diameter if you get too
close (We're working on that part).

Take, for example, a woodgrain. Using POV-Ray's normal turbulence and other
texture modifier functions, you can get a nice, random appearance to the
grain. But in its randomness it is regular - it is regularly random! Adding a
black hole allows you to create a localised disturbance in a woodgrain in
either one or multiple locations. The black hole can have the effect of
either sucking the surrounding texture into itself (like the real thing) or
pushing it away. In the latter case, applied to a woodgrain, it would look to
the viewer as if there were a knothole in the wood. In this text we use a
woodgrain regularly as an example, because it is ideally suitable to
explaining black holes. However, black holes may in fact be used with any
texture.

The effect that the black hole has on the texture can be specified. By
default, it sucks with the strength calculated exponentially
(inverse-square). You can change this if you like.

Black holes may be used anywhere a Warp is permitted. The syntax is:

  warp
  {
    black_hole <CENTER>, RADIUS
    [falloff VALUE]
    [strength VALUE]
    [repeat <VECTOR>]
    [turbulence <VECTOR>]
    [inverse]
  }


Some examples are given by

  warp
  {
    black_hole <0, 0, 0>, 0.5
  }

  warp
  {
    black_hole <0.15, 0.125, 0>, 0.5
    falloff 7
    strength 1.0
    repeat <1.25, 1.25, 0>
    turbulence <0.25, 0.25, 0>
    inverse
  }

  warp
  {
    black_hole <0, 0, 0>, 1.0
    falloff 2
    strength 2
    inverse
  }


In order to fully understand how a black hole works, it is important to know
the theory behind it. A black hole (or any warp) works by taking a point and
perturbing it to another location. The amount of perturbation depends on the
strength of the black hole at the original point passed in to it. The amount
of perturbation directly relates to the amount of visual movement that you
can see occur in a texture. The stronger the black hole at the input
co-ordinate the more that original co-ordinate is moved to another location
(either closer to or further away from the center of the black hole.)

Movement always occurs on the vector that exists between the input point and
the center of the black hole.

Black holes are considered to be spheres. For a point to be affected by a
black hole, it must be within the sphere's volume.

Suppose you have a black hole at <1,1,1> and a point at <1,2,1>. If this
point is perturbed by a total amount of +1 units its new location is <1,3,1>,
which is on a direct line extrapolated from the vector between <1,1,1> and
<1,2,1>. In this case the point is pushed away from the black hole, which is
not normal behaviour but is good for demonstration purposes.

The internal properties of a black hole are as follows.

  Falloff          The power of two by which the effect falls off (default
  Turbulence       If set, each new repeated black hole's position isem in.
  Turbulence_VectorThe maximum <x,y,z> factor for turbulence randomness.


Each of these are discussed below.

Center: A vector defining the center of the sphere that represents the black
hole. If the black hole has Repeat set it is the offset within each block.

Radius: A number giving the length, in units, of the radius of the sphere
that represents the black hole.

If a point is not within radius units of <center> it cannot be affected by
the black hole and will not be perturbed.

Falloff: The power by which the effect of the black hole falls off. The
default is two. The force of the black hole at any given point, before
applying the Strength modifier, is as follows.

First, convert the distance from the point to the center to a proportion (0
to 1) that the point is from the edge of the black hole. A point on the
perimeter of the black hole will be 0.0; a point at the centre will be 1.0; a
point exactly halfway will be 0.5, and so forth.

Mentally you can consider this to be a closeness factor. A closeness of 1.0
is as close as you can get to the center (i. e. at the center), a closeness
of 0.0 is as far away as you can get from the center and still be inside the
black hole and a closeness of 0.5 means the point is exactly halfway between
the two.

Call this value c. Raise c to the power specified in Falloff. By default
Falloff is 2, so this is c^2 or c squared. The resulting value is the force
of the black hole at that exact location and is used, after applying the
Strength scaling factor as described below, to determine how much the point
is perturbed in space.

For example, if c is 0.5 the force is 0.5^2 or 0.25. If c is 0.25 the force
is 0.125. But if c is exactly 1.0 the force is 1.0.

Recall
that as c gets smaller the point is farther from the center of the black
hole. Using the default power of 2, you can see that as c reduces, the force
reduces exponentially in an inverse-square relationship. Put in plain
english, it means that the force is much stronger (by a power of two) towards
the center than it is at the outside.

By increasing Falloff, you can increase the magnitude of the falloff. A large
value will mean points towards the perimeter will hardly be affected at all
and points towards the center will be affected strongly.

A value of 1.0 for Falloff will mean that the effect is linear. A point that
is exactly halfway to the center of the black hole will be affected by a
force of exactly 0.5.

A value of Falloff of less than one but greater than zero means that as you
get closer to the outside, the force increases rather than decreases. This
can have some uses but there is a side effect. Recall that the effect of a
black hole ceases outside its perimeter. This means that points just within
the permiter will be affected strongly and those just outside not at all.
This would lead to a visible border, shaped as a sphere.

A value for Falloff of 0 would mean that the force would be 1.0 for all
points within the black hole, since any number larger 0 raised to the power
of 0 is 1.0.

The magnitude of the movement of the point is determined basically by the
value of force after scaling. We'll consider scaling later. Lets take an
example.

Suppose we have a black hole of radius 2.0 and a point that is exactly 1.0
units from the center. That means it is exactly half-way to the center and
that c would be 0.5. If we use the default falloff of 2 the force at that
point is 0.5^2 or 0.25. What this means is that we must move the point by
0.25 of its distance from the center. In this case it is 1.0 units from the
center, so we move it by 1.0*0.25 or 0.25 units. This gives a final distance
of 1.0-(1.0*0.25) or 0.75 units from the center, on a direct line in 3D space
between the original position and the center.

If the point were part of, say, a wood grain, the wood grain would appear to
bend towards the (invisible) center of the black hole. If the Inverse flag
were set, however, it would be pushed away, meaning its final position would
be 1.0+(1.0*0.25) or 1.25 units from the center.

Strength: The Strength gives you a bit more control over how much a point is
perturbed by the black hole. Basically, the force of the black hole (as
determined above) is multiplied by the value of Strength, which defaults to
1.0. If you set Strength to 0.5, for example, all points within the black
hole will be moved by only half as much as they would have been. If you set
it to 2.0 they will be moved twice as much.

There is a rider to the latter example, though - the movement is clipped to a
maximum of the original distance from the center. That is to say, a point
that is 0.75 units from the center may only be moved by a maximum of 0.75
units either towards the center or away from it, regardless of the value of
Strength. The result of this clipping is that you will have an exclusion area
near the centre of the black hole where all points whose final force value
exceeded or equaled 1.0 were moved by a fixed amount.

Inverted: If Inverted is set points are pushed away from the center instead
of being pulled in.

Repeat: Repeat allows you to simulate the effect of many black holes without
having to explicitly declare them. Repeat is a vector that tells POV-Ray to
use this black hole at multiple locations.

If you're not interested in the theory behind all this, just skip the
following text and use the values given in the summary below.

Using Repeat logically divides your scene up into cubes, the first being
located at <0,0,0> and going to < repeat>. Suppose your repeat vector was
<1,5,2>. The first cube would be from <0,0,0> to < 1,5,2>. This cube repeats,
so there would be one at < -1,-5,-2>, <1,5,2>, <2,10,4> and so forth in all
directions, ad infinitum.

When you use Repeat, the center of the black hole does not specify an
absolute location in your scene but an offset into each block. It is only
possible to use positive offsets. Negative values will produce undefined
results.

Suppose your center was <0.5,1,0.25> and the repeat vector is <2,2,2>. This
gives us a block at < 0,0,0> and <2,2,2>, etc. The centers of the black
hole's for these blocks would be <0,0,0> + < 0.5,1.0,0.25>, i. e.
<0.5,1.0,0.25>, and < 2,2,2> + <0.5,1.0,0.25>, i. e. < 2,5,3.0,2.25>.

Due to the way repeats are calculated internally, there is a restriction on
the values you specify for the repeat vector. Basically, each black hole must
be totally enclosed within each block (or cube), with no part crossing into a
neighbouring one. This means that, for each of the x, y and z dimensions, the
offset of the center may not be less than the radius, and the repeat value
for that dimension must be >=the center plus the radius since any other
values would allow the black hole to cross a boundary. Put another way, for
each of x, y and z

radius <= offset or center <= repeat - radius.


If the repeat vector in any dimension is too small to fit this criteria, it
will be increased and a warning message issued. If the center is less than
the radius it will also be moved but no message will be issued.

Note that none of the above should be read to mean that you can't overlap
black holes. You most certainly can and in fact this can produce some most
useful effects. The restriction only applies to elements of the same black
hole which is repeating. You can declare a second black hole that also
repeats and its elements can quite happily overlap the first and causing the
appropriate interactions.

It is legal for the repeat value for any dimension to be 0, meaning that
POV-Ray will not repeat the black hole in that direction.

Turbulence: Turbulence can only be used with Repeat. It allows an element of
randomness to be inserted into the way the black holes repeat, to cause a
more natural look. A good example would be an array of knotholes in wood - it
would look rather artificial if each knothole were an exact distance from the
previous.

The turbulence vector is a measurement that is added to each individual back
hole in an array, after each axis of the vector is multiplied by a different
random amount ranging from 0 to 1.

For example, suppose you have a repeating element of a black hole that is
supposed to be at <2,2,2>. You have specified a turbulence vector of <4,5,3>,
meaning you want the position to be able to vary by no more than 1.0 units in
the X direction, 3.0 units in the Y direction and 2.0 in Z. This means that
the valid ranges of the new position are as follows

X can be from 2 to 6.

Y can be from 2 to 7.
Z can be from 2 to 5.


The resulting actual position of the black hole's center for that particular
repeat element is random (but consistent, so renders will be repeatable) and
somewhere within the above co-ordinates.

There is a rider on the use of turbulence, which basically is the same as
that of the repeat vector. You can't specify a value which would cause a
black hole to potentially cross outside of its particular block.

Since POV-Ray doesn't know in advance how much a position will be changed due
to the random nature of the changes, it enforces a rule that is similar to
the one for Repeat, except it adds the maximum possible variation for each
axis to the center. For example, suppose you had a black hole with a center
of <1.0, 1.0, 1.0>, radius of 0.5 and a turbulence of <0.5, 0.25, 0> -
normally, the minimum repeat would be <1.5, 1.5, 1.5>. However, now we take
into account the turbulence, meaning the minimum repeat vector is actually
<2.0, 1.75, 1.5>.

Repeat summarized: For each of x, y and z the offset of the center must be
>=radius and the value of the repeat must be \ge center + radius +
turbulence. The exception being that repeat may be 0 for any dimension, which
means do not repeat in that direction.

7.6.8.8.2        Repeat Warp

The repeat warp causes a section of the pattern to be repeated over and over.
It takes a slice out of the pattern and makes multiple copies of it
side-by-side. The warp has many uses but was originally designed to make it
easy to model wood veneer textures. Veneer is made by taking very thin slices
from a log and placing them side-by-side on some other backing material. You
see side-by-side nearly identical ring patterns but each will be a slice
perhaps 1/32th of an inch deeper.

The syntax for a repeat warp is

  warp { repeat VECTOR  offset VECTOR  flip VECTOR }


The repeat vector specifies the direction in which the pattern repeats and
the width of the repeated area. This vector must lie entirely along an axis.
In other words, two of its three components must be 0. For example

  pigment {
    wood
    warp {repeat 2*x}
  }


which means that from x=0 to x=2 you get whatever the pattern usually is. But
from x=2 to x=4 you get the same thing exactly shifted two units over in the
x-direction. To evaluate it you simply take the x-coordinate modulo 2.
Unfortunately you get exact duplicates which isn't very realistic. The
optional offset vector tells how much to translate the pattern each time it
repeats. For example

  pigment {
    wood
    warp {repeat x*2  offset z*0.05}
  }


means that we slice the first copy from x=0 to x=2 at z=0 but at x=2 to x=4
we offset to z=0.05. In the 4 to 6 interval we slice at z=0.10. At the n-th
copy we slice at 0.05 n z. Thus each copy is slightly different. There are no
restrictions on the offset vector.

Finally the flip vector causes the pattern to be flipped or mirrored every
other copy of the pattern. The first copy of the pattern in the positive
direction from the axis is not flipped. The next farther is, the next is not,
etc. The flip vector is a three component x, y, z vector but each component
is treated as a boolean value that tells if you should or should not flip
along a given axis. For example

  pigment {
    wood
    warp {repeat 2*x  flip <1,1,0>}
  }


means that every other copy of the pattern will be mirrored about the x- and
y- axis but not the z-axis. A non-zero value means flip and zero means do not
flip about that axis. The magnitude of the values in the flip vector doesn't
matter.

7.6.8.8.3        Turbulence Warp

The POV-Ray language contains an ambiguity and limitation on the way you
specify turbulence and transformations such as translate, rotate, scale and
matrix transforms. Usually the turbulence is done first. Then all translate,
rotate, scale and matrix operations are always done after turbulence
regardless of the order in which you specify them. For example this

 pigment {
   wood
   scale .5
   turbulence .2
 }


works exactly the same as

 pigment {
   wood
   turbulence .2
   scale .5
 }


The turbulence is always first. A better example of this limitation is with
uneven turbulence and rotations.

  pigment {
    wood
    turbulence 0.5*y
    rotate z*60
  }

  // as compared to

  pigment {
   wood
   rotate z*60
   turbulence 0.5*y
  }


The results will be the same either way even though you'd think it should
look different.

We cannot change this basic behavior in POV-Ray now because lots of scenes
would potentially render differently if suddenly the order transformation vs
turbulence suddenly mattered when in the past, it didn't.

However, by specifying our turbulence inside warp statement you tell POV-Ray
that the order in which turbulence, transformations and other warps are
applied is significant. Here's an example of a turbulence warp.

  warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }


The significance is that this

 pigment {
   wood
   translate <1,2,3> rotate x*45 scale 2
   warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }
 }


produces different results than this...

 pigment {
   wood
   warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }
   translate <1,2,3> rotate x*45 scale 2
 }


You may specify turbulence without using a warp statement. However you cannot
control the order in which they are evaluated unless you put them in a warp.

The evaluation rules are as follows:

  1)First any turbulence not inside a warp statement is applied regardless of
  2)Next each warp statement, translate, rotate, scale or matrix one-by-one,
    is applied in the order the user specifies. If you want turbulence done
    in a specific order, you simply specify it inside a warp in the proper
place.

7.6.8.9          Bitmap Modifiers

A bitmap modifier is a modifier used inside an image_map, bump_map or
material_map to specify how the 2-D bitmap is to be applied to the 3-D
surface. Several bitmap modifiers apply to specific kinds of maps and they
are covered in the appropriate sections. The bitmap modifiers discussed in
the following sections are applicable to all three types of bitmaps.

7.6.8.9.1        The once Option

Normally there are an infinite number of repeating image maps, bump maps or
material maps created over every unit square of the x-y-plane like tiles. By
adding the once keyword after a file name you can eliminate all other copies
of the map except the one at (0,0) to (1,1). In image maps, areas outside
this unit square are treated as fully transparent. In bump maps, areas
outside this unit square are left flat with no normal modification. In
material maps, areas outside this unit square are textured with the first
texture of the texture list.

For example:

  image_map {
    gif "mypic.gif"
    once
  }


7.6.8.9.2        The "map_type" Option

The default projection of the bump onto the x-y-plane is called a planar map
type. This option may be changed by adding the map_type keyword followed by a
number specifying the way to wrap the bump around the object.

A map_type 0 gives the default planar mapping already described.

A map_type 1 gives a spherical mapping. It assumes that the object is a
sphere of any size sitting at the origin. The y-axis is the north/south pole
of the spherical mapping. The top and bottom edges of the bitmap just touch
the pole regardless of any scaling. The left edge of the bitmap begins at the
positive x-axis and wraps the pattern around the sphere from west to east in
a -y-rotation. The pattern covers the sphere exactly once. The once keyword
has no meaning for this type.

With map_type 2 you get a cylindrical mapping. It assumes that a cylinder of
any diameter lies along the y-axis. The bump pattern wraps around the
cylinder just like the spherical map but remains one unit tall from y=0 to
y=1. This band of the pattern is repeated at all heights unless the once
keyword is applied.

Finally map_type 5 is a torus or donut shaped mapping. It assumes that a
torus of major radius 1 sits at the origin in the x-z-plane. The pattern is
wrapped around similar to spherical or cylindrical maps. However the top and
bottom edges of the map wrap over and under the torus where they meet each
other on the inner rim.

Types 3 and 4 are still under development.

For example:

  sphere{<0,0,0>,1
    pigment{
      image_map {
        gif "world.gif"
        map_type 1
      }
    }
  }


7.6.8.9.3        The interpolate Option

Adding the interpolate keyword can smooth the jagged look of a bitmap. When
POV-Ray asks an image map color or a bump amount for a bump map, it often
asks for a point that is not directly on top of one pixel but sort of between
several differently colored pixels. Interpolations returns an in-between
value so that the steps between the pixels in the map will look smoother.

Although interpolate is legal in material maps the color index is
interpolated before the texture is chosen. It does not interpolate the final
color as you might hope it would. In general, interpolation of material maps
serves no useful purpose but this may be fixed in future versions.

There are currently two types of interpolation:

  Bilinear            --- interpolate 2
  Normalized Distance --- interpolate 4


For example:

  image_map {
    gif "mypic.gif"
    interpolate 2
  }


Default is no interpolation. Normalized distance is the slightly faster of
the two, bilinear does a better job of picking the between color. Normally
bilinear is used.

If your map looks jaggy, try using interpolation instead of going to a higher
resolution image. The results can be very good.

7.7              Atmospheric Effects

Atmospheric effects are a loosely-knit group of features that affect the
background and/or the atmosphere enclosing the scene. POV-Ray includes the
ability to render a number of atmospheric effects, such as fog, haze, mist,
rainbows and skies.

7.7.1            Atmosphere

Important notice: The atmosphere feature in POV-Ray 3.0 are somewhat
experimental. There is a high probability that the design and implementation
of these features will be changed in future versions. We cannot guarantee
that scenes using these features in 3.0 will render identically in future
releases or that full backwards compatibility of language syntax can be
maintained.

Computer generated images normally assume a vacuum space that does not allow
the rendering of natural phenomena like smoke, light beams, etc. A very
simple approach to add fog to a scene is explained in section "Fog". This
kind of fog does not interact with any light sources though. It will not show
light beams or other effects and is therefore not very realistic.

The atmosphere effect overcomes some of the fog's limitations by calculating
the interaction between light and the particles in the atmosphere using
volume sampling. Thus shaft of light beams will become visible and objects
will cast shadows onto smoke or fog.

The syntax of the atmosphere is:

  atmosphere {
    type TYPE
    distance DISTANCE
    [ scattering SCATTERING ]
    [ eccentricity ECCENTRICITY ]
    [ samples SAMPLES ]
    [ jitter JITTER ]
    [ aa_threshold AA_THRESHOLD ]
    [ aa_level AA_LEVEL ]
    [ colour <COLOUR> ]
  }


The type keyword determines the type of scattering model to be used. There
are five different phase functions representing the different models:
isotropic, Rayleigh, Mie (haze and murky atmosphere) and Henyey-Greenstein.

Isotropic scattering is the simplest form of scattering because it is
independent of direction. The amount of light scattered by particles in the
atmosphere does not depend on the angle between the viewing direction and the
incoming light.

Rayleigh scattering models the scattering for extremely small particles such
as molecules of the air. The amount of scattered light depends on the
incident light angle. It is largest when the incident light is parallel or
anti-parallel to the viewing direction and smallest when the incident light
is perpendicular to the viewing direction. You should note that the Rayleigh
model used in POV-Ray does not take the dependency of scattering on the
wavelength into account.

The Rayleigh scattering function.

Mie scattering is used for relatively small particles such as minuscule water
droplets of fog, cloud particles, and particles responsible for the polluted
sky. In this model the scattering is extremely directional in the forward
direction i. e. the amount of scattered light is largest when the incident
light is anti-parallel to the viewing direction (the light goes directly to
the viewer). It is smallest when the incident light is parallel to the
viewing direction. The haze and murky atmosphere models differ in their
scattering characteristics. The murky model is much more directional than the
haze model.

The Mie "haze" scattering function.

The Mie "murky" scattering function.

The Henyey-Greenstein scattering is based on an analytical function and can
be used to model a large variety of different scattering types. The function
models an ellipse with a given eccentricity e. This eccentricity is specified
by the optional keyword eccentricity which is only used for scattering type
five. An eccentricity value of zero defines isotropic scattering while
positive values lead to scattering in the direction of the light and negative
values lead to scattering in the opposite direction of the light. Larger
values of e (or smaller values in the negative case) increase the directional
property of the scattering.

The Heyney-Greenstein scattering function for different eccentricity values.


The easiest way to use the different scattering types will be to declare some
constants and use those in your atmosphere definition:

  #declare ISOTROPIC_SCATTERING         = 1
  #declare MIE_HAZY_SCATTERING          = 2
  #declare MIE_MURKY_SCATTERING         = 3
  #declare RAYLEIGH_SCATTERING          = 4
  #declare HENYEY_GREENSTEIN_SCATTERING = 5


The distance keyword is used to determine the density of the particles in the
atmosphere. This density is constant for the whole atmosphere. The distance
parameter works in the same way as the fog distance.

With the scattering keyword you can change the amount of light that is
scattered by the atmosphere, thus increasing or decreasing the brightness of
the atmosphere. Smaller scattering values decrease the brightness while
larger values increase it.

The colour or color keyword can be used to create a colored atmosphere, i. e.
it can be used to get particles that filter the light passing through. The
default color is black.

The light passing through the atmosphere (either coming from light sources or
the background) is filtered by the atmosphere's color if the specified color
has a non-zero filter value. In other words, the amount by which the light is
filtered by the atmosphere's color is given by the filter value (pretty much
in the same way as it is done for the fog). Using a color of rgbf
<1,0,0,0.25> will result in a slightly reddish atmosphere because 25% of the
light passing through the atmosphere is filtered by (multiplied with) the
color of the atmosphere, i. e. rgb <1,0,0> (and that's red).

The transmittance channel of the atmosphere's color is used to specify a
minimum translucency. If a value larger than zero is used you'll always see
that amount of the background through the atmosphere, regardless of how dense
the atmosphere is. This works in the same way as it does for fogs.

Since the atmosphere is calculated by sampling along the viewing ray and
looking for contributions from light sources, it is prone to aliasing (just
like any sampling technique). There are four parameters to minimize the
artifacts that may be visible: samples, jitter, aa_level and aa_threshold.

The samples keyword determines how many samples are calculated in one
interval along the viewing ray. The length of the interval is either the
distance as given by the distance keyword or the length of the lit part of
the viewing ray, whichever is smaller. This lit part is a section of the ray
that
is most likely lit by a light source. In the case of a spotlight it is the
part of the ray that lies in the cone of light. In other cases it becomes
more difficult. The only thing you should keep in mind is that the actual
sampling interval length is variable but there will never be fewer than the
specified samples in the specified distance.

One technique to reduce the visibility of sampling artifacts is to jitter the
sample points, i. e. to add random noise to their location. This can be done
with the jitter keyword.

Another technique is super-sampling (an anti-aliasing method). This helps to
avoid missing features by adding additional samples in places were high
intensity changes occur (e. g. the edge of a shadow). The anti-aliasing is
turned on by the aa_level keyword. If this is larger than zero super-sampling
will be used. The additional samples will be recursively placed between two
samples with a high intensity change. The level to which subdivision takes
places is specified by the aa_level keyword. Level one means one subdivision
(one additional sample), level two means two subdivisions (up to three
additional samples), etc.

The threshold for the intensity change is given by the aa_threshold keyword.
If the intensity change is greater than this threshold anti-aliasing will be
used for those two samples.

With spotlights you'll be able to create the best results because their cone
of light will become visible. Pointlights can be used to create effects like
street lights in fog. Lights can be made to not interact with the atmosphere
by adding atmosphere off to the light source. They can be used to increase
the overall light level off the scene to make it look more realistic.

You should note that the atmosphere feature will not work if the camera is
inside a non-hollow object (see section "Empty and Solid Objects" for a
detailed explanation).

7.7.2            Background

A background color can be specified if desired. Any ray that doesn't hit an
object will be colored with this color. The default background is black. The
syntax for background is:

  background { colour <COLOUR> }


7.7.3            Fog

Fog is defined by the following statement:

  fog {
    fog_type FOG_TYPE
    distance DISTANCE
    colour <COLOUR>
    [ turbulence <TURBULENCE> ]
    [ turb_depth TURB_DEPTH ]
    [ omega OMEGA ]
    [ lambda LAMBDA ]
    [ octaves OCTAVES ]
    [ fog_offset FOG_OFFSET ]
    [ fog_alt FOG_ALT ]
    [ up <FOG_UP> ]
    [ TRANSFORMATION ]
  }


The optional up vector specifies a direction pointing up, generally the same
as the camera's up vector. All calculations done during the ground fog
evaluation are done relative to this up vector, i. e. the actual heights are
calculated along this vector.

The up vector can also be modified using any of the known transformations
described in "Transformations". Though it may not be a good idea to scale the
up vector - the results are hardly predictable - it is quite useful to be
able to rotate it. You should also note that translations do not affect the
up direction (and thus don't affect the fog).

Currently there are two fog types, constant fog and ground  fog. The constant
fog has a constant density everywhere while the ground fog has a constant
density for all heights below a given point on the up axis and thins out
along this axis. The height below which the fog has constant density is
specified by the fog_offset keyword. The fog_alt keyword is used to specify
the rate by which the fog fades away. At an altitude of fog_offset+fog_alt
the fog has a density of 25%. The density of the fog at a given height y is
calculated by the formula:

           /
           |                  1
           | -------------------------------------, y > fog_alt
           |  (1 + (y - fog_offset) / fog_alt) ^2
density = -|
           |
           |                  1,                   y <= fog_alt
           |
           \


The total density along a ray is calculated by integrating from the height of
the starting point to the height of the end point.

Two constants are defined for easy use of the fog types in the file
const.inc:

   // FOG TYPE CONSTANTS
   #declare Constant_Fog = 1
   #declare Ground_Fog   = 2


The color of a pixel with an intersection depth d is calculated by

  C_pixel = exp(-d/D) * C_object + (1-exp(-d/D)) * C_fog


where D is the fog distance. At depth 0 the final color is the object's
color. If the intersection depth equals the fog distance the final color
consists of 64% of the object's color and 36% of the fog's color.

The fog color that is given by the color keyword has three purposes. First it
defines the color to be used in blending the fog and the background. Second
it is used to specify a translucency threshold. By using a transmittance
larger than zero one can make sure that at least that amount of light will be
seen through the fog. With a transmittance of 0.3 you'll see at least 30% of
the background. Third it can be used to make a filtering fog. With a filter
value larger than zero the amount of background light given by the filer
value will be multiplied with the fog color. A filter value of 0.7 will lead
to a fog that filters 70% of the background light and leaves 30% unfiltered.

Fogs may be layered. That is, you can apply as many layers of fog as you
like. Generally this is most effective if each layer is a ground fog of
different color, altitude and with different turbulence values. To use
multiple layers of fogs, just add all of them to the scene.

You may optionally stir up the fog by adding turbulence. The turbulence
keyword may be followed by a float or vector to specify an amount of
turbulence to be used. The omega, lambda and octaves turbulence parameters
may also be specified. See section "Pattern Modifiers" for details on all of
these turbulence parameters.

Additionally the fog turbulence may be scaled along the direction of the
viewing ray using the turb_depth amount. Typical values are from 0.0 to 1.0
or more. The default value is 0.5 but any float value may be used.

You should note that the fog feature will not work if the camera is inside a
non-hollow object (see section "Empty and Solid Objects" for a detailed
explanation).

7.7.4            Sky Sphere

The sky sphere is used create a realistic sky background without the need of
an additional sphere to simulate the sky. Its syntax is:

  sky_sphere {
    pigment { PIGMENT1 }
    pigment { PIGMENT2 }
    pigment { PIGMENT3 }
    ...
    [ TRANSFORMATION ]
  }


The sky sphere can contain several pigment layers with the last pigment being
at the top, i. e. it is evaluated last, and the first pigment being at the
bottom, i. e. it is evaluated first. If the upper layers contain filtering
and/or transmitting components lower layers will shine through. If not lower
layers will be invisible.

The sky sphere is calculated by using the direction vector as the parameter
for evaluating the pigment patterns. This leads to results independent from
the view point which pretty good models a real sky where the distance to the
sky is much larger than the distances between visible objects.

If you want to add a nice color blend to your background you can easily do
this by using the following example.

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [ 0.5  color CornflowerBlue ]
        [ 1.0  color MidnightBlue ]
      }
      scale 2
      translate -1
    }
  }


This gives a soft blend from CornflowerBlue at the horizon to MidnightBlue at
the zenith. The scale and translate operations are used to map the direction
vector values, which lie in the range from <-1, -1, -1> to <1, 1, 1>, onto
the range from <0, 0, 0> to <1, 1, 1>. Thus a repetition of the color blend
is avoided for parts of the sky below the horizon.

In order to easily animate a sky sphere you can transform it using the known
transformations described in "Transformations". Though it may not be a good
idea to translate or scale a sky sphere - the results are hardly predictable
- it is quite useful to be able to rotate it. In an animation the color
blendings of the sky can be made to follow the rising sun for example.

You should note that only one sky sphere can be used in any scene. It also
will not work as you might expect if you use camera types like the
orthographic or cylindrical camera. The orthographic camera uses parallel
rays and thus you'll only see a very small part of the sky sphere (you'll get
one color skies in most cases). Reflections in curved surface will work
though, e. g. you will clearly see the sky in a mirrored ball.

7.7.5            Rainbow

Rainbows are implemented using fog-like, circular arcs. Their syntax is:

  rainbow {
    direction <DIR>
    angle ANGLE
    width WIDTH
    distance DISTANCE
    color_map { COLOUR_MAP }
    [ jitter JITTER ]
    [ up <UP> ]
    [ arc_angle ARC_ANGLE ]
    [ falloff_angle FALLOFF_ANGLE ]
  }


The direction vector determines the direction of the (virtual) light that is
responsible for the rainbow. Ideally this is an infinitely far away light
source like the sun that emits parallel light rays. The position and size of
the rainbow are specified by the angle and width keywords. To understand how
they work you should first know how the rainbow is calculated.

For each ray the angle between the rainbow's direction vector and the ray's
direction vector is calculated. If this angle lies in the interval from
ANGLE-WIDTH/2 to ANGLE+WIDTH/2 the rainbow is hit by the ray. The color is
then determined by using the angle as an index into the rainbow's colormap.
After the color has been determined it will be mixed with the background
color in the same way like it is done for fogs.

Thus the angle and width parameters determine the angles under which the
rainbow will be seen. The optional jitter keyword can be used to add random
noise to the index. This adds some irregularity to the rainbow that makes it
look more realistic.

The distance keyword is the same like the one used with fogs. Since the
rainbow is a fog-like effect it's possible that the rainbow is noticeable on
objects. If this effect is not wanted it can be avoided by using a large
distance value. By default a sufficiently large value is used to make sure
that this effect does not occur.

The color_map keyword is used to assign a color map that will be mapped onto
the rainbow. To be able to create realistic rainbows it is important to know
that the index into the color map increases with the angle between the ray's
and rainbow's direction vector. The index is zero at the innermost ring and
one at the outermost ring. The filter and transmittance values of the colors
in the color map have the same meaning as the ones used with fogs (see
section "Fog").

The default rainbow is a 360 degree arc that looks like a circle. This is no
problem as long as you have a ground plane that hides the lower, non-visible
part of the rainbow. If this isn't the case or if you don't want the full arc
to be visible you can use the optional keywords up, arc_angle and
falloff_angle to specify a smaller arc.

The arc_angle keyword determines the size of the arc in degrees (from 0 to
360 degrees). A value smaller than 360 degrees results in an arc that
abruptly vanishes. Since this doesn't look nice you can use the falloff_angle
keyword to specify a region in which the rainbow will smoothly blend into the
background making it vanish softly. The falloff angle has to be smaller or
equal to the arc angle.

The up keyword determines were the zero angle position is. By changing this
vector you can rotate the rainbow about its direction. You should note that
the arc goes from -ARC_ANGLE/2 to +ARC_ANGLE/2. The soft regions go from
-ARC_ANGLE/2 to -FALLOFF_ANGLE/2 and from +FALLOFF_ANGLE/2 to +ARC_ANGLE/2.

The following example generates a 120 degrees rainbow arc that has a falloff
region of 30 degrees at both ends:

  rainbow {
    direction <0, 0, 1>
    angle 42.5
    width 5
    distance 1000
    jitter 0.01
    color_map { Rainbow_Color_Map }
    up <0, 1, 0>
    arc_angle 240
    falloff_angle 60
  }


It is possible to use any number of rainbows and to combine them with other
atmospheric effects.

7.8              Global Settings

The global_settings statement is a catch-all statement that gathers together
a number of global parameters. The statement may appear anywhere in a scene
as long as its not inside any other statement. You may have multiple
global_settings statements in a scene. Whatever values were specified in the
last global_settings statement override any previous settings. Regardless of
where you specify the statement, the feature applies to the entire scene.

Note that some items which were language directives in previous versions of
POV-Ray have been moved inside the global_settings statement so that it is
more obvious to the user that their effect is global. The old syntax is
permitted but generates a warning.

  global_settings {
    adc_bailout FLOAT
    ambient_light COLOR
    assumed_gamma FLOAT
    hf_gray_16 BOOLEAN
    irid_wavelength COLOR
    max_intersections INTEGER
    max_trace_level INTEGER
    number_of_waves INTEGER
    radiosity { RADIOSITY_ITEMS... }
  }


Each item is optional and may appear in and order. If an item is specified
more than once, the last setting overrides previous values. Details on each
item are given in the following sections.

7.8.1            ADC_Bailout

In scenes with many reflective and transparent surfaces, POV-Ray can get
bogged down tracing multiple reflections and refractions that contribute very
little to the color of a particular pixel. The program uses a system called
Adaptive Depth Control (ADC) to stop computing additional reflected or
refracted rays when their contribution is insignificant.

You may use the global setting adc_bailout keyword followed by float value to
specify the point at which a ray's contribution is considered insignificant.

  global_settings { adc_bailout FLOAT }


The default value is 1/255, or approximately 0.0039, since a change smaller
than that could not be visible in a 24 bit image. Generally this setting is
perfectly adequate and should be left alone. Setting adc_bailout to 0 will
disable ADC, relying completely on max_trace_level to set an upper limit on
the number of rays spawned.

See section "Max_Trace_Level" for details on how ADC and max_trace_level
interact.

7.8.2            Ambient Light

Ambient light is used to simulate the effect of inter-diffuse reflection that
is responsible for lighting areas that partially or completely lie in shadow.
POV-Ray provides an ambient light source to let you easily change the
brightness of the ambient lighting without changing every ambient value in
all finish statements. It also lets you create interesting effects by
changing the color of the ambient light source. The syntax is:

  global_settings { ambient_light COLOR }


The default is a white ambient light source set at rgb <  1,1,1>. The actual
ambient used is:    AMBIENT = FINISH_AMBIENT * GLOBAL_AMBIENT


7.8.3            Assumed_Gamma

Many people may have noticed at one time or another that some images are too
bright or dim when displayed on their system. As a rule, Macintosh users find
that images created on a PC are too bright, while PC users find that images
created on a Macintosh are too dim.

The assumed_gamma global setting works in conjunction with the Display_Gamma
INI setting (see section "Display Hardware Settings") to ensure that scene
files render the same way across the wide variety of hardware platforms that
POV-Ray is used on. The assumed gamma setting is used in a scene file by
adding

  global_settings { assumed_gamma FLOAT }


where the assumed gamma value is the correction factor to be applied before
the pixels are displayed and/or saved to disk. For scenes created in older
versions of POV-Ray, the assumed gamma value will be the same as the display
gamma value of the system the scene was created on. For PC systems, the most
common display gamma is 2.2, while for scenes created on Macintosh systems
should use a scene gamma of 1.8. Another gamma value that sometimes occurs in
scenes is 1.0.

Scenes that do not have an assumed_gamma global setting will not have any
gamma correction performed on them, for compatibility reasons. If you are
creating new scenes or rendering old scenes, it is strongly recommended that
you put in an appropriate assumed_gamma global setting. For new scenes, you
should use an assumed gamma value of 1.0 as this models how light appears in
the real world more realistically.

The following sections explain more thoroughly what gamma is and why it is
important.

7.8.3.1          Monitor Gamma

The differences in how images are displayed is a result of how a computer
actually takes an image and displays it on the monitor. In the process of
rendering an image and displaying it on the screen, several gamma values are
important, including the POV scene file or image file gamma and the monitor
gamma.

Most image files generated by POV-Ray store numbers in the range from 0 to
255 for each of the red, green and blue components of a pixel. These numbers
represent the intensity of each color component, with 0 being black and 255
being the brightest color (either 100% red, 100% green or 100% blue). When an
image is displayed, the graphics card converts each color component into a
voltage which is sent to the monitor to light up the red, green and blue
phosphors on the screen. The voltage is usually proportional to the value of
each color component.

Gamma becomes important when displaying intensities that aren't the maximum
or minimum possible values. For example, 127 should represent 50% of the
maximum intensity for pixels stored as numbers between 0 and 255. On systems
that don't do gamma correction, 127 will be converted to 50% of the maximum
voltage, but because of the way the phosphors and the electron guns in a
monitor work, this may be only 22% of the maximum color intensity on a
monitor with a gamma of 2.2. To display a pixel which is 50% of the maximum
intensity on this monitor, we would need a voltage of 73% of the maximum
voltage, which translates to storing a pixel value of 186.

The relationship between the input pixel value and the displayed intensity
can be approximated by an exponential function

  obright = ibright ^ display_gamma


where obright is the output intensity and ibright is the input pixel
intensity. Both values are in the range from 0 to 1 (0% to 100%). Most
monitors have a fixed gamma value in the range from 1.8 to 2.6. Using the
above formula with display_gamma values greater than 1 means that the output
brightness will be less than the input brightness. In order to have the
output and input brightness be equal an overall system gamma of 1 is needed.
To do this, we need to gamma correct the input brightness in the same manner
as above but with a gamma value of 1/display_gamma before it is sent to the
monitor. To correct for a display gamma of 2.2, this pre-monitor gamma
correction uses a gamma value of 1.0/2.2 or approximately 0.45.

How the pre-monitor gamma correction is done depends on what hardware and
software is being used. On Macintosh systems, the operating system has taken
it upon itself to insulate applications from the differences in display
hardware. Through a gamma control panel the user may be able to set the
actual monitor gamma and MacOS will then convert all pixel intensities so
that the monitor will appear to have the specified gamma value. On Silicon
Graphics machines, the display adapter has built-in gamma correction
calibrated to the monitor which gives the desired overall gamma (the default
is 1.7). Unfortunately, on PCs and most UNIX systems, it is up to the
application to do any gamma correction needed.

7.8.3.2          Image File Gamma

Since most PC and UNIX applications and image file formats don't understand
display gamma, they don't do anything to correct for it. As a result, users
creating images on these systems adjust the image in such a way that it has
the correct brightness when displayed. This means that the data values stored
in the files are made brighter to compensate for the darkening effect of the
monitor. In essence, the 0.45 gamma correction is built in to the image files
created and stored on these systems. When these files are displayed on a
Macintosh system, the gamma correction built in to the file, in addition to
gamma correction built into MacOS, means that the image will be too bright.
Similarly, files that look correct on Macintosh or SGI systems because of the
built-in gamma correction will be too dark when displayed on a PC.

The new PNG format files generated by POV-Ray 3.0 overcome the problem of too
much or not enough gamma correction by storing the image file gamma (which is
1.0/display_gamma) inside the PNG file when it is generated by POV-Ray. When
the PNG file is later displayed by a program that has been set up correctly,
it uses this gamma value as well as the current display gamma to correct for
the potentially different display gamma used when originally creating the
image.

Unfortunately, of all the image file formats POV-Ray supports, PNG is the
only one that has any gamma correction features and is therefore preferred
for images that will be displayed on a wide variety of platforms.

7.8.3.3          Scene File Gamma

The image file gamma problem itself is just a result of how scenes themselves
are generated in POV-Ray. When you start out with a new scene and are placing
light sources and adjusting surface textures and colors, you generally make
several attempts before the lighting is how you like it. How you choose these
settings depends upon the preview image or the image file stored to disk,
which in turn is dependent upon the overall gamma of the display hardware
being used.

This means that as the artist you are doing gamma correction in the POV-Ray
scene file for your particular hardware. This scene file will generate an
image file that is also gamma corrected for your hardware and will display
correctly on systems similar to your own. However, when this scene is
rendered on another platform, it may be too bright or too dim, regardless of
the output file format used. Rather than have you change all the scene files
to have a single fixed gamma value (heaven forbid!), POV-Ray 3.0 allows you
to specify in the scene file the display gamma of the system that the scene
was created on.

The assumed_gamma global setting, in conjunction with the Display_Gamma INI
setting lets POV-Ray know how to do gamma correction on a given scene so that
the preview and output image files will appear the correct brightness on any
system. Since the gamma correction is done internally to POV-Ray, it will
produce output image files that are the correct brightness for the current
display, regardless of what output format is used. As well, since the gamma
correction is performed in the high-precision data format that POV-Ray uses
internally, it produces better results than gamma correction done after the
file is written to disk.

Although you may not notice any difference in the output on your system with
and without an assumed_gamma setting, the assumed gamma is important if the
scene is ever rendered on another platform.

7.8.4            HF_Gray_16

The hf_gray_16 setting is useful when using POV-Ray to generate heightfields
for use in other POV-Ray scenes. The syntax is...

  global_settings { hf_gray_16 BOOLEAN }


The boolean value turns the option on or off. If the keyword is specified
without the boolean value then the option is turned on. If hf_gray_16 is not
specified in any global_settings statement in the entire scene then the
default is off.

When hf_gray_16 is on, the output file will be in the form of a heightfield,
with the height at any point being dependent on the brightness of the pixel.
The brightness of a pixel is calculated in the same way that color images are
converted to grayscale images:

  height = 0.3 * red + 0.59 * green + 0.11 * blue


Setting the hf_gray_16 option will cause the preview display, if used, to be
grayscale rather than color. This is to allow you to see how the heightfield
will look because some file formats store heightfields in a way that is
difficult to understand afterwards. See section "Height Field" for a
description of how POV-Ray heightfields are stored for each file type.

7.8.5            Irid_Wavelength

Iridescence calculations depend upon the dominant wavelengths of the primary
colors of red, green and blue light. You may adjust the values using the
global setting irid_wavelength as follows...   global_settings { irid_wavelen


The default value is rgb <0.25,0.18,0.14> and any filter or transmit values
are ignored. These values are proportional to the wavelength of light but
they represent no real world units.

In general, the default values should prove adequate but we provide this
option as a means to experiment with other values.

7.8.6            Max_Trace_Level

In scenes with many reflective and transparent surfaces POV-Ray can get
bogged down tracing multiple reflections and refractions that contribute very
little to the color of a particular pixel. The global setting max_trace_level
defines the maximum number of recursive levels that POV-Ray will trace a ray.


  global_settings { max_trace_level INTEGER }


This is used when a ray is reflected or is passing through a transparent
object and when shadow rays are cast. When a ray hits a reflective surface,
it spawns another ray to see what that point reflects. That is trace level
one. If it hits another reflective surface another ray is spawned and it goes
to trace level two. The maximum level by default is five.

One speed enhancement added to POV-Ray in version 3.0 is Adaptive  Depth
Control (ADC). Each time a new ray is spawned as a result of reflection or
refraction its contribution to the overall color of the pixel is reduced by
the amount of reflection or the filter value of the refractive surface. At
some point this contribution can be considered to be insignificant and there
is no point in tracing any more rays. Adaptive depth control is what tracks
this contribution and makes the decision of when to bail out. On scenes that
use a lot of partially reflective or refractive surfaces this can result in a
considerable reduction in the number of rays fired and makes it safer to use
much higher max_trace_level values.

This reduction in color contribution is a result of scaling by the reflection
amount and/or the filter values of each surface, so a perfect mirror or
perfectly clear surface will not be optimizable by ADC. You can see the
results of ADC by watching the Rays Saved and Highest Trace Level displays on
the statistics screen.

The point at which a ray's contribution is considered insignificant is
controlled by the adc_bailout value. The default is 1/255 or approximately
0.0039 since a change smaller than that could not be visible in a 24 bit
image. Generally this setting is perfectly adequate and should be left alone.
Setting adc_bailout to 0 will disable ADC, relying completely on
max_trace_level to set an upper limit on the number of rays spawned.

If max_trace_level is reached before a non-reflecting surface is found and if
ADC hasn't allowed an early exit from the ray tree the color is returned as
black. Raise max_trace_level if you see black areas in a reflective surface
where there should be a color.

The other symptom you could see is with transparent objects. For instance,
try making a union of concentric spheres with a clear texture on them. Make
ten of them in the union with radius's from 1 to 10 and render the scene. The
image will show the first few spheres correctly, then black. This is because
a new level is used every time you pass through a transparent surface. Raise
max_trace_level to fix this problem.

Note that raising max_trace_level will use more memory and time and it could
cause the program to crash with a stack overflow error, although ADC will
alleviate this to a large extent. Values for max_trace_level are not
restricted, so it can be set to any number as long as you have the time and
memory. However, increasing its setting does not necessarily equate to
increased image quality unless such depths are really needed by the scene.

7.8.7            Max_Intersections

POV-Ray uses a set of internal stacks to collect ray/object intersection
points. The usual maximum number of entries in these I-Stacks is 64. Complex
scenes may cause these stacks to overflow. POV-Ray doesn't stop but it may
incorrectly render your scene. When POV-Ray finishes rendering, a number of
statistics are displayed. If you see I-Stack Overflows reported in the
statistics you should increase the stack size. Add a global setting to your
scene as follows:

  global_settings { max_intersections INTEGER }


7.8.8            Number_Of_Waves

The wave and ripples pattern are generated by summing a series of waves, each
with a slightly different center and size. By default, ten waves are summed
but this amount can be globally controlled by changing the number_of_waves
setting.

  global_settings { number_of_waves INTEGER }


Changing this value affects both waves and ripples alike on all patterns in
the scene.

7.8.9            Radiosity

Important notice: The radiosity feature in POV-Ray 3.0 are somewhat
experimental. There is a high probability that the design and implementation
of these features will be changed in future versions. We cannot guarantee
that scenes using these features in 3.0 will render identically in future
releases or that full backwards compatibility of language syntax can be
maintained.

Radiosity is an extra calculation that more realistically computes the
diffuse interreflection of light. This diffuse interreflection can be seen if
you place a white chair in a room full of blue carpet, blue walls and blue
curtains. The chair will pick up a blue tint from light reflecting off of
other parts of the room. Also notice that the shadowed areas of your
surroundings are not totally dark even if no light source shines directly on
the surface. Diffuse light reflecting off of other objects fills in the
shadows. Typically ray-tracing uses a trick called ambient light to simulate
such effects but it is not very accurate.

Radiosity is more accurate than simplistic ambient light but it takes much
longer to compute. For this reason, POV-Ray does not use radiosity by
default. Radiosity is turned on using the Radiosity INI file option or the
+QR command line switch.

The following sections describes how radiosity works, how to control it with
various global settings and tips on trading quality vs. speed.

7.8.9.1          How Radiosity Works

The problem of ray-tracing is to figure out what the light level is at each
point that you can see in a scene. Traditionally, in ray tracing, this is
broken into the sum of these components:

  - Diffuse, the effect that makes the side of things facing the light
  - Specular, the effect that makes shiny things have dings or sparkles on
  - Ambient, the general all-over light level that any scene has, which keeps
    things in shadow from being pure black.


POV's radiosity system, based on a method by Greg Ward, provides a way to
replace the last term - the constant ambient light value - with a light level
which is based on what surfaces are nearby and how bright in turn they are.

The first thing you might notice about this definition is that it is
circular: the light of everything is dependent on everything else and vice
versa. This is true in real life but in the world of ray-tracing, we can make
an approximation. The approximation that is used is: the objects you are
looking at have their ambient values calculated for you by checking the other
objects nearby. When those objects are checked during this process, however,
a traditional constant ambient term is used.

How does POV-Ray calculate the ambient term for each point? By sending out
more rays, in many different directions, and averaging the results. A typical
point might use 200 or more rays to calculate its ambient light level
correctly.

Now this sounds like it would make the ray-tracer 200 times slower. This is
true, except that the software takes advantage of the fact that ambient light
levels change quite slowly (remember, shadows are calculated separately, so
sharp shadow edges are not a problem). Therefore, these extra rays are sent
out only once in a while (about 1 time in 50), then these calculated values
are saved and reused for nearby pixels in the image when possible.

This process of saving and reusing values is what causes the need for a
variety of tuning parameters, so you can get the scene to look just the way
you want.

7.8.9.2          Adjusting Radiosity

As described earlier, radiosity is turned on by using the Radiosity INI file
option or the +QR command line switch. However radiosity has many parameters
that are specified in a radiosity statement inside a global_settings
statement as follows:

   global_settings {
     radiosity {
       brightness FLOAT
       count INTEGER
       distance_maximum FLOAT
       error_bound FLOAT
       gray_threshold FLOAT
       low_error_factor FLOAT
       minimum_reuse FLOAT
       nearest_count INTEGER
       recursion_limit INTEGER
     }
   }


Each item is optional and may appear in and order. If an item is specified
more than once the last setting overrides previous values. Details on each
item is given in the following sections.

7.8.9.2.1        brightness

This is the degree to which ambient values are brightened before being
returned upwards to the rest of the system. If an object is red < 1, 0, 0>,
with an ambient value of 0.3, in normal situations a red component of 0.3
will be added in. With radiosity on, assume it was surrounded by an object of
gra color <0.6, 0.6, 0.6>. The average color returned by the gathering
process will be the same. This will be multiplied by the texture's ambient
weight value of 0.3, returning <0.18, 0.18, 0.18>. This is much darker than
the 0.3 which would be added in normally. Therefore, all returned values are
brightened by the inverse of the average of the calculated values, so the
average ambient added in does not change. Some will be higher than specified
(higher than 0.3 in this example) and some will be lower but the overall
scene brightness will be unchanged.


7.8.9.2.2        count

The number of rays that are sent out whenever a new radiosity value has to be
calculated is given by count. Values of 100 to 150 make most scenes look
good. Higher values might be needed for scenes with high contrast between
light levels or small patches of light causing the illumination. This would
be used only for a final rendering on an image because it is very compute
intensive. Since most scenes calculate the ambient value at 1% to 2% of
pixels, as a rough estimate, your rendering will take 1% to 2% of this number
times as long. If you set it to 300 your rendering might take 3 to 6 times as
long to complete (1% to 2% times 300).

When this value is too low, the light level will tend to look a little bit
blotchy, as if the surfaces you're looking at were slightly warped. If this
is not important to your scene (as in the case that you have a bump map or if
you have a strong texture) then by all means use a lower number.


7.8.9.2.3        distance_maximum

The distance_maximum is the only tuning value that depends upon the size of
the objects in the scene. This one must be set for scenes to render
properly... the rest can be ignored for a first try. It is difficult to
describe the meaning simply but it sets the distance in model units from a
sample at which the error is guaranteed to hit 100% (radiosity_error_bound
>=1): no samples are reused at a distance larger than this from their
original calculation point.

Imagine an apple at the left edge of a table. The goal is to make sure that
samples on the surface of the table at the right are not used too close to
the apple and definitely not underneath the apple. If you had enough rays
there wouldn't be a problem since one of them would be guaranteed to hit the
apple and set the reuse radius properly for you. In practice, you must limit
this.

We use this technique: find the object in your scene which might have the
following problem: a small object on a larger flatter surface that you want
good ambient light near. Now, how far from this would you have to get to be
sure that one of your rays had a good chance of hitting it? In the
apple-on-the-table example, assuming I used one POV-Ray unit as one inch, I
might use 30 inches. A theoretically sound way (when you are running lots of
rays) is the distance at which this object's top is 5 degrees above the
horizon of the sample point you are considering. This corresponds to about 11
times the height of the object. So, for a 3-inch apple, 33 inches makes some
sense. For good behavior under and around a 1/3 inch pea, use 3 inches etc.
Another VERY rough estimate is one third the distance from your eye position
to the point you are looking at. The reasoning is that you are probably no
more than 90 inches from the apple on the table, if you care about the
shading underneath it.


7.8.9.2.4        error_bound

The error_bound is one of the two main speed/quality tuning values (the other
is of course the number of rays shot). In an ideal world, this would be the
only value needed. It is intended to mean the fraction of error tolerated.
For example, if it were set to 1 the algorithm would not calculate a new
value until the error on the last one was estimated at as high as 100%.
Ignoring the error introduced by rotation for the moment, on flat surfaces
this is equal to the fraction of the reuse distance, which in turn is the
distance to the closest item hit. If you have an old sample on the floor 10
inches from a wall, an error bound of 0.5 will get you a new sample at a
distance of about 5 inches from the wall. 0.5 is a little rough and ready,
0.33 is good for final renderings. Values much lower than 0.3 take forever.


7.8.9.2.5        gray_threshold

Diffusely interreflected light is a function of the objects around the point
in question. Since this is recursively defined to millions of levels of
recursion, in any real life scene, every point is illuminated at least in
part by every other part of the scene. Since we can't afford to compute this,
we only do one bounce and the calculated ambient light is very strongly
affected by the colors of the objects near it. This is known as color bleed
and it really happens but not as much as this calculation method would have
you believe. The gray_threshold variable grays it down a little, to make your
scene more believable. A value of .6 means to calculate the ambient value as
60% of the equivalent gray value calculated, plus 40% of the actual value
calculated. At 0%, this feature does nothing. At 100%, you always get
white/gray ambient light, with no hue. Note that this does not change the
lightness/darkness, only the strength of hue/grayness (in HLS terms, it
changes H only).


7.8.9.2.6        low_error_factor

If you calculate just enough samples, but no more, you will get an image
which has slightly blotchy lighting. What you want is just a few extra
interspersed, so that the blending will be nice and smooth. The solution to
this is the mosaic preview: it goes over the image one or more times
beforehand, calculating radiosity values. To ensure that you get a few extra,
the radiosity algorithm lowers the error bound during the pre-final passes,
then sets it back just before the final pass. This tuning value sets the
amount that the error bound is dropped during the preliminary image passes.
If your low error factor is 0.8 and your error bound is set to 0.4 it will
really use an error bound of 0.32 during the first passes and 0.4 on the
final pass.


7.8.9.2.7        minimum_reuse

The minimum effective radius ratio is set by minimum_reuse. This is the
fraction of the screen width which sets the minimum radius of reuse for each
sample point (actually, it is the fraction of the distance from the eye but
the two are roughly equal). For example, if the value is 0.02 the radius of
maximum reuse for every sample is set to whatever ground distance corresponds
to 2% of the width of the screen. Imagine you sent a ray off to the horizon
and it hits the ground at a distance of 100 miles from your eyepoint. The
reuse distance for that sample will be set to 2 miles. At a resolution of
300*400 this will correspond to (very roughly) 8 pixels. The theory is that
you don't want to calculate values for every pixel into every crevice
everywhere in the scene, it will take too long. This sets a minimum bound for
the reuse. If this value is too low, (which is should be in theory) rendering
gets slow, and inside corners can get a little grainy. If it is set too high,
you don't get the natural darkening of illumination near inside edges, since
it reuses. At values higher than 2% you start getting more just plain errors,
like reusing the illumination of the open table underneath the apple.

Remember that this is a unitless ratio.


7.8.9.2.8        nearest_count

The nearest_count value is the maximum number of old ambient values blended
together to create a new interpolated value. It will always be the n
geometrically closest reusable points that get used. If you go lower than 4,
things can get pretty patchy. This can be good for debugging, though. Must be
no more than 10, since that is the size of the array allocated.


7.8.9.2.9        radiosity_quality


7.8.9.2.10       recursion_limit

This value determines how many recursion levels are used to calculate the
diffuse inter-reflection. Valid values are one and two.


7.8.9.3          Tips on Radiosity

If you want to see where your values are being calculated set radiosity_count
down to about 20, set radiosity_nearest_count to 1 and set radiosity_gray to
0. This will make everything maximally patchy, so you'll be able to see the
borders between patches. There will have been a radiosity calculation at the
center of most patches. As a bonus, this is quick to run. You can then change
the radiosity_error_bound up and down to see how it changes things. Likewise
modify radiosity_reuse_dist_min and max.

One way to get extra smooth results: crank up the sample count (we've gone as
high as 1300) and drop the low_error_factor to something small like 0.6. Bump
up the reuse_count to 7 or 8. This will get better values, and more of them,
then interpolate among more of them on the last pass. This is not for people
with a lack of patience since it is like a squared function. If your
blotchiness is only in certain corners or near certain objects try tuning the
error bound instead. Never drop it by more than a little at a time, since the
run time will get very long.

If your scene looks good but right near some objects you get spots of the
right (usually darker) color showing on a flat surface of the wrong color
(same as far away from the object), then try dropping reuse_dist_max. If that
still doesn't work well increase your ray count by 100 and drop the error
bound just a bit. If you still have problems, drop reuse_nearest_count to
about 4.
