**New 2013 version** HTML5 based

- Bezier spline curves

DeCasteljau algorithm. Linear, quadratic and cubic Bezier splines. Bezier spline subdivision. Bernstein polynomials. Recurrence relations. How to plot Bezier spline and basis functions. Proof of the deCasteljau algorithm. - More Bezier splines Math

Affine invariance. Convex hull. Linear precision. Differentiation of the Bezier curve. Deriving the deCasteljau algorithm. Two remarks. - Interpolating Lagrange curve

Interpolating curves. Lagrange polynomials. Knots. Aitken algorithm. Lagrange curve oscillations. - Interpolating Cardinal and Catmull-Rom splines

Continuity. Building a complex spline. Getting rid of tangents. Cardinal curve subdivision. - B-splines
- Building cubic B-spline

C^{2}continuity. de Boor points. Cox - de Boor algorithm. Local coordinates. - B-spline basis functions

Recurrence relations. Knot vectors. Uniform B-splines. Closed curves. - Nonuniform B-splines

Handling endpoints. - Interpolating cubic B-splines

Bezier control points. Solving banded equations. Handling the terminal tangents.

- Building cubic B-spline
- NURBS

Weighted control points. Perspective projection. Conic sections. Circular arcs.**3D Spline Surfaces**(with interactive VRMLs) - Tensor product spline surfaces

Bezier, NURBS and Cardinal spline patches. Normals. SplineGlobe. - Points, Nets, Patches...
*(mainly questions yet :)*

NURBS, "Hash" or triangular patches? - Cubic Bezier patch with adaptive
subdivision
*WebGL***3D Examples** - Spline
based nonlinear morphing

"How to teach shark to swim" - Flight animation
- 3D gallery
- WebGL Demos

I used these courses and papers

- "Interactive Curves and Surfaces" by
*Alyn Rockwood, Peter Chambers* - "Introduction to Computer Graphics" University of Waterloo, Department of Computer Science (html copy)
- "Advanced
Graphics Study Guide, 2000-2001. Splines" by
*Neil Dodgson* - Introduction
to Computing with Geometry Notes by
*C.-K. Shene* - NURBS
in VRML by
*Holger Grahn, Thomas Volk, Hans J. Wolters* - A complete algorithm for real-time spline-based
character animation by
*Martin D. Hash*

All sources are free.
The whole Splines.zip (200 kb)
*Evgeny Demidov*

E-notes Bezier spline curves