One answer to this question is to create a measure of the aesthetics of a curve that the computer can calculate and use this number as a measure of the aesthetics of the curve. For example, suppose that a curve defined on the parameter interval [a,b] has curvature k(s) where s is arc length. Then compute
for some l where 0 <= l <= 1 and say that the smaller the value of A, the nicer the curve. The value of l determines the precise nature of this measure:
Since everyone can have their own opinion on what makes a curve look nice, there are many different possible choices of l. Go to the discussion page to see some values of A for various curves and see which l you think is the best choice.
Curves with smaller values of A have less sharp corners and smaller overall turning angle. This means they look nicer. Using the Fundamental Theorem of Calculus, a geometric interpretation of the integrals used to define A can be derived. Go to the practice section to do this.
Many applications demand that hundreds of curve segments be created that all look nice. The large number of curves requires that some of this task be automated. To do this, one would define a whole family of curves that all meet the design constraints but still have some freedom about the exact nature of the curve. Then an algorithm is constructed that chooses remaining degrees of freedom to get a specific curve that has the value of A as small as possible. This automatically produces a nice-looking curve.