Fitting a Cubic Bezier to a Parametric Function

What is it about?

A common problem encountered in vector graphics is how to express complicated functions in terms of simpler functions which can be quickly rendered on a computer. To this end, fitting a cubic Bezier curve to a known parametric function is studied. Three criteria are used: fitting curvature at endpoints, fitting center of mass, and least squares orthogonal distance fitting. We apply the curvature method to a curve that has a singularity at one endpoint and show that it fails in this limit. We apply the center of mass method to a curve that has multiple solutions and show that it fails to detect them all. The least squares method succeeds in all cases, but is more complex to apply, since it involves successive approximations.

Featured Image