ABSTRACT
If we are going to build useful computer models of freeform shapes using Bezier curves and surfaces, we need procedures to do more than simply evaluate points along these curves and surfaces. We need algorithms to analyze their geometry. For example, to ray trace a Bezier patch, we need algorithms both for finding surface normals and for computing ray-surface intersections. In Chapter 24 we developed an algorithm for differentiating Bezier curves and surfaces, which allows us to find the surface normal of a Bezier patch at any parameter value by taking the cross product of the partial derivatives of the patch. Here we shall develop an algorithm that will permit us to compute the intersection of an arbitrary ray with a Bezier patch.
