Subject 5.08: How do I find the intersection of a ray and a bezier surface?
Joy I.K. and Bhetanabhotla M.N., “Ray tracing parametric surfaces utilizing numeric techniques and ray coherence”, Computer Graphics, 16, 1986, 279-286 Joy and Bhetanabhotla is only one approach of three major method classes: tessellation, direct computation, and a hybrid of the two. Tessellation is relatively easy (you intersect the polygons making up the tessellation) and has no numerical problems, but can be inaccurate; direct is cheap on memory, but very expensive computationally, and can (and usually does) suffer from precision problems within the root solver; hybrids try to blend the two.
