Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces

Raytracing has become a popular method for generating realistic images and movies. The progress in hardware development shows that the real time raytracing on a single PC might be possible in the ongoing future. Obviously, that new generation of raytracing based applications will require more visualization precision and flexibility. Most of the modern raytracing based applications only deal with triangles as basic primitives, which brings limitations to an application and may cause visual artifacts to appear. NURBS surface representation is common for most of 3D modeling tools because of its compactness and useful geometric properties of NURBS surfaces. Using the direct raytracing NURBS surfaces, one can achieve better quality of rendered images. Although, many such approaches have already been presented, almost all of them suffer from numerical problems or do not work in some special cases. This paper presents a modified Bézier clipping method for finding ray - NURBS surface intersection points, which is fast, robust, and numerically stable