An efficient and stable ray tracing algorithm for parametric surfaces

Abstract

In this paper, we propose an efficient and stable algorithm for finding the ray-surface intersections. Newton's method and Bezier clipping are adapted to form the core of our algorithm. Ray coherence is used to find starting points for Newton iteration. We introduce an obstruction detection technique to verify whether an intersection point found by using Newton's method is the closest one. When Newton's method fails to achieve convergence, we use Bezier clipping as the substitution to find the intersection points. This combination achieves significant improvement in tracing primary rays. A similar approach also successfully improves the performance in tracing secondary rays.