Abstract: A new algorithm for ray tracing parametric surface patches is presented. The method uses quasi-Newton iteration to solve the ray/surface intersection and utilizes ray-to-ray coherence by using numerical information from adjoining rays as initial approximations to the quasi-Newton algorithm. Techniques based upon object space subdivisions are used to insure convergence to the correct intersection point. Examples are given of the use of the algorithm in scenes containing Bézier surface patches. Results show that a significant number of ray/surface intersections on these parametric surface patches can be found using very few iterations, giving a significant computational savings.