document: An efficient and stable ray tracing algorithm for parametric surfaces In this paper , we propose an efficient and stable algorithm for finding 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 using Newton 's method is the closest . When Newton 's method fails to achieve convergence , we use Bezier clipping substitution to find the intersection points . This combination achieves a significant improvement in tracing primary rays . A similar approach successfully improves the performance of tracing secondary rays
doc_bio_tags: O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O B I O O O O B I I O O O O O O O O O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: parametric surfaces bezier clipping ray coherence newton iteration obstruction detection technique convergence
abstractive_keyphrases: efficient stable ray tracing algorithm ray-surface intersections newton method primary ray tracing secondary ray tracing