An efficient and stable ray tracing algorithm for parametric surfaces

Shyue Wu Wang*, Zen-Chung Shih, Ruei Chuan Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


In this paper, we propose an efficient and stable algorithm for finding the ray-surface intersections. Newton's method and Bézier clipping are adapted to form the core of our algorithm. Ray coherence is used to find starting points of 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 Bézier 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.

Original languageEnglish
Pages (from-to)541-561
Number of pages21
JournalJournal of Information Science and Engineering
Issue number4
StatePublished - 1 Jul 2002


  • Bézier clipping
  • Bézier surface
  • Newton's method
  • Parametric surfaces
  • Ray coherence
  • Ray tracing

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