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Ray Tracing Triangular Bézier Patches
Author(s) -
Roth S. H. Martin,
Diezi Patrick,
Gross Markus H.
Publication year - 2001
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.00535
Subject(s) - bézier curve , clipping (morphology) , computer science , bounding overwatch , tracing , subdivision , hierarchy , ray tracing (physics) , set (abstract data type) , mathematics , simple (philosophy) , algorithm , geometry , artificial intelligence , epistemology , philosophy , linguistics , physics , archaeology , quantum mechanics , economics , market economy , history , programming language , operating system
We present a new approach to finding ray–patch intersections with triangular Bernstein–Bézier patches of arbitrary degree. This paper extends and complements on the short presentation 17 . Unlike a previous approach which was based on a combination of hierarchical subdivision and a Newton–like iteration scheme 21 , this work adapts the concept of Bézier clipping to the triangular domain. The problem of reporting wrong intersections, inherent to the original Bézier clipping algorithm 14 , is inves‐tigated and opposed to the triangular case. It turns out that reporting wrong hits is very improbable, even close to impossible, in the triangular set–up. A combination of Bézier clipping and a simple hierarchy of nested bounding volumes offers a reliable and accurate solution to the problem of ray tracing triangular Bézier patches.