filename     : pg00_roth
entry        : inproceedings
pages        : to appear
year         : 2000
title        : Ray Tracing Triangular Bézier Patches
author       : S. H. Martin Roth and Patrick Diezi and Markus H. Gross
booktitle    : Proceedings of the Eurographics 2001 (Manchester, UK, September 4-7, 2001), COMPUTER GRAPHICS Forum, Conference Issue
editor       : A. Chalmers and T.-M. Rhyne
publisher    : Blackwell Publishers
language     : English
month        : September
keywords     : Bernstein-Bézier, Ray Tracing, Triangular Patches, Bézier Clipping
abstract     :
We present a new approach to finding ray­patch intersections with triangular Bernstein­Bézier patches of arbitrary degree. This paper extends and complements on our short presentation at Pacific Graphics 2000. Unlike a previous approach which was based on a combination of hierarchical subdivision and a Newton­like iteration scheme, 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, is investigated and opposed to the triangular case. It turns out that reporting wrong hits is very improbable, even close to impossible, in the triangular set­up. 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.