Ray Tracing Triangular Bezier Patches

Abstract

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 presentation17 . Unlike a previous approach which was based on a combination of hierarchical subdivision and a Newton–like iteration scheme21 , this work adapts the concept of Bézier clipping to the triangular domain. The problem of reporting wrong intersections, inherent to the original Bézier clipping algorithm14 , 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.