Raytracing Triangular Bézier Patches

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 investigated 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.