Triangular Bezier clipping

Abstract

Introduces a new approach to finding ray-patch intersections with triangular Bernstein-Bezier patches of arbitrary degree. Unlike the approach of W.Sturzlinger (1998), which was based on a combination of hierarchical subdivision and a Newton-like iteration scheme, this work extends the concept of Bezier clipping to the triangular domain. The problem of reporting wrong intersections, which was inherent to the original Bezier clipping algorithm of T. Nishita et al. (1990), 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.