Interactive Ray Tracing of Trimmed Bicubic Bézier Surfaces without Triangulation

Abstract

By carefully exploiting the resources of today's computer hardware, interactive ray tracing recently became reality even on a single commodity PC. In most of these implementations triangles are used as the only geometric primitive. However, direct rendering of free-form surfaces would be advantageous for a large number of applications, since robust tessellation of complex scenes into triangles is a very time-consuming process. Additionally, scenes consisting of free-form surfaces require less memory and provide a much higher precision resulting in less rendering artifacts. In this paper, we present our implementation of an efficient and robust algorithm for rapidly finding intersections between rays and trimmed bicubic Bézier surfaces. Using SIMD instructions provided by many of today's CPUs, we perform the intersection test of a packet of four rays with a single Bézier surface in parallel. An optimized bounding volume hierarchy provides good initial guesses needed for fast convergence of the Newton iteration, which forms the core of our intersection algorithm. As a result, we demonstrate that it is feasible to render complex scenes of several thousand Bézier surfaces at video resolution with interactive frame rates on a single PC.