Ray Tracing Bézier Surfaces on GPU

In this report, we show how to implement direct ray tracing of B´ezier surfaces on graphics processing units (GPUs), in particular bicubic rectangular Bézier surfaces and nonparametric cubic Bézier triangles. We use Newton’s method for the rectangular case and show how to use this method to find the ray-surface intersection. For Newton’s method to work we must build a spatial partitioning hierarchy around each surface patch, and in general, hierarchies are essential to speed up the process of ray tracing. We have chosen to use bounding box hierarchies and show how to implement stackless traversal of such a structure on a GPU. For the nonparametric triangular case, we show how to find the wanted intersection by simply solving a cubic polynomial. Because of the limited precision of current GPUs, we also propose a numerical approach to solve the problem, using a one-dimensional Newton search