Realtime Rendering of Parametric Surfaces

(20.07.2008)

Parametric Surfaces, e.g. Bezier surfaces, have a solid mathematical foundation and are used in many areas. However the optimal way of rendering those is not immediately obvious.
Raytracing the surface directly has to deal with numerical instabilities, especially near silhouettes. Therefore most applications tesselate the surface into a triangle mesh. This usually implies a compromise between quality and speed/memory consumption.
An interesting approach is the REYES algorithm, which tesselates the parametric surface for each frame. It aims to generate triangles such that each triangle has an area of approximately one pixel on screen.
This provides a sampling of the geometry, that is close to perfect; However it is computationally very expensive. It is the goal of this project to develop an algorithm similar to REYES that works on modern GPUs to bring the qualitative advantages to real-time applications.