Generative CSG Models for Real Time Graphics

Generative parametric CSG models, introduced by Snyder in 1992, have many desirable properties. Their functional representation is generally quite compact and resolution independent, since surfaces are represented as piecewise continuous functional programs. However, in practice they have proven impractical for real time rendering because of the difficulty of compactly and exactly representing the implicit curves of intersection between general parametric surfaces and because there was no published algorithm for triangulating the surfaces in real time. Our new algorithm computes an exact, piecewise parametric representation for the implicit curves of intersection. The new piecewise parametric curve representation is very compact and can be evaluated efficiently at run time, making it possible to change triangulation density dynamically. We have also developed a triangulation algorithm which effectively uses modern GPU’s to render generative CSG models at high speed. Complex generative CSG models made with our system have a memory footprint of just 7-11 KBytes, which is orders of magnitude smaller than the equivalent polygonal mesh representation.