Near Real-Time CSG (Constructive Solid Geometry) Rendering Using Tree Normalization and Geometric Pruning

Abstract

Abstract : Described is a set of algorithms for efficiently rendering a CSG- defined objective directly into a frame buffer without converting first to a boundary representation. The method requires only that the frame buffer contain sufficient memory to hold two color values, two z values, and three one-bit flags. The algorithm first converts the CSG tree to a normalized form that is analogous to the sum-of-products form for boolean switching functions. Expanding on results previously reported the authors, introduce 1) an improved algorithm for converting a CSG expression to sum-of-products form, 2) a technique for minimizing the tree using don't care conditions based on geometry, 3) the dynamic interleaving of the above two algorithms, allowing very efficient rendering for most CSG objects, 4) a method for extending the technique to non- convex primitives, and 5) an implementation of these ideas in an interactive CSG design system on Pixelplanes 4. In this system the designer directly manipulates the CSG structure while continuously viewing the color rendering of the object under design. It is believed these algorithms will attain similar speeds on many of the next generation high-performance graphics system that have frame buffers with many bits per pixel.