A description is given of a set of algorithms for efficiently rendering an object defined by constructive solid geometry (CSG) directly onto a frame buffer without converting first to a boundary representation. This method requires only that the frame buffer contain sufficient memory to hold two color values, two depth 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. The following are developed: dynamic interleaving of Boolean tree normalization with bounding-box pruning, allowing efficient rendering for most CSG objects; a method for extending the technique to nonconvex primitives; and implementation of these ideas in an interactive CSG design system on the Pixel-planes 4 solid modeling system. In the design system the designer directly manipulates the CSG structure while continuously viewing the color rendering of the object being designed.
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