Correct Shading of Regularized CSG Solids Using a Depth-Interval Buffer

Abstract

A convenient interactive design environment requires efficient facilities for shading solid models represented in CSG. Shading techniques based on boundary eval­ uation or ray casting that require calculations of geometric intersections are too ineffi­ cient for interactive graphics when eSG primitives with curved (parametric) surfaces are involved. Projective approaches, where the primitive surfaces are scan-converted using standard hardware-supported graphic functions are preferred. Since not all the points of the faces of a CSG primitive lie on the CSG solid, scan conversion must be combined with a procedure that tests the produced 3D surface-points against the original CSG ex­ pression. Point classifications against primitives defined by arbitrary curved boundaries may be performed, without geometric intersections, through depth-comparisons at each pixel. This approach has been implemented for the Pixel-Power machine by researchers at UNC. It deals with complex CSG trees by converting CSG expressions into sum-of­ product form and repeatedly scan-converting the primitives of each product. The Trickle algorithm, which considerably reduces the number of scan-conversions in the general case has been developed at IBM Research and presented elsewhere. This paper discusses sev­ eral recent improvements to the original Trickle algorithm. The overall algorithm has been simplified. The scan-conversion process and the point classification tests have been modified to correctly handle cases where several primitive faces coincide within an arbi­ trary numerical resolution. These enhancements are not only necessary for on/on cases in regularized Boolean expressions, but also for processing pairs of faces near their common edges. Finally, we point out that a simple two-pass extension of the trickle algorithm using an auxiliary shadow buffer suffices to compute directly from CSG shaded images with shadows.