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ACM Transactions on Graphics (TOG), Volume 17 Issue 3, July 1998

Computing moments of objects enclosed by piecewise polynomial surfaces
Carlos Gonzalez-Ochoa, Scott McCammon, Jörg Peters
Pages: 143-157
DOI: 10.1145/285857.285858
Combining a polynomial free-form surface representation with Gauss' divergence theorem allows efficient and exact calculation of the moments of the enclosed objects. For example, for an cubic representation, volume, center of mass, and the...

Sampling procedural shaders using affine arithmetic
Wolfgang Heidrich, Philipp Slusallek, Hans-Peter Seidel
Pages: 158-176
DOI: 10.1145/285857.285859
Procedural shaders have become popular tools for describing surface reflectance functions and other material properties. In comparison to fixed resolution textures, they have the advantage of being resolution-independent and...

V-Clip: fast and robust polyhedral collision detection
Brian Mirtich
Pages: 177-208
DOI: 10.1145/285857.285860
This article presents the Voronoi-clip, or V-Clip, collision detection alogrithm for polyhedral objects specified by a boundary representation. V-Clip tracks the closest pair of features between convex polyhedra, using an approach reminiscent of...