Adaptive polygonization of geometrically constrained surfaces

Many surfaces in geometric and solid modeling, including offsets and blends , are naturally defined from given surfaces subject to geometric constraint s. Surfaces that are geometrically constrained can be uniformly defined as the projection of two-dimensional manifolds (2-surfaces) in n-dimensional s pace, where n>3. This definition can be used for given surfaces that are im plicit or parametric. This paper presents a robust, adaptive polygonization algorithm for evaluating and visualizing geometrically constrained surface s. Let F be the constrained surface, a 2-surface in n-space, and let pi(F) be its projection into the subspace spanned by the first three coordinates. Our polygonization algorithm computes pi(F). The method works directly wit h the n-space representation, but performs all major computations in 3-spac e. Techniques for triangulation, polygon decimation, and local refinement a re also presented.