Orthogonal polyhedra as geometric bounds in constructive solid geometry

Abstract

Set membership classification and, specifically, the evaluation of a CSG tree are problems of a certain complexity. Several techniques to speed up these processes have been proposed such as Active Zones, Geometric Bounds and the Extended Convex Differences Tree. Boxes are the most common geometric bounds studied but other bounds such as spheres, convex hulls and prisms have also been proposed. In this work we propose orthogonal polyhedra as geometric bounds in the CSG model. CSG primitives are approximated by orthogonal polyhedra and the orthogonal bound of the object is obtained by applying the corresponding boolean algebra. A specific model for orthogonal polyhedra is presented that allows a simple and robust boolean operations algorithm between orthogonal polyhedra. This algorithm has linear complexity (is based on a merging process) and avoids floating-point computation.