CLASSIFICATION OF A POINT WITH RESPECT TO A POLYHEDRON VERTEX

Abstract

Algorithms for solid boolean operations are strongly based on classifying points with respect to solids. Several algorithms for solving the point-in- polyhedron problem in Brep schemes have been proposed in the literature. In this context, this paper describes an algorithm for the classification of an arbitrary point in the region dose to a polyhe-dron vertex. The algorithm is simple, has linear complexity and does not suffer from singularities. It performs better than previous algorithms, which would be too expensive in this particular case. The proposed algorithm is especially well suited for Brep schemes including spatial data structures for geometric data localization and searching, for operations on octree and extended octree structures, and for boundary evaluation of CSG trees with polyhedral primitives. Its use in the general point-in-polyhedron classification problem is also discussed. The algorithm is based on an extension to point in unbounded polygon of the kinetic framework of Guibas et al.