An algorithm on discrimination of point-set in polyhedron based on three-dimensional convex hull

Abstract

This paper presents an algorithm to determine whether a point-set composed of n-points is in the polyhedron or not-which is called the convex hull method. With this method, it is not necessary to judge whether each point in a point set within a polyhedron. By constructing three-dimensional convex hull of the remain target points, by means of collision detection of spatial objects to judge the adjacency relations of the polyhedron and the three-dimensional convex hull of the point set, and then to judge whether the vertices of three-dimensional convex hull are within the polyhedron, or the vertices of polyhedron are within the three-dimensional convex hull, thus which points are spots within the polyhedron can be determined. The algorithm can be applied not only to a general polyhedron, but also to concave polyhedron. The efficiency of checking whether the three-dimensional point set is within the polyhedron can be greatly improved by this approach, which is an important support for the realization of real-time spatial analysis algorithm for three-dimensional Geographic Information System (3D GIS). The experimental results show that the algorithm is simple, reliable and highly efficient.