A quick point-in-polyhedron test

Abstract To decide whether a point is contained in a polyhedron, one may use the parity of the number of intersections of a halfline with the boundary of the polyhedron. Difficulties arise if the halfline meets an edge or a vertex. To resolve such singularities, we propose to associate to each point of intersection a certain positive or negative weight and then to consider the sum of these weights.

[1]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[2]  Yehuda E. Kalay Determining the spatial containment of a point in general polyhedra , 1982, Comput. Graph. Image Process..

[3]  Dean L. Taylor,et al.  A theorem to determine the spatial containment of a point in a planar polyhedron , 1989, Comput. Vis. Graph. Image Process..

[4]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[5]  Jeff Lane,et al.  An efficient point in polyhedron algorithm , 1984, Comput. Vis. Graph. Image Process..