Deterministic point inclusion methods for computational applications with complex geometry

Abstract

A fundamental problem in computation is finding practical and efficient algorithms for determining if a query point is contained within a model of a three-dimensional solid. The solid is modeled using a general boundary representation that can contain polygonal elements and/or parametric patches. We have developed two such algorithms: the first is based on a global closest feature query, and the second is based on a local intersection query. Both algorithms work for two- and three-dimensional objects. This paper presents both algorithms, as well as the spatial data structures and queries required for efficient implementation of the algorithms. Applications for these algorithms include computational geometry, mesh generation, particle simulation, multiphysics coupling, and computer graphics. These methods are deterministic in that they do not involve random perturbations of diagnostic rays cast from the query point in order to avoid 'unclean' or 'singular' intersections of the rays with the geometry. Avoiding the necessity of such random perturbations will become increasingly important as geometries become more convoluted and complex.