Determining Algorithm of Three-Dimensional Convex Hull Used for Set Operations of Solids and Its Application to Interference Problems

Abstract

This paper discusses a determining algorithm for the three-dimensional convex hull which is well-fitted to deal with interference problems of solids requiring a three-dimensional convex hull of a given shape for their solution and is available for set operations. The paper also deals with the application of this algorithm to specific interference problems. The proposed algorithm is devised to determine the smallest convex polyhedron containing a concave polyhedron given by a solid model beforehand, as a solid model having the same data structure as that of the concave polyhedron. It features the use of Euler operators, a general method for determining a solid model. This means that the proposed algorithm does not depend on the data structure of a solid model and that all convex polyhedrons obtained during the process of determining a three-dimensional convex hull are also in the form of solid model. Because of such a feature, the three-dimensional convex hull determined by the algorithm can be used for set operations with the given concave polyhedrons, and therefore, the algorithm provides a convenient approach to interference problems of solids requiring a three-dimensional convex hull of a given shape for their solution. As an example of the application of the proposed algorithm to practical purposes, this paper also discusses a study on the extraction of undercuts in mold design using this algorithm. The findings indicate that the proposed algorithm is useful in solving such practical problems.