삼차원 공간에서 두 다면체 사이의 최소거리 계산을 위한 효율적인 알고리즘의 개발

Development of an Efficient Algorithm for the Minimum Distance Calculation between two Polyhedra in Three-Dimensional Space

This paper develops an efficient algorithm for the minimum distance calculation between two general polyhedra(convex and/or concave) in three-dimensional space. The polyhedra approximate objects using flat polygons which composed of more than three vertices. The algorithm developed in this paper basically computes minimum distance between two polygons(one polygon per object) and finds a set of two polygons which makes a global minimum distance. The advantage of the algorithm is that the global minimum distance can be computed in any cases. But the big disadvantage is that the minimum distance computing time is rapidly increased with the number of polygons which used to approximate an object. This paper develops a method to eliminate sets of two polygons which have no possibility of minimum distance occurrence, and an efficient algorithm to compute a minimum distance between two polygons in order to compensate the inherent disadvantage of the algorithm. The correctness of the algorithm is verified not only comparing analytically calculated exact minimum distance with one calculated using the developed algorithm but also watching a line which connects two points making a global minimum distance of a convex object and/or a concave object. The algorithm efficiently finds minimum distance between two convex objects made of 224 polygons respectively with a computation time of about 0.1 second.