A Robust BSP Tree Construction Algorithm Using Tolerance Based Degenerate Case Classification and Topological Oriented Method

Abstract

A Binary Space Partitioning (BSP) tree of a polygon can accelerate various geometric computations of the polygon. Because of the numerical unstability of the BSP tree construction, the utilization of BSP trees in practical applications is limited. Topological oriented method proposed by Sugihara can realize robust geometric problem solving if degenerate intersections of geometric elements in the problem can be ignored. Since proper treatment of degenerate intersections between a partitioning line and polygon edges is important in constructing a BSP tree, direct application of the topological oriented method is difficult. In this paper, the authors propose a new algorithm for stably constructing a BSP tree. This algorithm is based on tolerance based classifications of degenerate placements of the partitioning line and edges of a polygon. Each classified placement is then treated as a pseudo intersection between the partitioning line and a polygon edge. This treatment enables the application of the topological oriented method for constructing a BSP tree. The algorithm is implemented and computational experiments are demonstrated.