同次処理に基づく整数演算を用いた多面体ソリッドモデラ

Abstract

In solid modeling systems, the stability of Boolean set operations is an important issue. Solid modeling systems that employ floating-point arithmetic tend to be unstable because of inconsistent decisions caused by numerical errors. The use of exact integer arithmetic solves this problem. By using exact integer arithmetic based on totally homogeneous processing, error-free arithmetic is implemented. In this paper, we propose a robust polyhedral solid modeling system. The system employs exact integer arithmetic based on totally homogeneous processing. All of the numerical data of solid models for Boolean set operations are represented in terms of integer representations. Boolean set operations and transformations of solid models are performed in the integer domain. Several examples of Boolean set operations, which are very difficult in floating point arithmetic, are presented to show that our system does not cause failure in such situations. Methods that improve the efficiency of exact integer arithmetic are also presented to avoid the increase of computation time caused by the increase of the data lengths of integers.