浮動小数点演算ユニットを利用した適応的符号判定処理 ３×３行列式の符号判定

Abstract

In solid modeling systems, Boolean set operations are very sensitive to numerical errors. These problems can be solved by adopting the variable length integer computations based on the extended 4×4 determinant method. The efficiency of these computations, however, goes to worse as the lengths of integers increase. In practice, many geometric algorithms such as Boolean set operations can be reduced to detecting the signs of determinants. By using the adaptive sign detection method, the signs can be detected in nearly constant time for any length of integer. In this paper, a method is proposed that improves the efficiency of the adaptive sign detection. All of internal numerical computations with this method are processed as the floating point number arithmetic by using an FPU (Floating point Processing Unit). It is remarkable that this method never outputs wrong results although floating point computations are performed. The performance experiment shows that the new sign detection method is about 15 times faster than the old one.