4×4行列式法における適応的符号判定処理 (第1報)

Abstract

Boolean set operations of two solids are essential in any solid modeling system. Geometric computations in Boolean operations are unified by employing the 4 × 4 determinant method. The stability of Boolean operation algorithms is achieved by employing the exa, ct integer arithmetic under the method. However, the increase of the data lengths of integers impairs the efficiency of geometric computations. Boolean operation algorithms modify the topological data structures according to the signs of determinants. An adaptive sign detection method of n-dimensional inner products is presented and the method is applied to the computation of 4 × 4 determinants. The minimum number of bits necessary to obtain the sign is analyzed both experimentally and theoretically. The result shows that the minimum number of bits depends mainly on the a, ngle between two vectors. Other factors that influence the minimum number of bits are the dimension and the positions of the two vectors. Their influence is relatively small when the dimension is small.