多変数Sturm列を利用した曲線・曲面の交点の存在判定

概要

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The interference processing of curves and surfaces is an important technique in CAD/CAM applications. The lack of the stability in the interference processing is due to numerical errors caused by floating point arithmetic and the approximate computations. In the interference processing, the geometric Newton-Raphson method is generally used for approximations, because the solutions of high degree polynomial equations cannot be exactly computed. Most geometric algorithms, such as Boolean set operation algorithms, modify the topological data structure according to the existence of the solutions of polynomial equations. The number of solutions of algebraic equations can be exactly counted with Sturm's theorem and exact arithmetic, In this paper, a stable interference method for curves and surfaces using Sturm's theorem and exact arithmetic is proposed. The proposed approach can exactly evaluate the existence of intersection points in curve/surface intersection.
公益社団法人精密工学会の論文
2001-03-05