曲線・曲面に対する4×4行列式法の適用(第2報) : 曲線分割にともなう行列式の収束性

概要

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The 1st report mainly presented an algorithm for applying the 4×4 Determinant Method to geometric interference problems involving parametric rational cubic Bezier curve segments. This paper describes convergence properties of determinants used in a curve subdivision process. The convergence rate of each determinant is theoretically derived. The result is that the convergence rates of determinants containing one control point as its element have order O, those containing two have order 1,those containing three have order 3 and those containing four have order 6. The rates of convergence depend on the number of control points that are elements of a determinant, and are independent of the order of the determinant. This result is applied to find the convergence rates of geometric quantities related to a curve segment. Since geometric quantities are calculated only from determinants, the convergence rates of geometric quantities are easily derived from those of determinants.
公益社団法人精密工学会の論文
1992-05-05