曲線・曲面に対する4×4行列式法の適用(第1報) : パラメトリック曲線に対する適用

概要

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This paper presents a method for applying the 4 × 4 Determinant Method to interference problems involving rational parametric cubic Bezier curve segments. The 4 × 4 Determinant Method has already been shown to be effective in the processing of polyhedral shapes. As the first step toward a unified approach to all interference problems including problems concerning free-formed surfaces, this paper derives the recursive relationships between determinants required to calculate intersections with the convex hulls of rational cubic Bezier curve segments. The calculations in these relationships do not require multiplication and division operations and thus this provides an efficient and robust method for intersection detection and calculation. As an example, these relationships are applied to Point-in-Polygon tests for polygons with curved edges.
公益社団法人精密工学会の論文
1991-07-05