M多边形Bézier曲线拐点的分布规律

DISTRIBUTIVE LAW OF INFLECTIONS ON Bézier CURVE of M-SHAPED CONTROL POLYGON

摘要: 采用直观的几何方法,对控制多边形为M形状的Bézier曲线的拐点分布进行了详细的研究,并证明了拐点分布规律的几个定理及其定性判定的方法.这些定理和方法具有几何直观性,对于分析M控制多边形Bézier曲线的形状,以及在CAD/CAM工程设计中控制曲线的形状有理论和实践意义.

Abstract: By a visual geometric method，this paper makes an investigation on the distribution of inflection of Bézier curve whose control polygon is M-shaped，proves some theorems about the distribution，and gives out a way to classify it．This is useful for the shape control in designing curves in CAD／CAM ．