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

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．

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.