带有给定切线多边形的保形非均匀B样条曲线

Non-Uniform Cubic B-Spline Curve with Given Tangent Polygon

摘要: 讨论并给定切线多边形相切的非均匀三次B样条曲线,所构造的曲线是C²连续的闭曲线,且对切线多边形保形.非均匀三次B样条的所有deBoor点由切线多边形的顶点直接计算生成.构造了与给定切线多边形相切的Cm连续m+1次非均匀B样条曲线.最后的实例表明,所构造的非均匀三次B样条逼近曲线比分段4次Bézier曲线更有效.

Abstract: An algorithm for constructing closed and shape preserving non-uniform cubic B-spline curve with given tangent polygon is presented. The algorithm for constructing （m ＋1）th degree B-spline curve with Cm continuity is given too. Practical example illustrates that the constructed curve approximates the tangent polygon quite well.