与给定多边形相切的C2和C3 广义 Ball闭曲线

B样条曲线和Bezier曲线在CAD、CAGD及逼近中非常有用,例如,在服装CAD纸样的设计过程中,通常先根据尺寸要求确定控制点,再根据控制点用直线段绘制样片的大体轮廓,即绘制多边形,在多边形内用直线和曲线绘制封闭的图形,由于样片的形状不规则,即构成样片的曲线比较复杂,为了使曲线光滑、丰满、有弹性,经常遇到曲线与控制多边形相切

C2 AND C3 CONTINUOUS CLOSED GENERALIZED BALL CURVE WITH GIVEN TANGENT POLYGON

This paper proposes an approach of constructing planar piecewiseclosed generalized Ball curve of 4th or 5th degree with all edges tangent to a givencontrol polygon and the curve segments are joined together with C2 and C3 conti-nuity. The segmented generalized Ball curve is shape-preserving to its tangentpolygon. Finally, one numerical example is given.