带有给定切线多边形的C-Bézier闭曲线和B-型样条闭曲线

§1.引 言 Bézier曲线和B样条曲线已广泛应用到汽车、航空、造船等许多领域中.Hering讨论了与凸多边形每边相切的分段三(四)次 Bézier闭曲线和三(四)次B样条闭曲线.它的所有Bézier点必须通过求解大型方程组得到,计算量大,且曲线易出现拐点,而B样条闭曲线的控制点要通过反算得到1].方逵改进了Hering的方法,构造了G2连续的分段三次曲线2],基本上克服了Hering方法的两个缺点,但局部修改仍然是比较复杂的.方逵等再次研究了与任意多边形相切的分段四次和五次Bézier曲线3],但五次Béier曲线不能作局部修改.本文的第二节研究了与任意多边形相切的分段C-Bézier曲线,该曲线C1连续的,且对切线多边形具有保形性,每段C-Bézier曲线上的控制点由切线多边形的顶点计算

CLOSED C-BEZIER CURVE AND B-TYPE SPLINE CURVE WITH GIVEN TANGENT POLYGON

This paper proposes an algorithm of constructing planar piecewise C-Bezier curve with all edges tangent to a given control polygon and another algorithm of B-type spline curve with all edges tangent to a given control polygon is discribed. The segmented C-Bezier curve and B-type spline curve are shape-preserving to their tangent polygon. The all control points of the C-Bezier curve segments and B-type spline curve segments can be calculated simply by the vertices of the given tangent polygon. Finally, two nnumerical examples are given.