与给定多边形相切的可调广义Ball闭曲线

Closed Adjustable Generalized Ball Curves with Given Tangent Polygon

讨论了与给定控制多边形相切的分段三次、五次和六次可调广义Ball曲线的构造方法,所构造的曲线分别是C1,C2和C3连续的,而且对切线多边形是保形的.曲线上的所有广义Ball曲线段的控制点由切线多边形的顶点直接计算产生.给出了在保持公共连接点处相应连续的情况下,内控制点的活动范围.曲线可以在一定范围内做局部修改.计算实例表明使用本文的方法灵活、方便、有效.

This paper proposes an approach of constructing planar piecewise closed generalized Ball curve of 3th、 5th and 6th degree with all edges tangent to a given control polygon and the curve segments can be joined together with C1,C2 and C3continuity respectively.The control points of the generalized Ball curve segments are computed simply by the vertices of the given tangent polygon.The admissible scope of the inner control points is given in order to guarantee corresponding continuity.Local modifications for these curves are possible.The effectiveness as well as adaptability of the method is manifested by experimental results.