一类带有给定切线多边形的样条曲线

A Class of Spline Curve with Given Tangent Polygon

利用带有形状参数的基函数,构造与给定切线多边形相切的样条曲线,所构造的曲线是C2和C3连续的,且对切线多边形是保形的.曲线上的所有控制点可由多边形顶点直接计算产生,曲线具有局部修改性.最后,以实例说明算法是有效的.

An algorithm for constructing a class of Spline curve which is tangent to the given polygon using basis function with shape parameter is described. The constructed curve is shape-preserving to the tangent polygon and C2 or C3-continuous. The control points of the curve to be constructed are computed simply by the vertices of the given tangent polygon. Finally an example illustrate that the method given in this paper is effective.