带有切线多边形的C^2连续类三次三角可调样条曲线

C^2 Continuous Quasi-cubic Trigonometric Adjustable Spline Curve with Given Tangent Polygon

提出一种带形状参数的C2连续类三次三角样条曲线.该曲线不仅与三次均匀B样条曲线具有相似的性质,而且在控制顶点保持不变时,其形状可通过形状参数的取值进行调整.描述了一种与给定多边形相切的类三次三角可调的样条曲线的算法,所有的类三次三角可调的样条曲线的控制点可以通过对多边形的顶点简单计算产生.所构造的曲线对多边形具有保形性,曲线可以局部修改.

A kind of C2 continuous quasi-cubic trigonometric spline curve is presented. The curve inherits the major advantages of the cubic uniform B-spline curve, and the shape can be adjusted by using the shape parameter when the control points are fixed. An algorithm for constructing quasi-cubic trigonometric adjustable spline curve which is tangent to the given polygon is described. The control points of the quasi-cubic trigonometric adjustable spline curve to be constructed are computed simply by the vertices of the given polygon. The constructed curve is shape-preserving to the polygon , the local modification to the spline curve can be completed by simply adjusting the corresponding control parameters. Two examples are given.