给定切失混合有理插值曲线

在曲线的设计中,尤其是反向设计,通常所取的数据点都是关键点,譬如:逗留点(曲线上的一阶导失与二阶导失叉积为零矢量的点)。因此,设计的曲线希望在该数据点也是逗留点。利用三角函数对三次Bernstein基函数改进为混合基函数,该基函数具有规范性,对称性等类似Bernstein基函数的性质和特点。给定一组确定切方向的数据点,用此基函数,可以构造一种带形状因子的有理插值曲线。生成的有理插值曲线具有G2-连续和曲率连续,插值点均是逗留点等特点。若通过加强形状因子的条件限制可达到C2-连续,并可以通过修改形状因子来调节曲线的形状,并且这种影响是局部的。最后还给出了实例,并与三次Hermite插值曲线进行了比较。

Blending Rational Interpolation Curves with Given Tangent Vector

The data,which choosed in designing curve,especial in reverse designing,are usually key points,such as standing points.Blending basic functions,improved by cubic Bernstein polynomial basic functions with trigonometric functions,have much properties resembling latter.In this paper,the rational interpolation curve generated with new basic 2 functions by analogy B6zier curve,which is G^2-continuity and curvature continuity.In addition,all interpolation data points are standing points,the problem of constructing a space new interpolation C^2-continuity curves is considered,and the interpolation curve can be adjusted through changing shape parameters of each interpolation points.