基于三点分段的一类三角样条曲线的扩展

基于文献[5]中三点分段的一次和二次三角基函数的扩展,首先给出了带参数的二次和三次三角调配函数,当λi=0时,二次和三次三角基函数分别退化为文献[5]中的一次和二次三角基函数,然后建立了一种带局部调节参数λi的分段三角样条曲线。通过调整参数λi,能够使得当参数λi越大时,分段三角样条曲线越逼近控制多边形。对于曲线的连续性也做了相关的讨论,二次最高可达G2连续,三次最高可达G4连续。最后给出了两个数值例子,分别利用文中给出的二次和三次调配函数构造了达到G1连续和G3连续的两条曲线。

Extention of Piecewise Trigonometric Spline Curves by Three-Points

A class of quadratic and cubic triangle blending functions~ith parameters is presented,which is the expansion of the linear and quadratic triangle basis function by three-points. When Ai= 0, the quadratic and cubic triangle basis function reduce to linear and quadratic triangle basis function in References [-5] respectively. Then a piecewise triangular spline curve with local regulation parameters 2i is established based on quadratic and cubic triangle blending functions. By adjusting the parameters ,li,the curve will have better approximability to the con- trol polygon when the parameter ,t, is greater. A related discussion for the continuity of the curve is made. The quadratic triangle blending functions can be up to G2 continuous and the cubic can be up to G4 continuous. At last,some computing examples of the curve with G1 and G3 continuous are given.