摘要
在构造插值曲线与曲面时,传统的方法多基于多项式函数空间,而基于三角函数空间也能构造插值曲线与曲面.首先基于函数空间Ω=span{1,sint,cost,sin2t,cos2t}构造了一种样条插值曲线与曲面,称之为拟三次三角样条插值曲线与曲面.该曲线与曲面不仅满足C2连续,而且直接插值于给定的控制顶点,避免了通过方程组反求控制顶点.进一步地,为了使所构造的拟三角样条插值曲线与曲面具有局部可调性,利用奇异混合技术在拟三次三角样条插值曲线与曲面中引入了局部形状参数,修改某些形状参数的取值可实现对插值曲线与曲面的局部调整,为样条插值曲线与曲面的构造提供了两种新方法.
The interpolation curves and surfaces are usually constructed based on the space of polynomial functions.However,interpolation curves and surfaces also could be constructed by the space of trigonometric functions.A class of spline interpolation curves and surfaces,called quasi-cubic trigonometric spline interpolation curves and surfaces,are established based on the space Ω=span {1,sint,cost,sin2t,cos2t} in this paper firstly.The proposed curves and surfaces satisfy C2 continuous and interpolate the given control points directly,which avoid solving equations to obtain the control points.In order to make the proposed curves and surfaces have the property of local adjustment,the interpolation curves and surfaces with shape parameters are constructed by the singular blending technique.The shapes of the curves and surfaces can be local adjusted easily and freely by changing the values of some shape parameters.The proposed curves and surfaces present two new methods for constructing interpolation curves and surfaces.
出处
《小型微型计算机系统》
CSCD
北大核心
2013年第3期680-684,共5页
Journal of Chinese Computer Systems
基金
国家自然科学基金项目(51175261)资助
湖南省教育厅资助科研项目(11C0707)资助
关键词
三角样条
插值
奇异混合
形状参数
trigonometric spline
interpolation
singular blending
shape parameter
