拟三次三角B样条曲线曲面构造及其应用  

Construction and Application of Quasi-cubic Trigonometric B-spline Curves and Surfaces

作　　者：陈素根[1] 赵正俊[1] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246133

出　　处：《小型微型计算机系统》2015年第6期1331-1335,共5页Journal of Chinese Computer Systems

基　　金：国家自然科学基金项目(11326052)资助;安徽省高等学校自然科学研究项目(KJ2012B089)资助;安庆师范学院级教学研究项目(120006000031)资助

摘　　要：在函数空间{1,t,sint,cost,sin2t,cos2t}中构造了带有形状参数的拟三次三角B样条基函数,并定义了相应的拟三次三角B样条曲线和曲面,该样条曲线和曲面具有类似于三次均匀B样条曲线和曲面的性质.分析了形状参数对曲线曲面的调节作用,并利用奇异混合技术引入局部形状参数,构造了拟三次三角B样条插值曲线和曲面,该曲线和曲面不仅满足C2连续,而且无需求解方程组反求控制顶点就可以实现插值给定型值点.实例说明,拟三次三角B样条曲线曲面可作为自由曲线曲面造型方法的有效补充.A kind of quasi-cubic trigonometric B-spline blending functions with a shape parameter over space { 1, t, sint, cost, sin2t, cos2t} is constructed,and then, the corresponding quasi-cubic trigonometric B-spline curves and surfaces are defined, which have the similar properties to cubic uniform B-spline curves and surfaces. The effect of parameter to adjust the curves shape is also analyzed. Quasi-cubic trigonometric B-spline interpolation curves and surfaces with local shape parameters are constructed by the singular blend- ing technique,and the proposed interpolation curves and surfaces not only satisfy C2 continuous but also directly interpolate the given points without solving equations to obtain the control points. Example indicates that the quasi-cubic trigonometric B-spline curves and surfaces can be used as an effective complement of free-form curve and surface modeling method.

关 键 词：计算机辅助几何设计 三次三角样条 插值样条 形状参数 奇异混合 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]