摘要
本文根据均匀B样条基函数的de Boor-Cox递推公式提出了一种新的样条曲线曲面设计方法。该方法从满足正性、局部支柱性和权性的初始基函数出发,可构造出具有高阶低次或低次高阶的多项式样条基函数和多种函数类型的样条函数。给出了设计这种样条曲线曲面的几种方法和实例,并对基函数的连续可微性进行了证明。该样条基函数和样条曲线曲面具有和均匀B样条类似的几何性质,且均匀B样条是其特例,可用于曲线曲面的几何造型和样条插值。
This paper presents a new scheme of design spline curves and surfaces by uniform B-spline de Boor-Cox recursion fon＇nula. The scheme can structure ＂high order and low degree＂ or ＂low degree and high order＂ polynomial spline curves and surfaces, starting from initial basic function of satisfying positivity and local support and weighting property, also can generate many types of spline functions. In this paper, several methods and examples of designing the spline functions are given, and differentiabilities of the basic functions are proved. This slpine curves and surfaces have many similar properties to uniform B-spline, and traditional uniform B-spline is its special case. And it may be used for geometric modeling and interpolation of curves and surfaces.
出处
《计算机科学》
CSCD
北大核心
2006年第9期225-228,共4页
Computer Science
基金
四川省应用基础研究项目(编号:06jy0286)
西南民族大学应用研究项目(编号:03N042)资助。
