摘要
针对α 均匀B样条曲线的局限性 ,引进α 非均匀B样条曲线 ,并相应地研究这种曲线保单调插值的可能性与算法 通过设置奇异混合函数 ,无需求解方程组或迭代计算 ,可方便地构造出一类带有形状控制参数的α 非均匀B样条插值曲线族 ;进一步 ,利用Bernstein多项式的正性条件 ,得到该形状参数α的取值范围 ,使得与该范围内每个形状参数相应的插值曲线都是保单调的 ,且得到的曲线为C2 (或G1)连续
Compared with uniform α -B spline it is very necessary to introduce non-uniform α -B spline and investigate the possibility as well as the algorithm for the monotonicity-preserving interpolation to this kind of curve In this paper, a family of non-uniform α -B spline interpolation curve with the shape control parameter α is constructed expediently by using singular blending function but dispensing with solving any system of equations or going at any iterative computation; then, the positive conditions of Bernstein polynomial can be used to obtain a range in which the shape parameter takes its value so as to make the corresponding interpolating curves monotonicity-preserving and C 2 (or G 1) continuity maintained Several numerical examples are given to illustrate the correctness and the validity of theoretical reasoning
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2004年第10期1386-1391,1395,共7页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金 (60 3 73 0 3 3
60 3 3 3 0 10 )
国家重点基础研究发展规划项目(2 0 0 2CB3 12 10 1)资助