一类带参B样条曲线的形状分析  

SHAPE ANALYSIS OF A CLASS OF B-SPLINE CURVE WITH SHAPE PARAMETERS

作　　者：吴荣军[1,2] 彭国华[1] 罗卫民[2] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]西安邮电学院应用数学系,西安710121

出　　处：《计算数学》2010年第4期349-360,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金(60672135);陕西省教育厅科研项目(08JK435;09JK728);西安邮电学院科技项目(ZL200813)

摘　　要：利用基于包络理论与拓扑映射的方法对一类带形状参数的B样条曲线进行了形状分析,得出其形状条件完全分布图,图中各区域分别对应于曲线的奇、拐点条件和凸性条件;并讨论了各形状参数对分布图的影响.The shape features of a class of B-spline curve with shape parameters are analyzed by using the method based on the theory of envelope and topological mapping. The obtained shape diagram is composed of the distribution regions which indicate the conditions for this curve having singularities and inflection points or being convex. The influences of shape parameters on the shape diagram are also discussed.

关 键 词：B样条曲线 形状参数 奇点 拐点 局部凸 全局凸 

分 类 号：O241.5[理学—计算数学]