摘要
首先提出一组基函数向量，它具有以下特定的性质：ＢＢ（０）Ｔ＝（０．０，１．０，０．０，０．０），ＢＢ（１）Ｔ＝（０．０，０．０，１．０，０．０）ＢＢ＇（０）Ｔ＝（－０．５，０．０，０．５，０．０），ＢＢ＇（１）Ｔ＝（０．０，－０．５，０．０，０．５）ＢＢ″（０）Ｔ＝－（１．０，－２．０，１，０，０．０），ＢＢ″（１）Ｔ＝（０．０，１．０，－２．０．１．０）。进而研究了以此函数向量的张量积形式定义的有理样条曲面。并得以下结论：（１）插值性；（２）Ｃ２连续性；（３）局部性和可调性。文中还分析了“权”的作用，并指出它与三次Ｂ－样条的类似性。
We first present a vector of function basis BB (t) that satisfied BB(0)T=(0. 0,1. 0,0. 0,0. 0), BB(1)T= (0. 0,0. 0, 1. 0,0. 0) BB' (0)T= (-0. 5,0. 0,0. 5,0. 0), BB'(1)T=(0. 0, -0. 5,0. 0,0. 5) BB'(0)T= (1. 0. -2. 0,1. 0,0. 0), BB'(1)T=(0. 0,1. 0, -2.0,1. 0) Secondly we discuss the rational surface defined in tension-product form using above function vector BB (t). The interpolation surface implies the following results: (1) The surface interpolates control points; (2) It is second order parametrically continuous;(3) It is local and can be adjusted by weights. The effect of weights is also analysed and has similar result as bicubic rational B-spline surface.
出处
《国防科技大学学报》
EI
CAS
CSCD
北大核心
1996年第3期147-151,共5页
Journal of National University of Defense Technology
基金
CAD/CG国家重点实验室资助
