New algorithms for evaluating parametric surface  

作　　者：王国瑾 成敏 

机构地区：[1]State Key Laboratory of CAD&CG, Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, China

出　　处：《Progress in Natural Science:Materials International》2001年第2期64-70,共7页自然科学进展·国际材料（英文版）

基　　金：Project supported jointly by the National Natural Science Foundation of China (Grant No. 69973041), Zhejiang Provincial Natural Science Foundation (Grant No. 698025) and the Foundation of State Key Basic Research 973 Item (Grant No.G1998030600).

摘　　要：Through generalization of mathematical model of surface lofting program in the CONSURF system, the definitions for two generalized Ball surfaces and their recursive algorithms are given. Furthermore, the conversion algorithms from Bezier surface to these two generalized Ball surfaces are presented. On the basis of these algorithms, two more efficient algorithms for evaluating parametric surfaces are also derived. One uses generalized Ball forms directly for evaluating surface, and the other converts the given Bezier surface to a generalized Ball surface firstly, and then evaluates the surface. Both theoretical analysis and example computations show that the two new algorithms are more efficient than the de Casteljau algorithm. Especially when Wang-Ball surface is used, the time complexity is reduced from cubic to quadratic of the degree of the surface. If these algorithms are applied to displaying, interactive rendering, designing, intersection-finding, offsetting and approximating for surfaces,Through generalization of mathematical model of surface lofting program in the CONSURF system, the definitions for two generalized Ball surfaces and their recursive algorithms are given. Furthermore, the conversion algorithms from Bezier surface to these two generalized Ball surfaces are presented. On the basis of these algorithms, two more efficient algorithms for evaluating parametric surfaces are also derived. One uses generalized Ball forms directly for evaluating surface, and the other converts the given Bezier surface to a generalized Ball surface firstly, and then evaluates the surface. Both theoretical analysis and example computations show that the two new algorithms are more efficient than the de Casteljau algorithm. Especially when Wang-Ball surface is used, the time complexity is reduced from cubic to quadratic of the degree of the surface. If these algorithms are applied to displaying, interactive rendering, designing, intersection-finding, offsetting and approximating for surfaces, considerable economic results can be achieved.

关 键 词：BEZIER SURFACE generalized BALL SURFACE EVALUATING algorithm time complexity. 

分 类 号：O29[理学—应用数学]