区间Bézier曲面逼近  

Approximation by Interval Bézier Surfaces

作　　者：刘利刚[1,2] 王国瑾[1,2] 寿华好[1,2] 

机构地区：[1]浙江大学CAD&CG国家重点实验室 [2]浙江大学数学系杭州310027

出　　处：《计算机辅助设计与图形学学报》2000年第9期645-650,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金!(6 9973 0 41);浙江省自然科学基金!(6 980 2 5 );国家重点基础研究"九七三"项目基金!(G19980 3 0 6 0 0 )

摘　　要：在区间算术分析的基础上 ,引进了区间 Bézier曲面的概念 ,给出了利用区间 Bézier曲面逼近一般曲面和有理参数曲面的两套算法 ,并通过实例展示了区间 Bézier曲面在这两种曲面逼近中的应用 ,最后研究了区间 Bézier曲面的边界结构 .结论是 m× n次区间 Bézier曲面的边界必由分片裁剪形式的 m× n次 Bézier曲面片。Interval Bézier surfaces are introduced based on the interval analysis. Two algorithms for approximating non rational and rational surface by interval Bézier surfaces are given. Applications of approximating these two types of surfaces by interval Bézier polynomial surface are presented. Then the boundaries of interval Bézier surfaces are investigated. It is proved that the boundary of degree m×n interval Bézier surface is made up from piecewise degree m×n trimmed Bézier patches, ruled surface patches with generating lines parallel to coordinate axis, and rectangular plane patches parallel to coordinate planes.

关 键 词：区间曲面 Bezier曲观 曲面逼近 CAD/CAM 

分 类 号：O186.11[理学—数学] TP391[理学—基础数学]