G^1端点约束的Bézier曲线曲面的Ribs和Fans  

Ribs and Fans of Bézier Curves and Surfaces with Endpoints G^1 Continuity

作　　者：黄伟贤[1] 王国瑾[2] 

机构地区：[1]浙江大学数学系计算机图像图形研究所,杭州310027 [2]CAD & CG国家重点实验室(浙江大学),杭州310058

出　　处：《计算机研究与发展》2011年第9期1781-1787,共7页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(60873111,60933007,61070065)

摘　　要：为了得到Bézier曲线曲面的更加适用于网络传输的分解和重构算法,研究了带1阶端点(角点)约束的Bézier曲线曲面的Ribs和Fans,并且得到了相应的曲线曲面的光滑部分和细节部分.反过来,给定Bézier曲线的光滑部分和细节部分,给出了重构原曲线的算法.另外,还把Ribs和Fans的概念与算法推广到三角Bézier曲面.1张n次的三角Bézier曲面能够分解为1张n-1次的Rib、1张n-3次的Fan和3条n-4次Bézier曲线(Fans).数值例子表明对曲线曲面的光滑部分和细节部分的分解是更优与更有效的.In order to obtain the decomposition and reconstruction of Bezier curves and surface that are more suitable to be used in Internet transmission, the ribs and fans of Bezier curves and surfaces with endpoints G^1 continuity are studied in this paper, and the corresponding smooth parts and detailed parts of the curves and surfaces are derived. On the other hand, given the smooth parts and detailed parts of a Bezier curve, the reconstruction algorithm of the curve is presented. In addition, the concepts of ribs and fans are generalized to triangular B6zier surfaces. The degree n triangular Bezier surface can be decomposed into one rib of degree n-1, one fan of degree n--3 and three Bezier curves （fans） of degree n-4. Numerical examples show that the decomposition of smooth parts and detailed parts of curves and surfaces in the paper is more effective and more convenient.

关 键 词：BÉZIER曲线 BÉZIER曲面 三角BÉZIER曲面 Ribs和Fans 端点约束 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]