张量积Bézier曲面的S幂基降多阶逼近  

Rational approximation of offset curves by S-power series

作　　者：张莉[1,2] 刘植[1,2] 

机构地区：[1]合肥工业大学数学系,安徽合肥230009 [2]合肥工业大学计算机与信息学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2008年第10期1710-1713,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高等学校青年教师科研资助计划项目(2007jq1001);合肥工业大学科学研究发展基金资助项目(061007F)

摘　　要：文章给出了张量积Bézier曲面一次降多阶的算法。给定张量积Bézier曲面,采用了分向降阶算法,对u向、v向Bézier曲线分别一次降多阶。这里曲线降阶,利用基转换矩阵将Bézier曲线的Bernstein基函数表示成S幂基函数,通过截断曲线中的高次项,可以得到相应的降多阶逼近曲线,所得的降多阶逼近曲面自动保角点高阶插值;最后给出了数值实例。A new algorithm for multi-degree reduction approximating tensor product Bézier surfaces is presented. For a given tensor product Bézier surface, multi-degree reduction algorithm is adopted on the u direction and v direction of the Bézier surface separately. First, the S-power basis is used to express Bézier curves by using transformation matrices, then multi-degree reduction approximating Bézier curves will be achieved by truncating terms of high degree. Approximating Bézier surfaces is achieved by using this method in two different directions of the Bézier surface separately. The approximating surfaces have the constraint of high order interpolations over four corners naturally. Numerical examples are given.

关 键 词：张量积BÉZIER曲面 降多阶 S幂基 逼近 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]