采用分割算法的Bézier曲线的S幂基降多阶逼近  

Multi-Degree Reduction Approximation of Bézier Curves by S-Power Series Based on Subdivision

作　　者：张莉[1,2] 檀结庆[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学院,安徽合肥230009

出　　处：《工程图学学报》2008年第6期80-85,共6页Journal of Engineering Graphics

基　　金：国家自然科学基金资助项目(60773043;60473114);安徽省自然科学基金资助项目(070416273X);安徽省教育厅科技创新团队基金资助项目(2005TD03);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：提出了一种结合分割算法的Bézier曲线一次降多阶逼近。利用Sánchez-Reyes提出的基转换矩阵将Bézier曲线用S幂基函数表示,只要通过截断曲线中的高次项,就可以得到降多阶逼近曲线,但得到的降阶曲线通常误差很大。鉴于S幂基的保端点高阶插值的优良性质,结合分割算法考察了Bézier曲线的一次降多阶逼近,分割后的每段曲线均自动保端点高阶插值,无须添加额外的约束条件。该算法简单,有效,文末给出了数值实例、误差分析与比较。An algorithm for multi-degree reduction approximating Brzier curves by S-power series based on subdivision is presented. Sanchez-Reyes used S-power series to express Bezier curves by using transformation matrices, then multi-degree reduction approximating Brzier curves can be achieved by truncating high terms, but errors are usually big by using this method. Considering S-power series＇ pretty property： keeping high continuum at the endpoints, subdivision algorithm is used here to avoid big errors in practical problems and the subdivided curves could keep high continuum at the endpoints automatically without appending any additional conditions. The algorithm is simple and effective proved by some numerical examples, error analysis and comparisons.

关 键 词：计算机应用 BEZIER曲线 降多阶 逼近 分割 S幂基 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]