区间有理Bézier曲线的降多阶逼近  

Multi-degree reduction approximation of interval rational Bézier curves

作　　者：李涛[1] 

机构地区：[1]苏州科技学院数理学院,江苏苏州215009

出　　处：《苏州科技学院学报（自然科学版）》2012年第3期14-19,40,共7页Journal of Suzhou University of Science and Technology （Natural Science Edition）

基　　金：苏州科技学院校科研基金项目(XKY201021)

摘　　要：通过分析有理多项式的约束不等式,把区间有理Bézier曲线的降阶转化为多项式的保上界降阶逼近问题,得到两种降阶算法:拟线性规划法和拟最优逼近法。前者可一次降多阶,后者可一次降一阶或降二阶且具有显式的计算公式。给出了两种算法降一阶时的误差上界估计。数值实例验证了两种算法的有效性。By analyzing the constraint inequalities of rational polynomials, the degree reduction problem of interval rational Bézier curves is converted into that of polynomials with upper bound. Then two degree reduction methods are acquired： pseudo linear programming method and pseudo optimal approximation method. With the first method, muhi-degree reduction can be executed each time, while, with the second method, only one or two- degree reduction with explicit formulae can be done each time. Approximation errors with upper bounds are esti- mated for both methods when one degree reduction is executed. Examples indicate the efficiency of the proposed algorithms.

关 键 词：降多阶逼近 区间曲线 有理BÉZIER曲线 线性规划 最优逼近 

分 类 号：O241.5[理学—计算数学]