OR插值曲线构造及Bézier曲线逼近  

Interpolation by OR Curve and Approximation for Bézier Curve

作　　者：郑志浩[1] 汪国昭[1] 

机构地区：[1]浙江大学数学系计算机图形图像研究所,杭州310027

出　　处：《计算机辅助设计与图形学学报》2006年第3期366-371,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(10371110);国家重点基础研究发展规划项目(2002CB312101);浙江省教育厅科研项目(20050924)

摘　　要：根据平面多项式曲线的等距有理参数化条件,构造了具有不同连续阶的OR插值曲线.由于OR曲线可通过恰当的参数变换产生有理形式的等距线,因此根据给定B啨zier曲线离散端点条件,可构造特定连续阶的OR样条曲线来逼近该Bézier曲线,而将OR样条曲线的精确等距线作为B啨zier曲线的逼近等距线.OR curve is polynomial and rational parametric plane curve whose offsets are rational. We here utilize the necessary and sufficient condition for properly parameterized plane curves to be offset-rational and the definite endpoint conditions, construct G^1 quadratic OR curve and G^1 cubic OR curve with a modulating factor,G^1 quartic OR curve, C^2 OR curve with transition point, C^2 OR curve. A given Bézier curve is subdivided several segments by inserting knots. An OR-spline curve which is an approximation for the Bézier curve is constructed according to the conditions of endpoints of each subdivision. The exact offset to OR- spline curve can be generated directly by means of properly parameterization, which further can be regarded as an approximation for the Bézier curve. The errors between the Bézier curve and OR-spline is also estimated.

关 键 词：OR曲线 BÉZIER曲线 逼近 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]