有理曲线曲面的降阶逼近

覃廉; 关履泰

doi:10.11834/jig.200608180

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专辑

有理曲线曲面的降阶逼近
Approximate Degree Reduction of Rational Curves and Surfaces
2006年11卷第8期页码：1062
纸质出版：2006
DOI： 10.11834/jig.200608180
稿件说明：

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覃廉, 关履泰. 有理曲线曲面的降阶逼近[J]. 中国图象图形学报, 2006,11(8):1062. DOI： 10.11834/jig.200608180.

Approximate Degree Reduction of Rational Curves and Surfaces[J]. Journal of Image and Graphics, 2006, 11(8): 1062. DOI： 10.11834/jig.200608180.

摘要

基于齐次坐标空间，提出了一种NURBS曲线曲面和有理Bezier曲线曲面降阶的简便方法。在齐次坐标空间中，使降阶后的曲线曲面与原曲线曲面的差的L2范数达到极小，将有理曲线曲面降多阶问题转化为二次规划问题求解，并给出了误差估计。实验结果表明，该方法计算速度快，降阶逼近效果好。

Abstract

Based on homogeneous coordinates

this paper presents a convenient algorithm for approximate degree reduction of NURBS and rational Bezier curves and surfaces. In homogeneous coordinates

the difference of the low degree curve/ surface and high degree curve/surface is minimized. The problem of approximate multi-degree reduction of rational curves and surfaces is transformed into quadratic programming. Error estimate is presented. Experimental results show that this algorithm is very efficient.