Sharp bounds on the approximation of a Bezier polynomial by its quasi-control polygon

Ren-Jiang Zhang; Guo-Jin Wang

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Sharp bounds on the approximation of a Bezier polynomial by its quasi-control polygon

机译：拟控制多边形近似贝塞尔多项式的尖锐边界

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摘要

By connecting the points which are the kind of linear combinations of Bezier control points, a broken line polygon called quasi-control polygon is produced. Using it to approximate Bezier segment, this paper obtains two sharp, quantitative bounds, besides depending on the degree of the polynomial, the bounds depend only on the maximal absolute second differences or the sum of absolute second differences of the control point sequence respectively. The advantage of this method is hardly increasing calculation, the effect of using quasi-control polygon to approximate is better than that of using control polygon to approximate.

机译：通过连接作为贝塞尔曲线控制点的线性组合的点，可以生成称为准控制多边形的虚线多边形。利用它来近似贝塞尔曲线，本文得到了两个尖锐的，定量的边界，除了取决于多项式的阶数外，边界还分别取决于控制点序列的最大绝对秒差或绝对秒差之和。这种方法的优点是几乎不增加计算量，使用准控制多边形逼近的效果要好于使用控制多边形逼近的效果。

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来源
《Computer Aided Geometric Design》 |2006年第1期|p.1-16|共16页
作者
Ren-Jiang Zhang; Guo-Jin Wang;
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作者单位

China Jiliang University, Zhejiang, Hangzhou 310018, PR China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类计算机的应用;
关键词
bezier curves; intersection testing; sharp bounds; approximation;

机译：贝塞尔曲线;相交测试;尖锐边界;逼近;

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1. Consolidated sharp bounds for Bezier curve approximation with cutdown polygon and corner cutting polygon [J] . Ren-Jiang Zhang, Weiyin Ma Computer Aided Geometric Design . 2010,第5期

机译：合并的锐利边界，用于使用削减多边形和拐角切割多边形的贝塞尔曲线逼近
2. SHARP, QUANTITATIVE BOUNDS ON THE DISTANCE BETWEEN A POLYNOMIAL PIECE AND ITS BEZIER CONTROL POLYGON [J] . D.NAIRN, J.PETERS, D.LUTTERKORT Computer Aided Geometric Design . 1999,第7期

机译：多项式片段及其贝塞尔控制多边形之间的距离的清晰定量边界
3. A Simple And Efficient Approximation Of A Bezier Piece By Its Cutdown Polygon [J] . Ren-Jiang Zhang, Weiyin Ma Computer Aided Geometric Design . 2009,第3期

机译：贝塞尔曲线片的下陷多边形简单有效地逼近
4. Efficient Piecewise Linear Approximation of Bezier Curves with Improved Sharp Error Bound [C] . Weiyin Ma, Renjiang Zhang International Conference on Geometric Modeling and Processing(GMP 2006); 20060726-28; Pittsburgh,PA(US) . 2006

机译：具有改进的尖锐误差界的贝塞尔曲线的有效分段线性逼近
5. Multi-objective particle swarm optimization of a modified Bernstein polynomial for curved phased array synthesis using Bezier curves, surfaces, and volumes. [D] . Boeringer, Daniel Wilharm. 2004

机译：修正的Bernstein多项式的多目标粒子群优化，用于使用Bezier曲线，曲面和体积进行弯曲相控阵合成。
6. Functional Data Approximation on Bounded Domains using Polygonal Finite Elements [O] . Juan Cao, Yanyang Xiao, Zhonggui Chen, -1

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7. Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon [O] . User Services University of Delaware Delaware USA ( host institution ), Nairn D., Peters J., 1999

机译：多项式片与其Bézier控制多边形之间的距离的清晰定量边界

Sharp bounds on the approximation of a Bezier polynomial by its quasi-control polygon

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