An accurate and fast method for computing offsets of high degree rational Bezier/NURBS curves with user-definable tolerance

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An accurate and fast method for computing offsets of high degree rational Bezier/NURBS curves with user-definable tolerance

机译：一种精确快速的方法，用于计算具有用户可定义公差的高阶有理Bezier / NURBS曲线的偏移量

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摘要

This paper focuses on the fast and accurate offset method of high degree rational Bezier/NURBS curves. Firstly, in order to solve the scaling problem of the subdivision error in the Bezier/NURBS curve offsetting, a novel dynamic offset error control method which is the extension of the fast subdivision method of Bezier curve, and can realize the fast offset of the Bezier/NURBS curves under the user's required offset accuracy is proposed. Secondly, for the interpolation of the offset points, the local interpolation is adopted, which can effectively solve the problem of the mass calculation caused by the re-segmentation of the original curve when the interpolation accuracy check fails. Finally, the paper validates the efficiency of the proposed method by comparing the offset accuracy of a series of Bezier/NURBS curves with those of other methods.

机译：本文重点研究高阶有理Bezier / NURBS曲线的快速准确偏移方法。首先，为了解决贝塞尔曲线/ NURBS曲线偏移中细分误差的缩放问题，提出了一种动态偏移误差控制方法，该方法是对贝塞尔曲线快速细分方法的扩展，可以实现贝塞尔曲线的快速偏移。提出了在用户要求的偏移精度下的/ NURBS曲线。其次，对于偏移点的插值，采用局部插值，可以有效解决插值精度检查失败时原曲线的重新分段导致的质量计算问题。最后，本文通过比较一系列Bezier / NURBS曲线与其他方法的偏移精度，验证了该方法的有效性。

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《Journal of Visual Languages & Computing》 |2019年第6期|1-9|共9页
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作者单位

Tianjin Univ Technol Sch Mech Engn Tianjin Key Lab Adv Mechatron Syst Design & Intel Tianjin 300384 Peoples R China|Tianjin Univ Technol Natl Demonstrat Ctr Expt Mech & Elect Engn Educ Tianjin Peoples R China;

Lingyun Ind Corp Ltd Baoding 072750 Hebei Peoples R China;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Offsetting; Interpolation; NURBS curve; Rational Bezier curve;

机译：抵销;插值NURBS曲线;有理贝塞尔曲线;

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专利

1. C~1 NURBS representations of G~1 composite rational Bezier curves [J] . Jianmin Zheng Computing . 2009,第2a3期

机译：G〜1复合有理贝塞尔曲线的C〜1 NURBS表示
2. Topology preserving voxelisation of rational Bezier and NURBS curves [J] . Wu Zhongke, Lin Feng, Seah Hock Soon Computers & Graphics . 2003,第1期

机译：有理Bezier和NURBS曲线的拓扑保留体素化
3. The homogeneous representation of quadratic rational bezier curve and NURBS [J] . Lin Lou, Norimasa Yoshida, Hiroaki Hanamitsu 精密工学会誌 . 1997,第4期

机译：二次有理贝塞尔曲线和NURBS的齐次表示
4. Conversion of Rational Bezier Curves into Non-rational Bezier Curves Using Progressive Iterative Approximation [C] . Chantakamo Anchisa, Dejdumrong Natasha International conference on computer graphics, imaging and visualization . 2013

机译：使用渐进式迭代逼近将有理贝塞尔曲线转化为非有理贝塞尔曲线
5. Linear approximation of offset curves to a cubic Bezier curve. [D] . Racherla, Sri Venkat R. 2003

机译：偏移曲线到三次贝塞尔曲线的线性近似。
6. 3D reconstruction of coronary arteries from 2D angiographic projections using non-uniform rational basis splines (NURBS) for accurate modelling of coronary stenoses [O] . Francesca Galassi, Mohammad Alkhalil, Regent Lee, -1

机译：使用非均匀有理基础样条（NURBS）从2D血管造影投影进行3D重建冠状动脉以精确建模冠状动脉狭窄
7. A novel approach for computing C-2-continuous offset of NURBS curves [O] . Chuang S.H.F., Shih J.L. 2014

机译：a novel approach for computing C-2-continuous offset of NURBs curves

An accurate and fast method for computing offsets of high degree rational Bezier/NURBS curves with user-definable tolerance

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