可重建圆锥样条曲线的带多参数三点细分法

doi:10.16182/j.issn1004731x.joss.201711004

系统仿真学报 ›› 2017, Vol. 29 ›› Issue (11): 2624-2628.doi: 10.16182/j.issn1004731x.joss.201711004

可重建圆锥样条曲线的带多参数三点细分法

赵欢喜^1,2, 丘夏^1,2

1.厦门理工学院计算机与信息工程学院,厦门 361024;
2.中南大学信息科学与工程学院,长沙 410083

收稿日期:2016-05-20 发布日期:2020-06-05
作者简介:赵欢喜(1967-),男,湖南邵阳,博士,副教授,硕导,研究方向为计算机图形学;丘夏(1985-),女,广西百色,硕士,研究方向为计算机图形学。
基金资助:
国家自然科学基金(61272024),厦门理工学院青年人才基金(YKJ13005R)

Three-point Subdivision Scheme with Multi-parameters for Reproducing Conic Splines

Zhao Huanxi^1,2, Qiu Xia^1,2

1. School of Computer & Information Engineering, Xiamen University of Technology, Xiamen 361024, China;
2. School of Information Science & Engineering, Central South University, Changsha 410083, China

Received:2016-05-20 Published:2020-06-05

摘要/Abstract

摘要： 提出了一个非静态多参数三点非稳定细分格式生成C¹的有理二次Bezier样条曲线,通过选取合适的参数,本细分格式可以重建圆锥曲线以及圆锥样条曲线。另外虽提出的细分格式是逼近型格式,但生成的极限曲线具有插值初始控制点,通过选取合适的参数,还具有保圆、保直线、保尖点等保形特性。数值实例说明提出的细分方法具有很强的造型能力。

关键词: 细分, 圆锥曲线, 插值, 逼近型

Abstract: A non-static and non-stationary three-point subdivision schemes with three parameters was proposed to generate piecewise C1 rational quadratic Bezier spline curves. In particular, for special values of the tension parameters, the proposed scheme will be capable of reproducing all conic sections exactly and conic spline curve. In addition, the proposed subdivision scheme is approximation-type, but the limit curve generated by such scheme interpolates the initial control points, and by selecting the appropriate parameters, the proposed scheme is circle-preserving, line-preserving, cusp-preserving. Numerical examples show that the proposed subdivision scheme has a strong modeling capability.

Key words: subdivision, conic curve, interpolation, approximation-type

中图分类号:

TP391.7

赵欢喜, 丘夏. 可重建圆锥样条曲线的带多参数三点细分法[J]. 系统仿真学报, 2017, 29(11): 2624-2628.

Zhao Huanxi, Qiu Xia. Three-point Subdivision Scheme with Multi-parameters for Reproducing Conic Splines[J]. Journal of System Simulation, 2017, 29(11): 2624-2628.

参考文献

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[9] J.E Sarlabous,V.H Mederos,N.L Gil, et al, Geodesic conic subdivision curves on surfaces[C]// Proceedings-24th SIBGRAPI Conference on Graphics, Patterns and Images. Washington, DC,: IEEE Computer Society, 2011: 56-63
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可重建圆锥样条曲线的带多参数三点细分法

Three-point Subdivision Scheme with Multi-parameters for Reproducing Conic Splines

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