A generalized curve subdivision scheme of arbitrary order with a tension parameter

Mei-e Fang; Weiyin Ma; Guozhao Wang

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A generalized curve subdivision scheme of arbitrary order with a tension parameter

机译：具有张力参数的任意阶数的广义曲线细分方案

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摘要

This article presents a generalized subdivision scheme of arbitrary order with a tension parameter for curve design. The scheme is built upon refinement of a family of generalized B-splines that unify classic B-splines with algebraic-trigonometric B-splines and algebraic-hyperbolic B-splines. The scheme of order k produces C~(k-2)-continuous limit curves representing such splines. Many known subdivisions are special cases of the proposed subdivision scheme. By assigning an appropriate initial tension parameter, many analytic curves commonly used in engineering applications, such as Lissajous curves, conics, trigonometric function curves, hyperbolic function curves, catenary curves and helixes, etc., can also be exactly defined under the generalized subdivision scheme. Numerous examples are also provided to illustrate how the initial tension parameter and the control points are assigned for reproducing such analytic curves.

机译：本文提出了具有张力参数的任意阶数的广义细分方案，用于曲线设计。该方案是建立在一系列广义B样条的精炼之上的，这些B样条将经典B样条与代数三角B样条和代数双曲B样条统一起来。 k阶方案生成代表此类样条的C〜（k-2）连续极限曲线。许多已知的细分都是建议的细分方案的特例。通过分配适当的初始张力参数，还可以在广义细分方案下精确定义许多工程应用中常用的分析曲线，例如李沙育曲线，圆锥曲线，三角函数曲线，双曲线函数曲线，悬链线和螺旋线等。。还提供了许多示例来说明如何分配初始张力参数和控制点以重现此类分析曲线。

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来源
《Computer Aided Geometric Design》 |2010年第9期|p.720-733|共14页
作者
Mei-e Fang; Weiyin Ma; Guozhao Wang;
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作者单位

School of Computer Science, Hongzhou Dianzi University, Hangzhou, China,Department of MEEM, City University of Hong Kong, Hong Kong, China;

Department of MEEM, City University of Hong Kong, Hong Kong, China;

Department of Mathematics, Zhejiang University, Hangzhou, 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
关键词
generalized subdivision; tension parameter; generalized b-spline curve; trigonometric spline curves; hyperbolic spline curves; analytic curves;

机译：广义细分;张力参数广义b样条曲线三角样条曲线;双曲样条曲线;分析曲线;

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1. A nonlinear generalized subdivision scheme of arbitrary degree with a tension parameter [J] . Zhang Zeze, Zheng Hongchan, Zhou Jie, Advances in Difference Equations . 2020,第a期

机译：带有张力参数的任意度的非线性广义细分方案
2. A generalized surface subdivision scheme of arbitrary order with a tension parameter [J] . Mei-e Fang, Weiyin Ma, Guozhao Wang Computer-Aided Design . 2014,第Null期

机译：具有张力参数的任意阶数的广义表面细分方案
3. A Note on the Continuity of the Generalized Curve Subdivision Scheme with Tension Parameter [J] . ZHANG Nan, FANG Mei-e 计算机辅助绘图设计与制造（英文版） . 2015,第001期

机译：带张力参数的广义曲线细分方案的连续性的一个注记
4. A Generalized Four Point Interpolatory Subdivision Scheme for Curve Design [C] . Xinfen Zhang International Conference on Advanced Materials and Information Technology Processing . 2012

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5. Hermite subdivision schemes and jet subdivision surfaces. [D] . Xue, Yonggang. 2004

机译：Hermite细分方案和射流细分曲面。
6. OXYGEN TENSION OF TISSUES BY THE POLAROGRAPHIC METHOD. IV. SKIN OXYGEN TENSION VS. ARTERIAL OXYGEN SATURATION; RELATIONSHIP TO OXYHEMOGLOBIN DISSOCIATION CURVE [O] . Raymond Penneys 1952

机译：极谱法测定组织的氧张力。 IV。皮肤氧气张力VS。动脉血氧饱和度；与氧合血红蛋白解离曲线的关系
7. On Subdivision Schemes Generalizing Uniform B-spline Surfaces of Arbitrary Degree [O] . Jos Stam 2000

机译：关于推广任意度均匀B样条曲面的细分方案

A generalized curve subdivision scheme of arbitrary order with a tension parameter

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