Continuity Conditions for Cubic Quasi-B&#233;zier Curves and Surfaces

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Continuity Conditions for Cubic Quasi-Bézier Curves and Surfaces

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- Continuity Conditions for Cubic Quasi-Bézier Curves and Surfaces
- Vol. 44, Issue 11, Pages: 46-50+60(2010)
- 作者机构：
  
  西安理工大学理学院,西安,710048
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP391.4
- Online First：10 November 2010，
  
  Published：2010
- 稿件说明：
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Continuity Conditions for Cubic Quasi-Bézier Curves and Surfaces[J]. 2010, 44(11): 46-50+60.
DOI：

Continuity Conditions for Cubic Quasi-Bézier Curves and Surfaces[J]. 2010, 44(11): 46-50+60. DOI：

摘要

针对工程中复杂自由曲线曲面难以用单一曲线曲面来表示的问题

研究了一种带形状参数的拟三次Bézier(三次Q-Bézier)曲线曲面的拼接技术. 在对三次Q-Bézier曲线基函数及其端点性质分析的基础上

给出了两相邻三次Q-Bézier曲线间G

、G

和C

、C

拼接的充要条件

运用张量积的方法给出了双三次Q-Bézier曲面的几何模型

同时分析了两相邻双三次Q-Bézier曲面片间G

光滑拼接的几何条件

并通过合理地选取形状参数

进一步简化了该曲面的G

拼接条件

给出了三次Q-Bézier曲线曲面光滑拼接的几何造型实例. 实例结果表明

所提方法简单、直观、易实现

有效地增强了三次Q-Bézier方法表达复杂曲线曲面的能力

可广泛地应用于工程复杂曲线曲面的造型系统中.

Abstract

Focusing on the fact that the engineering complex curves or surfaces can not be described by using a single curve or surface

the continuity conditions of cubic quasi-Bézier(cubic Q-Bézier)curves and surfaces with shape parameters are investigated. Following the analysis of basis functions and terminal properties

the necessary and sufficient conditions of G

continuity and C

continuity between two adjacent cubic Q-Bézier curves are proposed. And then

the geometric model of the cubic Q-Bézier surfaces is constructed and the condition of G

continuity between two adjacent cubic Q-Bézier surfaces in u and v directions is derived and simplified by choosing the control parameters properly. The modeling examples illustrate that the continuit

y condition of the cubic Q-Bézier curves and surfaces can be widely applied to the complex curves and surfaces modeling system.

关键词

Keywords

references

ZHANG Jiwen. C-curves and surfaces [J]. Graphical Models and Image Processing, 1999,61(1):2-15.

樊建华, 张纪文, 邬义杰. C-Bezier曲线的形状修改 [J]. 软件学报, 2002,13(11):2194-2200.

FAN Jianhua, ZHANG Jiwen,WU Yijie. Shape modification of C-Bézier curves [J]. Journal of Software, 2002,13(11): 2194-2200.

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丁敏, 汪国昭. 基于三角和代数多项式的T-Bézier曲线 [J]. 计算机学报, 2004,27(8):1021-1026.

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韩西安, 马逸尘, 黄希利. 拟三次Bézier曲线的形状调整 [J]. 西安交通大学学报, 2007,41(8): 903-906.

HAN Xi'an, MA Yichen, HUANG Xili. Shape modification of cubic quasi-Bézier curve [J]. Journal of Xi'an Jiaotong University, 2007,41(8):903-906.

WANG Guozhao, YANG Qinmin. Planar cubic hybrid hyperbolic polynomial curve and its shape classification [J]. Progress in Natural Science, 2004,14(1):41-46.

檀结庆, 王燕, 李志明. 三次H-Bézier曲线的分割、拼接及其应用 [J]. 计算机辅助设计与图形学学报, 2009,21(5):584-588.

TAN Jieqing, WANG Yan, LI Zhiming. Subdivision algorithm, connection and applications of cubic H-Bézier curves [J]. Journal of Computer-Aided Design Computer Graphics, 2009,21(5):584-588.

李鹏, 李原, 刘平,等. C-B样条曲线及曲面的光滑拼接与应用 [J]. 西北工业大学学报, 2007,25(6):890-895.

LI Peng, LI Yuan, LIU Ping, et al. On continuity conditions for C-B-Spline curves and surfaces [J]. Journal of Northwestern Polytechnical University, 2007,25(6):890-895.

FARIN G. Curves and surfaces for CAGD: a practical guide [M]. 5th ed.San Diego,USA: Academic Press, 2002:368-376.

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Related Institution

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⁰

Continuity Conditions for Cubic Quasi-Bézier Curves and Surfaces

DOI：

摘要

Abstract

关键词

Keywords

references