New Method for Constructing Quartic Quasi-B&#233;zier Rotation Surfaces with Multiple Shape Parameters

doi:10.7652/xjtuxb201406013

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New Method for Constructing Quartic Quasi-Bézier Rotation Surfaces with Multiple Shape Parameters

更新时间：2025-07-09

- New Method for Constructing Quartic Quasi-Bézier Rotation Surfaces with Multiple Shape Parameters
- Vol. 48, Issue 6, Pages: 74-79+109(2014)
- 作者机构：
  
  西安理工大学理学院,西安,710054
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201406013
  CLC： TP391.4
- Online First：10 June 2014，
  
  Published：2014
- 稿件说明：
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New Method for Constructing Quartic Quasi-Bézier Rotation Surfaces with Multiple Shape Parameters[J]. 2014, 48(6): 74-79+109.
DOI：

New Method for Constructing Quartic Quasi-Bézier Rotation Surfaces with Multiple Shape Parameters[J]. 2014, 48(6): 74-79+109. DOI： 10.7652/xjtuxb201406013.

摘要

为了方便解决传统旋转曲面计算复杂和形状难以调节的问题

研究了一种带多形状参数的四次拟Bézier旋转曲面的构造技术。首先

基于二元超限向量值有理插值函数的重要思想

利用带多形状参数的四次拟Bézier曲线作为母线进行旋转曲面的设计; 其次

推导了生成整个四次拟旋转曲面的一个显式函数表达式。该方法生成的旋转曲面不仅计算简单而且具有良好的形状可调性

同时还保留了传统Bézier旋转曲面的许多几何特性。最后

对所设计的旋转曲面进行了形状与性质分析

并给出了形状控制参数对旋转曲面形状的影响规律。造型实例表明

所提方法不仅直观、高效

而且易于调整旋转曲面的局部形状

在各种旋转曲面的构造与外形设计中将得到十分广泛的应用。

Abstract

To deal with the problems in adjusting and controlling shapes of rotation surfaces

a new efficient method for quick constructing rotary surfaces with local shape parameters is proposed. Following the essence of transfinite vectored rational interpolating function

the quartic quasi-Bézier rotary surfaces with multiple shape parameters are constructed and the explicit function for quartic quasi-Bézier rotary surfaces is presented. The so constructed surfaces inherit the outstanding properties of the Bézier rotary surfaces with good performance in adjusting local shapes by changing the shape parameters. Some properties of the quartic quasi-Bézier rotary surfaces and applications to surface design are discussed.

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references

CHEN Q Y, WANG G Z. A class of Bézier-like curves[J]. Computer Aided Geometric Design, 2003, 20(1): 29-39.

ORUC H, PHILLIPS G H. q-Bernstein polynomials and Bézier curves[J]. Journal of Computational and Applied Mathematics, 2003, 151(1): 1-12.

HAN Xian, MA Yichen, HUANG Xili. The cubic trigonometric Bézier curve with two shape parameters[J]. Applied Mathematic Letters, 2009, 22(3): 226-231.

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.

HAN Xian, MA Yichen, HUANG Xili. A novel generalization of Bézier curve and surface[J]. Journal of Computational and Applied Mathematics, 2008, 217(1): 180-193.

胡钢, 戴芳, 秦新强, 等. 四次带参Bézier曲线曲面的光滑拼接[J]. 上海交通大学学报, 2010, 44(11): 1481-1485, 1490.

HU Gang, DAI Fang, QIN Xinqiang, et al. On continuity conditions for quartic Bézier curves and surfaces with shape parameters[J]. Journal of Shanghai Jiaotong University, 2010, 44(11): 1481-1485, 1490.

吴荣军, 彭国华, 罗卫民, 等. 四次带参Bézier曲线的形状分析[J]. 计算机辅助设计与图形学学报, 2009, 21(6): 725-729.

WU Rongjun, PENG Guohua, LUO Weimin, et al. Shape analysis of quartic Bézier curve with shape parameter[J]. Journal of Computer Aided Design Computer Graphics, 2009, 21(6): 725-729.

胡钢, 段献葆, 秦新强, 等. 4次λ-Bézier曲线的近似合并算法[J]. 华中科技大学学报, 2011, 37(9): 45-49.

HU Gang, DUAN Xianbao, QIN Xiqiang, et al. Approximate merging of a pair of quartic λ-Bézier curves with shape parameters[J]. Journal of Huazhong University of Science and Technology, 2011, 37(9): 45-49.

胡钢, 秦新强, 韩西安, 等. 拟三次Bézier曲线曲面的拼接技术[J]. 西安交通大学学报, 2010, 44(11): 46-50, 60.

HU Gang, QIN Xinqiang, HAN Xi'an, et al. Continuity conditions for cubic quasi-Bézier curves and surfaces[J]. Journal of Xi'an Jiaotong University, 2010, 44(11): 46-50, 60.

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.

FARIN G. Curves and surfaces for CAGD: a practical guide fifth edition[M]. San Diego, USA: Academic Press, 2002: 229-303.

BOURGUIGNON D, CANI M P, DRETTAKIS G. Drawing for illustration and annotation in 3D[J]. Computer Graphics Forum, 2001, 20(3): 114-122.

DE ARAAU'UJO B R, JORGE J A P. Free form modeling with variational implicit surfaces[EB/OL].[2013-09- 12].http:∥citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.104.8535rep=rep1type=pdf.

韩丽, RAFFAELE D A. Cubic B样条旋转曲面的自由绘制技术[J]. 小型微型计算机系统, 2009, 30(7): 1141-1144.

HAN Li, RAFFAELE D A. Rotation surface modeling technique by cubic B-spline free drawing[J]. Journal of Chinese Computer Systems, 2009, 30(7): 1141-1144.

檀结庆. 连分式理论及其应用[M]. 北京: 科学出版社, 2007: 337-392.

朱晓临. 一种快速构造圆弧的新方法[J]. 合肥工业大学学报, 2002, 25(2): 269-272

ZHU Xiaolin. A new method for constructing circular arc[J]. Journal of Hefei University of Technology, 2002, 25(2): 269-272.

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Related Author

韩西安 1

马逸尘 1

黄希利 3

秦新强 1

韩西安 2

段现报 1

秦新强

Related Institution

西安交通大学理学院

装备指挥技术学院基础部

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New Method for Constructing Quartic Quasi-Bézier Rotation Surfaces with Multiple Shape Parameters

DOI：10.7652/xjtuxb201406013

摘要

Abstract

关键词

Keywords

references