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《山东大学学报(理学版)》 ›› 2022, Vol. 57 ›› Issue (6): 102-110.doi: 10.6040/j.issn.1671-9352.0.2021.613

• • 上一篇    

过Bézier三边形测地线的有理多项式Coons曲面片重构

王淑娟,杨火根*,柴莹   

  1. 江西理工大学理学院, 江西 赣州 341000
  • 发布日期:2022-06-10
  • 作者简介:王淑娟(1995— ),女,硕士研究生,研究方向为计算机辅助几何设计. E-mail:2691316982@qq.com*通信作者简介:杨火根(1975— ),男,博士,教授,硕士生导师, 研究方向为计算机辅助几何设计、应用逼近论. E-mail:yhg_98@jxust.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12161043);江西省自然科学基金资助项目(20192BAB201007)

Reconstruction of rational polynomial Coons surface patches throuth Bézier triangular geodesic

WANG Shu-juan, YANG Huo-gen*, CHAI Ying   

  1. Faculty of Science, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi, China
  • Published:2022-06-10

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摘要： 对满足一定约束的五次Bézier三边形曲线, 提出4种有理多项式Coons曲面构造格式, 使得所构造的曲面插值三边形曲线为边界测地线。首先, 分析插值曲面沿边界测地线的跨界切矢在角点处的相容性约束; 其次基于重心坐标表示的有理Hermite多项式基, 设计插值两相邻边界测地线的插值算子; 最后, 给出插值三边形测地线的有理多项式Coons曲面构造格式。本文提出的过Bézier三边形测地线的Coons曲面构造算法简便易实现, 计算结果表明算法的可行性。

关键词: 测地线, 三角域, Coons曲面, 重构

Abstract: For the quintic Bézier triangular curve that satisfies certain constraints, four rational polynomial Coons surfaces which interpolate the triangular curve as the geodesics is proposed. Firstly, the corner compatibility constraints of the cross-boundary tangent vector of the interpolated surface along the boundary geodesics are analyzed. Secondly, based on the rational Hermite polynomial basis represented by the barycentric coordinate, the interpolation operator for interpolating two adjacent boundary geodesics is designed. Finally, the construction scheme of rational polynomial Coons surface for interpolating triangular geodesics is presented. The construction algorithm of Coons surface through Bézier triangular geodesics proposed in this paper is simple and easy to implement, and the calculation results show the feasibility of the algorithm.

Key words: geodesic, triangular domain, Coons surface, reconstruction

中图分类号: 

  • O241
[1] WANG Guojin, TANG Kai, TAI Chiewlan. Parametric representation of a surface pencil with a common spatial geodesic[J]. Computer-Aided Design, 2004, 36(5):447-459.
[2] SÁNCHEZ-REYES J, DORADO R. Constrained design of polynomial surfaces from geodesic curves[J]. Computer-Aided Design, 2008, 40(1):49-55.
[3] 虞一琦,徐岗,王毅刚,等. 过测地线的调和Bézier曲面设计[J]. 计算机辅助设计与图形学学报, 2013, 25(10):1439-1445. YU Yiqi, XU Gang, WANG Yigang, et al. Harmonic Bézier surfaces passing given geodesic[J]. Journal of Computer-Aided Design & Computer Graphics, 2013, 25(10):1439-1445.
[4] 杨火根,汪国昭. 过测地线的B样条曲面优化设计[J]. 计算机辅助设计与图形学学报, 2013, 25(10):1433-1438. YANG Huogen, WANG Guozhao. Optimization design of B-spline surfaces through geodesics[J]. Journal of Computer-Aided Design & Computer Graphics, 2013, 25(10):1433-1438.
[5] PALUSZNY M. Cubic polynomial patches through geodesics[J]. Computer-Aided Design, 2008, 40(1):56-61.
[6] LI Caiyun, WANG Renhong, ZHU Chungang. Design and G1 connection of developable surfaces through Bézier geodesics[J]. Applied Mathematics and Computation, 2011, 218(7):3199-3208.
[7] FAROUKI R T, SZAFRAN N, BIARD L. Existence conditions for Coons patches interpolating geodesic boundary curves[J]. Computer Aided Geometric Design, 2009, 26(5):599-614.
[8] FAROUKI R T, SZAFRAN N, BIARD L. Construction of Bézier surface patches with Bézier curves as geodesic boundaries[J]. Computer-Aided Design, 2009, 41(11):772-781.
[9] LI Caiyun, WANG Renhong, ZHU Chungang. Designing approximation minimal parametric surfaces with geodesics[J]. Applied Mathematical Modelling, 2013, 37(9):6415-6424.
[10] YANG Huogen, WANG Guozhao. Optimized design of Bézier surface through Bézier geodesic quadrilateral[J]. Journal of Computational and Applied Mathematics, 2015, 273:264-273.
[11] YANG Huogen, WANG Guozhao. Construction of B-spline surface with B-spline curves as boundary geodesic quadrilateral[J]. Journal of Computational and Applied Mathematics, 2015, 290:104-113.
[12] YANG Huogen, PETERS J. Constraints for geodesic network interpolation at a vertex[J]. Computer Aided Geometric Design, 2018, 67:71-78.
[13] 杨火根,毛小红. 过测地线网的组合双三次Bézier曲面优化设计[J]. 南昌大学学报(理科版), 2020, 44(3):235-241,247. YANG Huogen, MAO Xiaohong. Optimization design of combined bicubic Bézier surface through geodesic network[J]. Journal of Nanchang University(Natural Science), 2020, 44(3):235-241,247.
[14] FAROUKI R T, SZAFRAN N, BIARD L. Construction and smoothing of triangular Coons patches with geodesic boundary curves[J]. Computer Aided Geometric Design, 2010, 27(4):301-312.
[15] 梅向明. 微分几何[M]. 北京: 高等教育出版社, 2008: 37-44, 146-152. MEI Xiangming. Differential geometry[M]. Beijing: Higher Education Press, 2008: 37-44, 146-152.
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