JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (6): 102-110.doi: 10.6040/j.issn.1671-9352.0.2021.613

Previous Articles    

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

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

CLC Number: 

  • 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.
[1] LIU Jing-shu, WANG Li, LIU Jing-lei. Nyström extension based on circulant matrix projection [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(7): 55-66.
[2] ZHANG Xiao-dong, DONG Wei-guang, TANG Min-an, GUO Jun-feng, LIANG Jin-ping. gOMP reconstruction algorithm based on generalized Jaccard coefficient for compressed sensing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 23-28.
[3] ZHANG Ben-hui, TANG Yuan-sheng, CHEN Wen-bing. Communication rate in the secret reconstruction phase [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 7-11.
[4] LIU Min, SONG Wei-dong. Totally real minimal submanifolds in quasi-complex projective space [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(12): 71-75.
[5] FAN Ting-jun, DIAO Jin-mei. Research advances of tissue-engineered human corneal endothelium [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(1): 1-7.
[6] CHEN Su-gen1, SU Ben-yue2, WANG Zhi-hua1. The triangular domain extension of T-Bézier basis for 4-order trigonometric polynomial space [J]. J4, 2013, 48(3): 31-36.
[7] WANG Wen-hua, CAO Huai-xin*, LI Wei. (A,B)-quantum measurements [J]. J4, 2012, 47(4): 70-76.
[8] JIANG Hua, LI Ming-zhen, WANG Xin. A  PPM probabilistic packet marking improving scheme [J]. J4, 2011, 46(9): 85-88.
[9] FAN Ting-jun, MA Xi-ya, ZHAO Jun, HU Xiu-zhong. Establishment of a human corneal endothelial cell strain and in vitro reconstruction of a tissue-engineered  human corneal endothelium [J]. J4, 2011, 46(10): 142-151.
[10] ZENG Weng-fu1, HUANG Tian-qiang1,2, LI Kai1, YU YANG-qiang1, GUO Gong-de1,2. A local linear emedding agorithm based on harmonicmean geodesic kernel [J]. J4, 2010, 45(7): 55-59.
[11] LI Na, LI Chang-jun*. A note on the collars in complex hyperbolic manifolds [J]. J4, 2010, 45(4): 39-42.
[12] . Studies on effects of tissue-engineered human corneal endothelia on maintaining corneal transparency of New Zealand white rabbits [J]. J4, 2010, 45(3): 1-5.
[13] HU Cheng-Zhong, GONG Yan-Xiang. Using the Post-Newtonian approximation method to calculate the geodesic equationsof a test particle in the gravitational field of a CM celestial body [J]. J4, 2009, 44(11): 40-43.
[14] LIU Ming-hui,ZHU Cheng-guang . The Monte Carlo study of W boson polarization [J]. J4, 2008, 43(5): 14-18 .
[15] ZHANG Shu-qin,HOU Wan-guo,*,WANG Wen-xing . Sorption removal of p-nitrophenol by uncalcined and calcined Mg2Al layered double hydroxides [J]. J4, 2007, 42(9): 19-24 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!