JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (10): 65-71.doi: 10.6040/j.issn.1671-9352.0.2015.429

Previous Articles     Next Articles

A class of trigonometric Bézier curve and surface which satisfy G2 continuity

LIU Hua-yong, XIE Xin-ping, LI Lu, ZHANG Da-ming, WANG Huan-bao   

  1. School of Mathematic &
    Physics, Anhui Jianzhu University, Hefei 230601, Anhui, China
  • Received:2015-09-04 Online:2016-10-20 Published:2016-10-17

PDF (PC)

566

Abstract: In order to meet the relatively high smooth jointing in relatively simple conditions, at the same time we can also modify the shape of curve and surface under without changing the control points, and then a group of low order trigonometric Bézier basis function with two shape parameters was constructed. Based on the group of basic functions, a class of curve and surface of arbitrary order trigonometric Bézier is defined by trigonometric function. The basic properties of the curves are discussed, and the conditions of the smooth blending of curves and surfaces are also discussed. According to the blending condition, the combination curves and surfaces of the piecewise smooth curves can be constructed. The blending curves and surfaces will not be changed the continuity of curve and surface by modifying the control points and parameters of the method and automatically meet with the G2 continuity and simple calculation. The results of numerical examples show the effectiveness of this method.

Key words: blending, trigonometric function, Bézier curves and surfaces, continuity, Jointing

CLC Number: 

  • TP391
[1] ZHANG Jiwen. C-curves: Two different forms of C-B-splines[J]. Computer Aided Geometric Design, 1997, 14(1):31-41.
[2] 王文涛,汪国昭.带形状参数的三角多项式均匀B样条[J]. 计算机学报,2005,28(7):1192-1198. WANG Wentao, WANG Guozhao. Trigonometric polynomial uniform B-spline with shape parameter[J]. Chinese Journal of Computers, 2005, 28(7):1192-1198.
[3] CAO Juan, WANG Guozhao. The structure of uniform B-spline curves with parameters[J]. Progress in Natural Science, 2008, 18(3):303-308.
[4] HAN Xuli, ZHU Yanpeng. Curve construction based on five trigonometric blending functions[J]. BIT Numerical Mathematics, 2012, 52(6):953-979.
[5] WANG Wentao, WANG Guohao. Bézier curves with shape parameter[J]. Journal of Zhejiang University Science A, 2005, 6(6):497-501.
[6] CHEN Qinyu, WANG Guozhao. A class of Bézier-like curve[J]. Computer Aided Geometric Design, 2003, 20(1):29-39.
[7] 严兰兰,韩旭里.具有多种优点的三角多项式曲线曲面[J].计算机辅助设计与图形学学报,2015, 27(10):1971-1979. YAN Lanlan, HAN Xuli.Trigonometric polynomial curve and surface with many advantages[J]. Journal of Computer-Aided Design & Computer Graphics, 2015, 27(10):1971-1979.
[8] 严兰兰, 韩旭里. 形状及光滑度可调的自动连续组合曲线曲面[J].计算机辅助设计与图形学学报,2014,26(10):1654-1662. YAN Lanlan, HAN Xuli. Automatic continuous composite curve and surface with adjustable shape and smoothness[J]. Journal of Computer-Aided Design & Computer Graphics, 2014, 26(10):1654-1662.
[9] HAN Xian, HUANG Xili. A novel generalization of Bézier curve and surface[J].Journal of Computational and Applied Mathematics, 2008, 217(1):180-193.
[10] LV Yonggang, WANG Guozhao, YANG Xunnian. Uniform hyperbolic polynomial B-spline curves[J]. Computer Aided Geometric Design, 2002, 19(6):379-393.
[11] HU Gang, QIN Xinqiang. The construction of λμ-B-spline curves and its application to rotational surfaces[J]. Applied Mathematics and Computation, 2015, 266(3):194-211.
[12] LIU Xumin, XU Weixiang, GUAN Yong. Hyperbolic polynomial uniform B-spline curves and surfaces with shape parameter[J]. Graphical Models, 2010, 72(1):1-6.
[13] 李军成.一种构造任意类三次三角曲线的方法[J]. 小型微型计算机系统, 2011, 32(7):1442-1445. LI Juncheng. A method for constructing arbitrary quasi-cubic trigonometric curves[J].Journal of Chinese Computer Systems, 2011, 32(7):1442-1445.
[14] YAN Lanlan, TAO Huang. An algebraic-trigonometric blended piecewise curve[J]. Journal of Information & Computational Science, 2015, 12(17):6491-6501.
[15] MRIDULA Dube, REENU Sharm. Cubic TP B-spline curves with a shape parameter[J]. International.Journal of Engineering Research in Africa, 2014, 11(1):59-72.
[16] ZHU Yungpeng, HAN Xuli. New cubic rational basis with tension shape parameters[J]. Applied Mathematics Journal of chinese Universities, 2015, 30(3):273-298.
[1] . Regularity for solutions of elliptic obstacle problems with subcritical growth [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 57-63.
[2] WANG Lu, LAI Chun-lu. A modifiedtwo-viewpoint DIBR based virtual view synthesis method [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(3): 122-131.
[3] FANG Rui, MA Jiao-jiao, FAN Sheng-jun. A stability theorem for solutions of a class of backward stochastic differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 39-44.
[4] LIU Hua-yong, WANG Huan-bao, LI Lu, ZHANG Da-ming. Shape blending Bézier-like curve with geometric continuity [J]. J4, 2012, 47(3): 51-55.
[5] YANG Shao-hua1, LIANG Feng2. Cellina approximation theorem in a hyperconvex metric  space and its applications [J]. J4, 2010, 45(12): 75-77.
[6] SONG Jia, LUO Minnan, LI Yongming. [J]. J4, 2009, 44(3): 67-70 .
[7] LI Yan-hong,WANG Gui-jun . Strongly order continuity and pseudo-S-property of generalized fuzzy valued Choquet integrals [J]. J4, 2008, 43(4): 76-80 .
[8] SUN Shou-bin,MENG Guang-wu ,ZHAO Feng . Dα-Continuity of order homomorphism [J]. J4, 2007, 42(7): 49-53 .
[9] LI Ning . Pre-continuity mapping in I-fuzzy topological space [J]. J4, 2007, 42(12): 42-45 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd