Computer Science ›› 2018, Vol. 45 ›› Issue (3): 46-50.

### A New Kind of Parametric Curves by Special Basis Function

LI Jing-gai, CHEN Qiu-yang, HAN Jia-qi, HUANG Qi-li and ZHU Chun-gang

• Online:2018-03-15 Published:2018-11-13

Abstract: The construction of parametric curves and surfaces is very important in computer aided geometric design.It’s well known that Bézier curve,which is defined by Bernstein basis functions is a basic method in curve design,and the B-spline curve and NURBS curve are generalizations of the Bézier curve .This paper defined a new kind of basis functions by a given real knot points set,which is a generalization of Bernstein basis functions,and defined a new parametric curve by these basis functions,called T-Bézier curve ,which preserves some properties of Bézier curve.What’s more,this paper presented the limit property of T-Bézier curve while some knots move and gave some examples to verify the properties of the curve.

 [1] 王仁宏,李崇君,朱春钢.计算几何教程[M].北京:科学出版社,2008. [2] 王国瑾,汪国昭,郑建民.计算机辅助几何设计[M].北京:高等教育出版社,2001. [3] FARIN G.Curves and Surfaces for CAGD,A Practical Guide(Fifth Edition)[M].New York:Academic Press,2002. [4] BERMSTEIN S N.Démonstration du théorème de Weierstrassf on déesurle calcul des probabilités.http://www.numdam.org/item？id:AIHBP_1975.11-03-203-0. [5] FARIN G.Chapter I-A History of Curves and Surfaces inCAGD [C]∥Handbook of Computer Aided Geometric Design.North Holland:Elsevier,2002:1-21. [6] FAROUKI R T.The Bernstein polynomial basis:A centennial retrospective [J].Computer Aided Geometric Design,2012,29(6):379-419. [7] CHEN Q Y,WANG G Z.A class of Bézier-like curves [J].Computer Aided Geometric Design,2003,20(1):29-39. [8] WANG G Z,CHEN Q Y,ZHOU M H.NUAT B-spline curves [J].Computer Aided Geometric Design,2004,21(2):193-205. [9] ORUC H,PHILLIPS G M.q-Bernstein polynomials and Bézier curves [J].Journal of Computational and Applied Mathematics,2003,151(1):1-12. [10] KRASAUSKAS R.Toric surface patches [J].Advances in Computational Mathematics,2002,17(1/2):89-113. [11] GARCIA-PUENTE L D,SOTTILE F,ZHU C G.Toric dege-nerations of Bezier patches [J].ACM Transactions on Graphics,2011,30(5):110. [12] ZHU Y P,HAN X L,LIU S J.Curve construction based on fourαβ-Bernstein-like basis functions [J].Journal of Computational and Applied Mathematics,2015,273(1):160-181. [13] GARCIA-PUENTE L D,SOTTILE F,GRACIUN G.Some geometrical aspects of control points for toric patches [C]∥ International Conference on Mathematical Methods for Curves and Surfaces.Heidelberg:Springer,2008:111-135. [14] POSTINGHEL E,SOTTILE F,VILLAMIZAR N.Degenerations of real irrational toric varieties [J].Journal of London Mathematical Society,2015,92(2):223-241.
 No related articles found!
Viewed
Full text

Abstract

Cited

Shared
Discussed
 [1] LEI Li-hui and WANG Jing. Parallelization of LTL Model Checking Based on Possibility Measure[J]. Computer Science, 2018, 45(4): 71 -75 . [2] SUN Qi, JIN Yan, HE Kun and XU Ling-xuan. Hybrid Evolutionary Algorithm for Solving Mixed Capacitated General Routing Problem[J]. Computer Science, 2018, 45(4): 76 -82 . [3] ZHANG Jia-nan and XIAO Ming-yu. Approximation Algorithm for Weighted Mixed Domination Problem[J]. Computer Science, 2018, 45(4): 83 -88 . [4] WU Jian-hui, HUANG Zhong-xiang, LI Wu, WU Jian-hui, PENG Xin and ZHANG Sheng. Robustness Optimization of Sequence Decision in Urban Road Construction[J]. Computer Science, 2018, 45(4): 89 -93 . [5] SHI Wen-jun, WU Ji-gang and LUO Yu-chun. Fast and Efficient Scheduling Algorithms for Mobile Cloud Offloading[J]. Computer Science, 2018, 45(4): 94 -99 . [6] ZHOU Yan-ping and YE Qiao-lin. L1-norm Distance Based Least Squares Twin Support Vector Machine[J]. Computer Science, 2018, 45(4): 100 -105 . [7] LIU Bo-yi, TANG Xiang-yan and CHENG Jie-ren. Recognition Method for Corn Borer Based on Templates Matching in Muliple Growth Periods[J]. Computer Science, 2018, 45(4): 106 -111 . [8] GENG Hai-jun, SHI Xin-gang, WANG Zhi-liang, YIN Xia and YIN Shao-ping. Energy-efficient Intra-domain Routing Algorithm Based on Directed Acyclic Graph[J]. Computer Science, 2018, 45(4): 112 -116 . [9] CUI Qiong, LI Jian-hua, WANG Hong and NAN Ming-li. Resilience Analysis Model of Networked Command Information System Based on Node Repairability[J]. Computer Science, 2018, 45(4): 117 -121 . [10] WANG Zhen-chao, HOU Huan-huan and LIAN Rui. Path Optimization Scheme for Restraining Degree of Disorder in CMT[J]. Computer Science, 2018, 45(4): 122 -125 .