Please wait a minute...
ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2008, Vol. 9 Issue (6): 816-821    DOI: 10.1631/jzus.A071490
Electrical & Electronic Engineering     
Paths of algebraic hyperbolic curves
Ya-juan LI, Li-zheng LU, Guo-zhao WANG
School of Science, Hangzhou Dianzi University, Hangzhou 310018, China; Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Download:     PDF (0 KB)     
Export: BibTeX | EndNote (RIS)      

Abstract  Cubic algebraic hyperbolic (AH) Bézier curves and AH spline curves are defined with a positive parameter α in the space spanned by {1, t, sinht, cosht}. Modifying the value of α yields a family of AH Bézier or spline curves with the family parameter α. For a fixed point on the original curve, it will move on a defined curve called “path of AH curve” (AH Bézier and AH spline curves) when α changes. We describe the geometric effects of the paths and give a method to specify a curve passing through a given point.

Key words： Algebraic hyperbolic (AH) Bézier curve      AH spline curve      Path      Shape modification     
Received: 15 September 2007     
CLC:  TP391.72  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Ya-juan LI
Li-zheng LU
Guo-zhao WANG
Cite this article:

Ya-juan LI, Li-zheng LU, Guo-zhao WANG. Paths of algebraic hyperbolic curves. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(6): 816-821.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A071490     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2008/V9/I6/816

[1] Yong Li, Jin Wang, Guo-dong Lu, Guo-jun Pan. A numerical study of the effects of roller paths on dimensional precision in die-less spinning of sheet metal[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2014, 15(6): 432-446.
[2] Wen-feng Gan, Jian-zhong Fu, Hong-yao Shen, Zhi-wei Lin. A morphing machining strategy for artificial bone[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2014, 15(3): 157-171.
[3] Hui LUO, Hong-ping ZHU, Yu MIAO, Chuan-yao CHEN. Simulation of top-down crack propagation in asphalt pavements[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2010, 11(3): 223-230.
[4] B. HEMMATIAN, B. VAHIDI, S. H. HOSSEINIAN. Earth return path impedances of underground cable for three-layer earth[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(8): 1191-1198.
[5] Jinhyung KIM, Dongwon JEONG, Doo-kwon BAIK. An XPath-based OWL storage model for effective ontology management in Semantic Web environment[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2009, 10(6): 843-857.
[6] WU Dong-lei, ZHENG Ping, MAHMOOD Qaisar, YANG Xiao-sheng. Isolation and characteristics of Arthrobacter sp. strain CW-1 for biodegradation of PAEs[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(9): 1469-1474.
[7] ZHU Zhong-xiang, CHEN Jun, YOSHIDA Toyofumi, TORISU Ryo, SONG Zheng-he, MAO En-rong. Path tracking control of autonomous agricultural mobile robots[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1596-1603.
[8] Taniyama Kenta, Morii Takeshi, Koizumi Shinya, Noguchi Kazuhiro, Kotani Yukihiro, Katto Jiro. Experimental evaluation of an on-demand multipath routing protocol for video transmission in mobile ad hoc networks[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(Supplement 1): 145-150.
[9] WAN Ming, ZHANG Wei, MURRAY Marie O., KAUFMAN Arie. Automatic target tracking on multi-resolution terrain[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(7 ): 23-.
[10] LI Ya-juan, WANG Guo-zhao. Symmetric alteration of four knots of B-spline and NURBS surfaces[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(6 ): 23-.
[11] Jurca Dan, Frossard Pascal. Media-specific rate allocation in heterogeneous wireless networks[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(5): 713-726.
[12] Zhu Xiao-qing, Singh Jatinder Pal, Girod Bernd. Joint routing and rate allocation for multiple video streams in ad-hoc wireless networks[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(5 ): 8-.
[13] Zhuang Hui-zhong, Du Shu-xin, Wu Tie-jun. On-line real-time path planning of mobile robots in dynamic uncertain environment[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(4 ): 6-.
[14] WU Qing-biao, XIA Fei-hai. Shape modification of Bézier curves by constrained optimization[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(Supplement 1): 124-127.
[15] WANG Mei, WU Tie-jun. Cooperative co-evolution based distributed path planning of multiple mobile robots[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6(7): 697-706.