Shape analysis of class of cubic curves

Computer Engineering and Applications ›› 2012, Vol. 48 ›› Issue (3): 165-168.

• 图形、图像、模式识别 • Previous Articles Next Articles

Shape analysis of class of cubic curves

WU Xiaoqin, CHEN Fulai, ZHU Xiuyun

School of Mathematics & Computation Science, Hunan University of Science & Technology, Xiangtan, Hunan 411201, China

Received:1900-01-01 Revised:1900-01-01 Online:2012-01-21 Published:2012-01-21

一类三次曲线的形状分析

吴晓勤，陈福来，朱秀云

湖南科技大学数学与计算科学学院，湖南湘潭 411201

Abstract

Abstract: This paper considers the shape features of the class of cubic curves based on the theory of envelop and topological mapping. Necessary and sufficient conditions are derived for this curve having one or two inflection points, a loop or a cusp, or be locally or globally convex. Those conditions are completely decided by control polygon and the shape parameter. Furthermore, it discusses the influences of shape parameter on the shape distribution diagram and the ability for adjusting the shape of the curve.

Key words: cubic curve, shape parameter, singularities, inflection points, local convexity, global convexity

摘要： 基于包络理论与拓扑映射的方法，对一类带有形状参数的三次曲线进行了形状分析，得出了曲线上含有奇点、拐点和曲线为局部凸或全局凸的充分必要条件，这些条件完全由控制多边形和形状参数所决定。进一步讨论了形状参数对形状分布图的影响及其对曲线形状的调节能力。

关键词: 三次曲线, 形状参数, 奇点, 拐点, 局部凸, 全局凸

WU Xiaoqin, CHEN Fulai, ZHU Xiuyun. Shape analysis of class of cubic curves[J]. Computer Engineering and Applications, 2012, 48(3): 165-168.

吴晓勤，陈福来，朱秀云. 一类三次曲线的形状分析[J]. 计算机工程与应用, 2012, 48(3): 165-168.

[1]	GAO Ning1, WANG Xingyuan1，2, WANG Xiukun1. Face Alignment Across Expression Based on Multi State Layered Model [J]. Computer Engineering and Applications, 2019, 55(7): 40-47.
[2]	WANG Kai, ZHANG Guicang, SU Jinfeng. Practical Method for Generating Trigonometric Polynomial Surfaces over Triangular Domains [J]. Computer Engineering and Applications, 2019, 55(22): 195-200.
[3]	YAN Lanlan, HUANG Tao. Unified expression of curves and surfaces from approximation to interpolation [J]. Computer Engineering and Applications, 2018, 54(5): 180-185.
[4]	GUO Dong1, XIAO Qingtai1，2, XU Jianxin1，2. Cloud computing energy consumption optimization model research based on Weibull distribution [J]. Computer Engineering and Applications, 2017, 53(15): 77-84.
[5]	LIU Xiaoqiong, YANG Guoying. Extension of quartic Bézier curve with parameters [J]. Computer Engineering and Applications, 2015, 51(6): 167-170.
[6]	HUANG Fei, TAN Shoubiao. Facial feature points localization based on improved active appearance models algorithm [J]. Computer Engineering and Applications, 2015, 51(16): 204-209.
[7]	LI Juncheng, ZHONG Yue’e, XIE Chun. Cubic trigonometric Hermite interpolating splines curves with shape parameters [J]. Computer Engineering and Applications, 2014, 50(17): 182-185.
[8]	QIN Xinqiang, SHEN Xiaoli, HU Gang. Shape modification for quartic C-Bézier curves [J]. Computer Engineering and Applications, 2014, 50(13): 178-181.
[9]	YU Desheng1, XU Yingbo1, ZENG Jiexian2. A class of quasi-quartic trigonometric polynomial Bézier curves with double parameters and its extension [J]. Computer Engineering and Applications, 2013, 49(18): 180-186.
[10]	PEI Fang1, HAN Xuli2, LI Yan2. Structure and splice of Coons patched with shape parameters [J]. Computer Engineering and Applications, 2013, 49(10): 163-166.
[11]	CHEN Xiaoyan, LIU Zhi, ZHANG Li. Quartic Bézier curves and surfaces with shape parameters [J]. Computer Engineering and Applications, 2012, 48(9): 172-175.
[12]	LI Juncheng, YNAG Lian. [C2] continuous quasi-cubic trigonometric spline curve with shape parameter [J]. Computer Engineering and Applications, 2012, 48(30): 201-204.
[13]	QIN Xinqiang, HUANG Ziyou, HU Gang, WANG Weiwei. On continuity conditions for CE-Bézier and H-Bézier curves and application in curve modeling [J]. Computer Engineering and Applications, 2012, 48(13): 171-175.
[14]	LI Yanhong1，MU Guowang2，GUO Zeng3. Application of genetic algorithm to determine shape parameters of β-spline curves [J]. Computer Engineering and Applications, 2011, 47(9): 175-177.
[15]	HAN Xi’an^1，2，HUANG Xili³，MA Yichen². Geometric construction of generalized cubic Bézier curves [J]. Computer Engineering and Applications, 2011, 47(3): 188-189.

Shape analysis of class of cubic curves

一类三次曲线的形状分析

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics