Geometric shape analysis for convolution curve of two compatible quadratic Bezier curves

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:288

Article

Lee, Ryeong¹  Ahn, Young Joon¹ 

[1] Chosun Univ, Dept Math Educ, Kwangju 501759, South Korea

关键词: Convolution curve;    Quadratic Bezier curve;    Classification of shapes;    Tangent direction;    Sign of curvature;   

DOI  :  10.1016/j.cam.2015.04.012

来源: Elsevier

【 摘 要 】

In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bezier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bezier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bezier curves of any degree n. We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free