Identification of two classes of planar septic Pythagorean hodograph curves

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:348

Article

Li, Yujun¹  Fang, Lincong²  Cao, Juan³  Wang, Guozhao⁴ 

[1] Zhejiang Univ Finance & Econ, Dongfang Coll, Haining 314408, Peoples R China

[2] Zhejiang Univ Finance & Econ, Sch Informat, Hangzhou 310018, Zhejiang, Peoples R China

[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

[4] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

关键词: Bezier curve;    Pythagorean hodograph;    Control polygon;    Arc length;    Geometric characteristic;   

DOI  :  10.1016/j.cam.2018.09.002

来源: Elsevier

【 摘 要 】

Polynomial Pythagorean hodograph (PH) curves have a polynomial arc length function and rational offsets, which distinguish PH curves from general polynomial parametric curves. However, these algebraic properties can hardly be used directly for the identification of PH curves. In order to determine whether or not a given septic planar polynomial curve is a PH curve, Zheng et al. (2016) studied a class of septic curves' geometric properties and proposed an efficient algorithm. In this paper, we further complete their work on Bezier control polygons of septic PH curves. We point out that there are three classes of septic PH curves according to different factorizations of their derivatives. Except the first class which has been studied, geometric characteristics of the other two classes are proposed. By introducing auxiliary points, the results are in terms of angles and lengths of legs of their Bezier control polygons. Moreover, we give feasible methods for the construction of auxiliary points, including various degenerate cases. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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