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Identification of Planar Sextic Pythagorean-Hodograph Curves
作者姓名:Hui WANG  Chungang ZHU  Caiyun LI
作者单位:School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China,School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China,School of Science, Dalian University of Technology, Liaoning 124221, P. R. China
基金项目:Supported by the National Natural Science Foundation of China (Grant Nos.11671068; 11401077; 11271060; 11290143), Fundamental Research of Civil Aircraft (Grant No.MJ-F-2012-04), the Program for Liaoning Excellent Talents in University (Grant No.LJQ2014010) and the Fundamental Research Funds for the Central Universities (Grant No.DUT16LK38).
摘    要:Pythagorean-hodograph (PH) curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs'' constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by $C^1$ Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.

关 键 词:Pythagorean-hodograph  sextic  curves    control  polygon    degree  elevation    geometric  characteristic
收稿时间:2016/9/30 0:00:00
修稿时间:2016/12/7 0:00:00

Identification of Planar Sextic Pythagorean-Hodograph Curves
Hui WANG,Chungang ZHU,Caiyun LI.Identification of Planar Sextic Pythagorean-Hodograph Curves[J].Journal of Mathematical Research with Applications,2017,37(1):59-72.
Authors:Hui WANG  Chungang ZHU and Caiyun LI
Affiliation:School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China,School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China and School of Science, Dalian University of Technology, Liaoning 124221, P. R. China
Abstract:Pythagorean-hodograph (PH) curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs'' constraints in the complex form. Such reconstruction of a PH sextic can be elaborated by $C^1$ Hermite data and another one condition. The second uses polar representation in two cases. One of them can produce a family of convex sextic PH curves related with a quintic PH curve, and the other one may naturally degenerate a sextic PH curve to a quintic PH curve. In the third identification, we use some odd PH curves to construct a family of sextic PH curves with convexity-preserving property.
Keywords:Pythagorean-hodograph sextic curves  control polygon  degree elevation    geometric characteristic
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