Hui WANG,Chungang ZHU,Caiyun LI.Identification of Planar Sextic PythagoreanHodograph Curves[J].数学研究及应用,2017,37(1):59~72 
Identification of Planar Sextic PythagoreanHodograph Curves 
Identification of Planar Sextic PythagoreanHodograph Curves 
投稿时间：20160930 最后修改时间：20161207 
DOI：10.3770/j.issn:20952651.2017.01.006 
中文关键词: Pythagoreanhodograph sextic curves control polygon degree elevation geometric characteristic 
英文关键词:Pythagoreanhodograph sextic curves control polygon degree elevation geometric characteristic 
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.MJF201204), the Program for Liaoning Excellent Talents in University (Grant No.LJQ2014010) and the Fundamental Research Funds for the Central Universities (Grant No.DUT16LK38). 

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中文摘要: 
Pythagoreanhodograph (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 convexitypreserving property. 
英文摘要: 
Pythagoreanhodograph (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 convexitypreserving property. 
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