| Identification of Planar Sextic Pythagorean-Hodograph Curves |
| Received:September 30, 2016 Revised:December 07, 2016 |
| Key Words:
Pythagorean-hodograph sextic curves control polygon degree elevation geometric characteristic
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| Fund Project: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). |
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| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.01.006 |
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