Pythagorean hodograph spline spirals that match G3 Hermite data from circles
| Autor: | Rachid Ait-Haddou, Zhong Li, Luc Biard |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Hermite spline
Applied Mathematics Mathematical analysis Convex curve Evolute 020207 software engineering 02 engineering and technology 01 natural sciences 0104 chemical sciences Cubic Hermite spline 010404 medicinal & biomolecular chemistry Computational Mathematics Spline (mathematics) Involute Hermite interpolation 0202 electrical engineering electronic engineering information engineering Piecewise Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 278:162-180 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2014.10.005 |
| Popis: | A construction is given for a G 3 piecewise rational Pythagorean hodograph convex spiral which interpolates two G 3 Hermite data associated with two non-concentric circles, one being inside the other. The spiral solution is of degree 7 and is the involute of a G 2 convex curve, referred to as the evolute solution, with prescribed length, and composed of two PH quartic curves. Conditions for G 3 continuous contact with circles are then studied and it turns out that an ordinary cusp at each end of the evolute solution is required. Thus, geometric properties of a family of PH polynomial quartics, allowing to generate such an ordinary cusp at one end, are studied. Finally, a constructive algorithm is described with illustrative examples. |
| Databáze: | OpenAIRE |
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