Rectifying control polygon for planar Pythagorean hodograph curves
| Autor: | Hwan Pyo Moon, Soo Hyun Kim |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Curve orientation
Mathematical analysis Equiangular polygon Aerospace Engineering 020207 software engineering Geometry 02 engineering and technology Computer Science::Computational Geometry 01 natural sciences Computer Graphics and Computer-Aided Design 0104 chemical sciences Pick's theorem 010404 medicinal & biomolecular chemistry Monotone polygon Modeling and Simulation Automotive Engineering Polygon 0202 electrical engineering electronic engineering information engineering Complex polygon Simple polygon Affine-regular polygon Mathematics |
| Zdroj: | Computer Aided Geometric Design. 54:1-14 |
| ISSN: | 0167-8396 |
| DOI: | 10.1016/j.cagd.2017.03.016 |
| Popis: | A Bezier control polygon is not appropriate to control a Pythagorean hodograph curve since it has redundant degrees of freedom. So we propose an alternative, which is the rectifying control polygon. A rectifying control polygon of a PH curve has the same degrees of freedom as the PH curve. It interpolates the end points of the PH curve, but not the end tangents. Most of all, it has the same arc length as the PH curve. In this paper, we present the method to compute the rectifying control polygon from the Bezier control polygon of the PH curve. We also present the procedure to compute the PH curves from a given rectifying control polygon. For the development of these algorithms, we employ the Gauss–Legendre quadrature method and the Bernstein–Vandermonde linear system. |
| Databáze: | OpenAIRE |
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