Offset-rational sinusoidal spirals in Bézier form
| Autor: | J. Sánchez-Reyes |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Sinusoidal spiral
Offset (computer science) Aerospace Engineering Geometry Bézier curve Computer Science::Computational Geometry Computer Graphics and Computer-Aided Design Polynomial interpolation Vertex (geometry) Computer Science::Graphics Modeling and Simulation Automotive Engineering Family of curves Curve fitting Polar coordinate system Mathematics |
| Zdroj: | Computer Aided Geometric Design. 24:142-150 |
| ISSN: | 0167-8396 |
| DOI: | 10.1016/j.cagd.2007.01.001 |
| Popis: | Mineur et al. [Mineur, Y., Lichah, T., Castelain, J.M., Giaume, H., 1998. A shape controlled fitting method for Bezier curves. Computer Aided Geometric Design 15 (9), 879-891] presented a remarkable family of Bezier curves, characterized by a control polygon with constant angle at each vertex and constant ratio between lengths of consecutive edges. We note that such curves belong to a classical family of polynomial sinusoidal spirals that encompasses Tschirnhausen's cubic, and can also be expressed as p-Bezier curves (Bezier curves in polar coordinates). These spirals have rational offsets, obtained simply by adding two p-Bezier curves, namely the spiral and a circle. Such a construction includes the offset to a parabola. |
| Databáze: | OpenAIRE |
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