Rational cubic spirals

Rational cubic spirals

We consider the problem of finding parametric rational Bézier cubic spirals (planar curves of monotonic curvature) that interpolate end conditions consisting of positions, tangents and curvatures. Rational cubics give more design flexibility than polynomial cubics for creating spirals, making them s...

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Veröffentlicht in:Computer aided design 2008, Vol.40 (1), p.3-12
Hauptverfasser: Dietz, Donna A., Piper, Bruce, Sebe, Elena
Format: Artikel
Sprache:eng
Schlagworte:
Bezier
Computational efficiency
Computer aided design
Curvature
Flexibility
Mathematical analysis
Monotonic curvature
Polynomial
Rational Bézier cubics
Robustness
Spiral
Spirals
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Zusammenfassung:We consider the problem of finding parametric rational Bézier cubic spirals (planar curves of monotonic curvature) that interpolate end conditions consisting of positions, tangents and curvatures. Rational cubics give more design flexibility than polynomial cubics for creating spirals, making them suitable for many applications. The problem is formulated to enable the numerical robustness and efficiency of the solution-algorithm which is presented and analyzed.
ISSN:0010-4485
1879-2685
DOI:10.1016/j.cad.2007.05.001