Rational cubic spirals

Authors:
Donna A. Dietz;Bruce Piper;Elena Sebe
Affiliations:
Department of Mathematics, Mansfield University, Mansfield, PA, 16933, USA;Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA;Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, USA
Venue:
Computer-Aided Design
Year:
2008

Citing 8
Cited 10

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Planar interpolation with a pair of rational spirals

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Applying inversion to construct planar, rational spirals that satisfy two-point G2 Hermite data

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Constraint-based LN-curves

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Admissible regions for rational cubic spirals matching G2 Hermite data

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Spiral fat arcs - Bounding regions with cubic convergence

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On the interpolation of concentric curvature elements

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Constraint-based LN curves

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A further generalisation of the planar cubic Bézier spiral

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Shape curvatures of planar rational spirals

Proceedings of the 7th international conference on Curves and Surfaces
Matching admissible G2 Hermite data by a biarc-based subdivision scheme

Computer Aided Geometric Design

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Abstract

We consider the problem of finding parametric rational Bezier 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.