Planar class A Bézier curves: The case of real eigenvalues

We consider planar, special Bézier curves, i.e., polynomial Bézier curves in the plane whose control polygon is fully identified by the first edge and a 2×2 matrix M. We focus on the case where M has two real eigenvalues and we formulate, in terms of the Schur form of M, necessary and sufficient con...

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Bibliographic Details
Published in:Computer aided geometric design 2021-08, Vol.89, p.102021, Article 102021
Main Authors: Romani, Lucia, Viscardi, Alberto
Format: Article
Language:English
Subjects:
Bézier curves
Class A curves
Monotone curvature
Planar curves
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Summary:We consider planar, special Bézier curves, i.e., polynomial Bézier curves in the plane whose control polygon is fully identified by the first edge and a 2×2 matrix M. We focus on the case where M has two real eigenvalues and we formulate, in terms of the Schur form of M, necessary and sufficient conditions for a regular, planar special Bézier curve to be a class A curve, i.e., a curve with monotone curvature, for any degree and any choice of the first edge. The result is simple in its formulation and can thus be easily used for both designing class A curves and analyzing given special Bézier curves.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2021.102021