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Geometric Properties and Algorithms for Rational q-Bézier Curves and Surfaces

by Jorge Delgado 1,*,† and J. M. Peña 2,†
1
Departamento de Matemática Aplicada, Universidad de Zaragoza, 44003-Teruel, Spain
2
Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009-Zaragoza, Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(4), 541; https://doi.org/10.3390/math8040541
Received: 2 March 2020 / Revised: 30 March 2020 / Accepted: 1 April 2020 / Published: 7 April 2020
(This article belongs to the Special Issue Computer Aided Geometric Design)
In this paper, properties and algorithms of q-Bézier curves and surfaces are analyzed. It is proven that the only q-Bézier and rational q-Bézier curves satisfying the boundary tangent property are the Bézier and rational Bézier curves, respectively. Evaluation algorithms formed by steps in barycentric form for rational q-Bézier curves and surfaces are provided. View Full-Text
Keywords: q-Bernstein; q-Bézier; rational curves; boundary tangent property q-Bernstein; q-Bézier; rational curves; boundary tangent property
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Delgado, J.; Peña, J.M. Geometric Properties and Algorithms for Rational q-Bézier Curves and Surfaces. Mathematics 2020, 8, 541.

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