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Math. Comput. Appl. 2016, 21(4), 44;

Adjustable Bézier Curves with Simple Geometric Continuity Conditions

School of Science, East China University of Technology, Nanchang 330013, China
Academic Editor: Fazal M. Mahomed
Received: 30 August 2016 / Revised: 27 October 2016 / Accepted: 31 October 2016 / Published: 17 November 2016
PDF [1661 KB, uploaded 17 November 2016]


This paper aims to simplify the continuity conditions of Bézier curves. For this purpose, a special family of Bézier curves with three parameters, to be called adjustable Bézier curves, is constructed. They have the same structure as the quartic Bézier curves. The newly constructed curves possess some of the basic properties of Bézier curves, such as the convex hull property, symmetry, geometric invariance, etc., and they have shape adjustability. Moreover, under the geometric continuity of order 1 ( G 1 ) conditions of the usual Bézier curves, the adjustable Bézier curves can reach geometric continuity of order k ( G k ); here, k is one of the parameters of the newly constructed curves. The recursive evaluation algorithm of the new curves is provided. We also discuss how to construct the adjustable Bézier curves with a given tangent polygon. Numerical examples illustrate the correctness and validity of the proposed method.
Keywords: Bézier curve; shape parameter; recursive algorithm; geometric continuity; tangent polygon Bézier curve; shape parameter; recursive algorithm; geometric continuity; tangent polygon
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Yan, L. Adjustable Bézier Curves with Simple Geometric Continuity Conditions. Math. Comput. Appl. 2016, 21, 44.

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