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Constructing G1 quadratic Bezier curves with arbitrary endpoint tangent vectors

He-Jin Gu 1 Jun-Hai Yong 2 Jean-Claude Paul 3 Fuhua (frank) Cheng 4
3 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
Abstract : Quadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G1 quadratic Bézier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the G1 quadratic Bézier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs.
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He-Jin Gu, Jun-Hai Yong, Jean-Claude Paul, Fuhua (frank) Cheng. Constructing G1 quadratic Bezier curves with arbitrary endpoint tangent vectors. The 11th IEEE International Conference on CAD/Graphics -CAD/GRAPHICS 2009, Aug 2009, Yellow Mountain City, China. pp.263-267, ⟨10.1109/CADCG.2009.5246892⟩. ⟨inria-00517260⟩

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