Limit curve of H-Bézier curves and rational Bézier curves in standard form with the same weight

• Ryeong Lee ^[1] ; Young Joon Ahn ^[1]
  1. [1] Chosun University

     Chosun University

     Corea del Sur

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 281, Nº 1 (June 2015), 2015, págs. 1-9
• Idioma: inglés
• DOI: 10.1016/j.cam.2014.12.007
• Enlaces
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• Resumen

  • The basis of H-Bézier curves of degree n is 1, t, . . . , tn−2, sinh αt and cosh αt, for t ∈ [0, 1].

    We find the limit curve of H-Bézier curves of degree n as a parameter α goes to∞, which is the Bézier curve of degree n − 2, and prove it using mathematical induction and special properties of H-basis functions. We also compare it to the limit curve of rational Bézier curves of degree n in standard form with the same weight w as it goes to∞, which is the rational Bézier curve of degree n − 2.