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

Ryeong Lee, Young Joon Ahn

• 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.