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

The basis of H-Bezier curves of degree n is 1 , t , ? , t n - 2 , sinh α t and cosh α t , for t ? 0 , 1 ] . We find the limit curve of H-Bezier curves of degree n as a parameter α goes to ∞ , which is the Bezier 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 Bezier curves of degree n in standard form with the same weight w as it goes to ∞ , which is the rational Bezier curve of degree n - 2 .

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