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

摘要

The basis of H-Bézier curves of degree n is 1,t,…,tn−2, sinhαt and coshαt, 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.