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

作者：Lee Ryeong; Ahn Young Joon^*

来源：Journal of Computational and Applied Mathematics, 2015, 281: 1-9.

DOI：10.1016/j.cam.2014.12.007

• H-Bezier curve
• Limit curve
• Rational Bezier curve in standard form
• Bernstein polynomial
• Mathematical induction

The basis of H-Bezier curves of degree n is 1,t,...,t(n-2), sinh at and cosh at, for t is an element of [0,1]. We find the limit curve of H-Bezier curves of degree n as a parameter a goes to infinity, 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 omega as it goes to infinity, which is the rational Bezier curve of degree n-2.

• 出版日期2015-6