Inversion approximations for functions via s-power series

✍ Scribed by J. Sánchez-Reyes

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 239 KB
• Volume: 18
• Category: Article
• ISSN: 0167-8396
• DOI: 10.1016/s0167-8396(01)00054-1

✦ Synopsis

Given a monotone function v = f (u) over u ∈ [0, 1], we propose a simple method for generating a polynomial approximation to the inverse u = f -1 (v). This novel method is based on employing s-power series, the two-point analogue of Taylor expansions. Truncating at the kth term the s-power expansion of a given function yields its order-k Hermite interpolant, that is, a polynomial that reproduces up to the kth derivative at each endpoint u = {0, 1}. Convergence can be always achieved through subdivision, which generates a spline approximation that exhibits C k continuity at the joints. Our approach constitutes an alternative to the use of Legendre series, advocated by in a recent article. As an application, we show how to generate almost arc-length parameterization of general parametric curves.