Inversion approximations for functions via s-power series Original Research Article

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 Ck continuity at the joints. Our approach constitutes an alternative to the use of Legendre series, advocated by Farouki (2000) in a recent article. As an application, we show how to generate almost arc-length parameterization of general parametric curves.