Determining tension parameters in rational gamma-spline interpolation

Abstract

Inspired by the classic gamma-spline, we propose a method for constructing a G(2) rational gamma-spline curve that interpolates a given set of distinct ordered data-points (planar or spatial). The only input of our method is just these data-points. We also present a procedure to solve the key problem of determining the tension parameters gamma(i) which are computed in terms of exponential functions that determine the eccentricities of the common conic osculants at the junction points while keeping in geometrical agreement with data-points. This allows the resulting curve to be modified in the close vicinity of each data-point. (C) 2010 Elsevier Inc. All rights reserved.