Interpolation of curvature and torsion using expo-rational B-splines

Abstract

Expo-rational B-splines (ERBS) are well adapted for Hermite interpolation of any prescribed order [1]. This property of ERBS can be used to interpolate and approximate a variety of differential geometric structures of smooth manifolds, such as length, curvature, torsion, area, volume, etc. In this paper we solve the simplest of these problems: finding the explicit formulae for ERBS-based interpolation of curvature and torsion of unit-speed 3D-space curves and the order of the rate of approximation it provides. © 2012 Springer-Verlag.