C 1 Interpolation with Cumulative Chord Cubics

Abstract

Cumulative chord C¹ piecewise-cubics, for unparameterized data from regular curves in Rⁿ, are constructed as follows. In the first step derivatives at given ordered interpolation points are estimated from ordinary (non-C¹) cumulative chord piecewise-cubics. Then Hermite interpolation is used to generate a C¹ piecewise-cubic interpolant. Theoretical estimates of orders of approximation are established, and their sharpness verified through numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data.