C¹ Interpolation with Cumulative Chord Cubics

Article type: Research Article

Authors: Kozera, Ryszard | Noakes, Lyle

Affiliations: School of Computer Science and Software Engineering, The University of Western Australia, 35 Stirling Highway, Crawley W.A. 6009, Perth, Australia | School of Mathematics and Statistics The University of Western Australia 35 Stirling Highway, Crawley W.A. 6009, Perth, Australia

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.

Keywords: interpolation, unparameterized data, cumulative chord, curve and length estimation, orders of approximation

Journal: Fundamenta Informaticae, vol. 61, no. 3-4, pp. 285-301, 2004