Research Seminar - May 03, 2002

Length and Shape Estimation for Curves in Rⁿ with e-Uniform Samplings

Abstract:

This paper discusses the problem of how to approximate the length and shape of a parametric curve from sampling points where the corresponding times t_i are not given. Of course, it is necessary to make some assumptions about the distribution of the t_i: in the present paper e-uniformity. Our theoretical result concerns an algorithm which uses piecewise-quadratic interpolants. Experiments are conducted to show that our theoretical estimates are sharp, and that the assumption of e-uniformity is needed. This work may be of interest in computer graphics, approximation theory, digitized geometry, and digital image processing.