Point-based methods for estimating the length of a parametric curve

Authors:
Michael S. Floater;Atgeirr F. Rasmussen
Affiliations:
CMA, University of Oslo, Oslo, Norway;CMA, University of Oslo, Oslo, Norway
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

This paper studies a general method for estimating the length of a parametric curve using only samples of points. We show that by making a special choice of points, namely the Gauss-Lobatto nodes, we get higher orders of approximation, similar to the behaviour of Gauss quadrature, and we derive some explicit examples.