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

摘要

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. (c) 2005 Elsevier B.V. All rights reserved.