On the Numerical Approximation of the Length of (Implicit) Level Curves

Authors:
Vicente F. Candela;Antonio Marquina
Affiliations:
Departamento de Matematica Aplicada, Universidad de Valencia, Burjassot-Valencia, Spain 46100;Departamento de Matematica Aplicada, Universidad de Valencia, Burjassot-Valencia, Spain 46100
Venue:
Journal of Scientific Computing
Year:
2008

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Abstract

The evaluation of the length of a curve, represented in an Eulerian way as the zero level set of an implicit function, depends mainly on the representation of the curve. In this paper, we propose a parameter to measure the complexity of the curve, and therefore the accuracy of the evaluation, based on the evolution of the representation in different scales. We will analyze this parameter, its properties and its relations with the regularity of the curve.