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Pré-Publication, Document De Travail Année : 2011

Computing the Distance between Piecewise-Linear Bivariate Functions

Résumé

We consider the problem of computing the distance between two piecewise-linear bivariate functions $f$ and $g$ defined over a common domain $M$. We focus on the distance induced by the $L_2$-norm, that is $\|f-g\|_2=\sqrt{\iint_M (f-g)^2}$. If $f$ is defined by linear interpolation over a triangulation of $M$ with $n$ triangles, while $g$ is defined over another such triangulation, the obvious naïve algorithm requires $\Theta(n^2)$ arithmetic operations to compute this distance. We show that it is possible to compute it in $\O(n\log^4 n)$ arithmetic operations, by reducing the problem to multi-point evaluation of a certain type of polynomials. We also present an application to terrain matching.
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Dates et versions

inria-00608255 , version 1 (12-07-2011)
inria-00608255 , version 2 (12-07-2011)

Identifiants

  • HAL Id : inria-00608255 , version 1
  • ARXIV : 1107.2312

Citer

Guillaume Moroz, Boris Aronov. Computing the Distance between Piecewise-Linear Bivariate Functions. 2011. ⟨inria-00608255v1⟩
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