Computing the Distance between Piecewise-Linear Bivariate Functions - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2012

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.
Fichier principal
Vignette du fichier
integral.pdf (145.81 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

  • HAL Id : inria-00608255 , version 2
  • ARXIV : 1107.2312

Citer

Guillaume Moroz, Boris Aronov. Computing the Distance between Piecewise-Linear Bivariate Functions. SODA - Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms - 2012, Jan 2012, Kyoto, Japan. ⟨inria-00608255v2⟩
257 Consultations
399 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More