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Article Dans Une Revue ACM Transactions on Algorithms Année : 2016

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 $M$, induced by the $L_2$~norm, that is $\|f-g\|_2=\sqrt{\int_M (f-g)^2}$. 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 na\"ive algorithm requires $\Theta(n^2)$ arithmetic operations to compute this distance. We show that it is possible to compute it in $\O(n\log^4 n\log\log n)$ arithmetic operations, by reducing the problem to multi-point evaluation of a certain type of polynomials. We also present several generalizations and an application to terrain matching.
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Dates et versions

hal-01112394 , version 1 (03-02-2015)

Identifiants

Citer

Guillaume Moroz, Boris Aronov. Computing the Distance between Piecewise-Linear Bivariate Functions. ACM Transactions on Algorithms, 2016, 12 (1), pp.3:1-3:13. ⟨10.1145/2847257⟩. ⟨hal-01112394⟩
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