TY - GEN

T1 - Computing the distance between piecewise-linear bivariate functions

AU - Moroz, Guillaume

AU - Aronov, Boris

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2012

Y1 - 2012

N2 - 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 L2-norm, that is ||f - g|| 2 = √∫∫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 Θ(n2) arithmetic operations to compute this distance. We show that it is possible to compute it in O(n log4 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.

AB - 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 L2-norm, that is ||f - g|| 2 = √∫∫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 Θ(n2) arithmetic operations to compute this distance. We show that it is possible to compute it in O(n log4 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.

UR - http://www.scopus.com/inward/record.url?scp=84860166197&partnerID=8YFLogxK

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U2 - 10.1137/1.9781611973099.27

DO - 10.1137/1.9781611973099.27

M3 - Conference contribution

AN - SCOPUS:84860166197

SN - 9781611972108

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 288

EP - 293

BT - Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012

PB - Association for Computing Machinery

T2 - 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012

Y2 - 17 January 2012 through 19 January 2012

ER -