## Computing the Distance between Piecewise-Linear Bivariate Functions

Citations: | 1 - 1 self |

### BibTeX

@MISC{Moroz_computingthe,

author = {Guillaume Moroz and Boris Aronov},

title = {Computing the Distance between Piecewise-Linear Bivariate Functions },

year = {}

}

### OpenURL

### Abstract

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(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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