Modern Computer Algebra
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Fast Modular Composition in any Characteristic
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Computing similarity between piecewise-linear functions
Proceedings of the twenty-sixth annual symposium on Computational geometry
Incidences in three dimensions and distinct distances in the plane
Proceedings of the twenty-sixth annual symposium on Computational geometry
Discrete & Computational Geometry
The Joints Problem in $\mathbb{R}^n$
SIAM Journal on Discrete Mathematics
On lines, joints, and incidences in three dimensions
Journal of Combinatorial Theory Series A
On computing the centroid of the vertices of an arrangement and related problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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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 [EQUATION]. 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.