1 citations · 1 across the 6 of their papers we have counts for
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Semi-discrete convex order and Laguerre tessellation fitting
David P. Bourne, Thomas Gallouët, Quentin Mérigot +1
Laguerre tessellations offer an efficient way to parameterize a large class of convex partitions of Euclidean space using only a set of points and scalar weights. For this reason,…
Polynomial diagrams for microstructure modelling
David P. Bourne, Maciej Buze, Thomas Gallouët +1
We formulate a framework of polynomial diagrams, which are a generalisation of power diagrams (PDs) and anisotropic power diagrams (APDs) allowing for boundaries between cells to b…
A definition of the background state of the atmosphere using optimal transport
Charlie Egan, John Methven, David P. Bourne +1
The dynamics of atmospheric disturbances are often described in terms of displacements of air parcels relative to their locations in a notional background state. Modified Lagrangia…
Inverting Laguerre tessellations: Recovering tessellations from the volumes and centroids of their cells using optimal transport
David P. Bourne, Mason Pearce, Steven M. Roper
In this paper we study an inverse problem in convex geometry, inspired by a problem in materials science. Firstly, we consider the question of whether a Laguerre tessellation (a pa…