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Voronoi Cells
Every real algebraic variety X determines aVoronoi decomposition of its ambient Euclidean space...
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Lifts for Voronoi Cells of Lattices
Many polytopes arising in polyhedral combinatorics are linear projections of higher-dimensional polytopes with significantly fewer facets. Such lifts...
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Crack modeling via minimum-weight surfaces in 3d Voronoi diagrams
As the number one building material, concrete is of fundamental importance in civil engineering. Understanding its failure mechanisms is essential...
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Unbounded Regions of High-Order Voronoi Diagrams of Lines and Line Segments in Higher Dimensions
We study the behavior at infinity of the farthest and the higher-order Voronoi diagram of n line segments or lines in a d -dimensional Euclidean...
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Discontinuous Galerkin method with Voronoi partitioning for quantum simulation of chemistry
To circumvent a potentially dense two-body interaction tensor and obtain lower asymptotic costs for quantum simulations of chemistry, the...
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Voronoi tiling and circle packing on spiral lattices with rotational symmetry
It is shown that the bifurcation diagram of circle packings on logarithmic spiral lattices with rotational symmetry is graph-theoretically dual to...
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Voronoi Recursive Binary Trees for the Optimization of Nonlinear Functionals
We propose an algorithm for the approximate solution of general nonlinear functional optimization problems through recursive binary Voronoi tree...
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Tropical Bisectors and Voronoi Diagrams
In this paper we initiate the study of tropical Voronoi diagrams. We start out with investigating bisectors of finitely many points with respect to...
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An Optimal Deterministic Algorithm for Geodesic Farthest-Point Voronoi Diagrams in Simple Polygons
Given in the plane a set S of m point sites in a simple polygon P of n vertices, we consider the problem of computing the geodesic farthest-point...
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Uniform Voronoi tessellation of digital manifolds: a GPU-based algorithm with applications to remeshing
We present here a GPU-friendly algorithm for uniform Voronoi tessellation (UVT) of a digital manifold, which, in particular, may be conceived as the...
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Voronoi summation formula for Gaussian integers
We prove a Voronoi–Oppenheim summation formula for divisor functions associated with Gaussian integers. This formula is a direct generalization of...
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High-Order Arbitrary-Lagrangian-Eulerian Schemes on Crazy Moving Voronoi Meshes
Hyperbolic partial differential equations (PDEs) cover a wide range of interesting phenomena, from human and hearth-sciences up to astrophysics: this...
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A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes
In this paper, we present a conservative semi-Lagrangian scheme designed for the numerical solution of 3D hydrostatic free surface flows involving...
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Calibration of agent based models for monophasic and biphasic tumour growth using approximate Bayesian computation
Agent-based models (ABMs) are readily used to capture the stochasticity in tumour evolution; however, these models are often challenging to validate...
