Publications related to Voronoi diagram

Quadratic serendipity element shape functions on general planar polygons

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

A virtual microstructure generator for 3D stone masonry walls

Katrin Beyer, Mahmoud S. M. Shaqfa

Detailed micromodel simulations of stone masonry walls require as input a 3D mesh that represents a realistic arrangement of stones in the masonry wall. In this paper, we constructed the first 3D masonry microstructures to derive 2D and 3D finite or discre ...

ELSEVIER2022

Convex Quantization Preserves Logconcavity

Pol del Aguila Pla

A logconcave likelihood is as important to proper statistical inference as a convex cost function is important to variational optimization. Quantization is often disregarded when writing likelihood models, ignoring the limitations of the physical detectors ...

IEEE Institute of Electrical and Electronics Engineers2022

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio and Voulgaris (SIAM J Comput 42(3):1364-1391, 2013) described a deterministic single-exponential time algorithm for the closest vector problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given ...

SPRINGER HEIDELBERG2020

A Low-Parametric Rhombic Microstructure Family for Irregular Lattices

Francis Julian Panetta

New fabrication technologies have significantly decreased the cost of fabrication of shapes with highly complex geometric structure. One important application of complex fine-scale geometric structures is to create variable effective elastic material prope ...

2020

Deforming Tessellations for the Segmentation of Cell Aggregates

Michaël Unser, Daniel Sage, Anaïs Laure Marie-Thérèse Badoual, Aymeric Alexandre Galan

We present a new active contour to segment cell aggregates. We describe it by a smooth tessellation that is attracted toward the cell membranes. Our approach relies on subdivision schemes that are tightly linked to the theory of wavelets. The shape is enco ...

IEEE2019

A finite element framework based on bivariate simplex splines on triangle configurations

Xiaodong Wei, Juan Cao

Recently, triangle configuration based bivariate simplex splines (referred to as TCB-spline) have been introduced to the geometric computing community. TCB-splines retain many attractive theoretic properties of classical B-splines, such as partition of uni ...

ELSEVIER SCIENCE SA2019

A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations

Jiri Vanicek, Konstantin Karandashev

We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an interpolation pr ...

2019

On compact representations of Voronoi cells of lattices

Matthias Schymura, Christoph Hunkenschröder

In a seminal work, Micciancio & Voulgaris (2010) described a deterministic single-exponential time algorithm for the Closest Vector Problem (CVP) on lattices. It is based on the computation of the Voronoi cell of the given lattice and thus may need exponen ...

SPRINGER INTERNATIONAL PUBLISHING AG2018

Graph Signal Processing: Overview, Challenges and Applications

Pascal Frossard, Pierre Vandergheynst

Research in graph signal processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper, we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing, along w ...

2018

Numerical simulation of mechanical deformation of semi-solid material using a level-set based finite element method

Roland Logé

In this work, a level-set based finite element method was used to numerically evaluate the mechanical behavior in a small deformation range of semi-solid materials with different microstructure configurations. For this purpose, a finite element model of th ...

Institute of Physics2017

Data-driven spatio-temporal discretization for pedestrian flow characterization

Michel Bierlaire, Marija Nikolic

We propose a novel approach to pedestrian flow characterization. The definitions of density, flow and velocity existing in the literature are extended through a data-driven spatio-temporal discretization framework. The framework is based on three-dimension ...

Elsevier Science Bv2017

Modeling of percolation of globular-equiaxed grains in Al-Cu alloys

Michel Rappaz, Jean-Luc Desbiolles, Christophe Mondoux

A new mesoscopic model able to describe percolation of globular-equiaxed grains, highly relevant for hot tearing formation in castings, has been developed. This model is inspired from the granular model of Sistaninia et al. [1-5] that considers polyhedral ...

Iop Publishing Ltd2015

Pedestrian-oriented Flow Characterization

Michel Bierlaire, Marija Nikolic

Definitions of flow indicators are derived by adapting Edie's definitions through a stream-based approach and a data-driven spatio-temporal discretization framework. The stream-based approach accounts for the multidirectional nature of pedestrian flows. Th ...

2014

An Algorithm to Improve Parameterizations of Rational Bézier Surfaces Using Rational Bilinear Reparameterization

Bailin Deng, Wei Zeng

The parameterization of rational Bézier surfaces greatly affects rendering and tessellation results. The uniformity and orthogonality of iso-parametric curves are two key properties of the optimal parameterization. The only rational Bézier surfaces with un ...

2013

A link between short-range and long-range properties of random sphere packings

Daniele Mari, Gérard Gremaud, Arnaud Comment, Riccardo Balzan, Alessandro Luigi Sellerio

We present a high precision particle-by-particle 3D reconstruction of granular systems composed of monodispersed spheres (sphere packings); the experimental approach is based on magnetic resonance imaging techniques. Our measurements revealed a strong corr ...

Springer Berlin Heidelberg2013

Design and Implementation of Multi-camera Systems Distributed over a Spherical Geometry

Alexandre Schmid, Yusuf Leblebici, Hossein Afshari, Kerem Seyid

The current trend in constructing high-end computing systems consists of parallelizing large numbers of processors. A similar trend is observed in digital imaging where multiple camera inputs are utilized to obtain multiple images of a scene and thus enhan ...

2012

A 3D coupled hydro-mechanical granular model for the prediction of hot tearing formation

Michel Rappaz, Jean-Marie Drezet, André Phillion, Meisam Sistaninia

A new 3D coupled hydro-mechanical granular model that simulates hot tearing formation in metallic alloys is presented. The hydro-mechanical model consists of four separate 3D modules. (I) The Solidification Module (SM) is used for generating the initial so ...

Iop Publishing Ltd2012

A 3D Granular Model Of Equiaxed-Granular Solidification

Michel Rappaz, Jean-Luc Desbiolles, André Phillion

The solidification of an aluminum-copper alloy has been simulated in 3D using a granular model. Compared to previous similar 2D approaches for where only one phase is continuous, the extension to 3D allows for concurrent continuity of the solid and liquid ...

Minerals, Metals & Materials Soc, 184 Thorn Hill Rd, Warrendale, Pa 15086-7514 Usa2009

A mesoscale granular model for the mechanical behavior of alloys during solidification

Michel Rappaz, Stéphane Vernède, Jonathan Dantzig

We present a two-dimensional granular model for the mechanical behavior of an ensemble of globular grains during solidification. The grain structure is produced by a Voronoi tessellation based on an array of predefined nuclei. We consider the fluid flow ca ...

Elsevier2009