Centroidal Voronoi Tessellations: Applications and Algorithms

Du, Qiang; Faber, Vance; Gunzburger, Max

doi:10.1137/s0036144599352836

Cited by 1,875 publications

(1,494 citation statements)

References 50 publications

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“…Centroidal Voronoi tessellation (CVT) [7] has been well studied and successfully applied to isotropic meshing [8] and anisotropic meshing [9], mainly computed by Lloyd's method. Liu et al [22] showed that the CVT energy has C 2 continuity and proposed to use the L-BFGS method, a variant of the quasi-Newton method, that outperforms the Lloyd's method for CVT computation.…”

Section: Optimization-based Methodsmentioning

confidence: 99%

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Chen¹,

Wang²,

Lévy³

et al. 2014

SIAM J. Sci. Comput.

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Abstract. This paper proposes a new algorithm to generate a graded three-dimensional tetrahedral mesh. It revisits the class of methods based on optimal Delaunay triangulation (ODT) and proposes a proper way of injecting a background density function into the objective function minimized by ODT. This continuous/analytic point of view leads to an objective function that is continuous and Delaunay consistent, in contrast with the discrete/geometrical point of view developed in previous work. To optimize the objective function, this paper proposes a hybrid algorithm that combines a local search (quasi-Newton) with a global optimization (simulated annealing). The benefits of the method are both improved performances and an improved quality of the result in terms of dihedral angles. This results from the combination of two effects. First, the local search has a faster speed of convergence than previous work due to the better behavior of the objective function, and second, the algorithm avoids getting stuck in a poor local minimum. Experimental results are evaluated and compared using standard metrics.

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Section: Optimization-based Methodsmentioning

confidence: 99%

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Chen¹,

Wang²,

Lévy³

et al. 2014

SIAM J. Sci. Comput.

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“…More optimal configurations can be reached through the perturbation of the robot team. This may also help to break off saddle points and symmetry configurations which sometimes result from CVTs [4].…”

Section: Perturbation Use Casementioning

confidence: 99%

“…Deployment and sweeping motion for robotic coverage of areas and boundaries (e.g., barriers) have previously also been referred to as blanket, barrier and sweep coverage [2]. A particular type of blanket coverage is Voronoi coverage [3], which arranges the robots in a final configuration that forms a so-called Centroidal Voronoi Tessellation (CVT) [4].…”

Section: Introductionmentioning

confidence: 99%

On Combining Multi-robot Coverage and Reciprocal Collision Avoidance

Breitenmoser

Martinoli

2016

Springer Tracts in Advanced Robotics

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Although robotic coverage and collision avoidance are active areas of robotics research, the avoidance of collision situations between robots has often been neglected in the context of multi-robot coverage tasks. In fact, for robots of physical size, collisions are likely to happen during deployment and coverage in densely packed multi-robot configurations. For this reason, we aim to motivate by this paper the combined use of multi-robot coverage and reciprocal collision avoidance. We present a taxonomy of collision scenarios in multi-robot coverage problems. In particular, coverage tasks with built-in heterogeneity such as multiple antagonistic objectives or robot constraints are shown to benefit from the combination. Based on our taxonomy, we evaluate four representative robotic use cases in simulation by combining the specific methods of Voronoi coverage and reciprocal velocity obstacles.

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“…La tassellatura Voronoi è producibile nel piano o anche nello spazio. La formulazione matematica completa dell'algoritmo di Voronoi può essere reperita ad esempio in [43]. Le celle di un reticolo così creato sono statisticamente rappresentative, nelle due o tre dimensioni, della struttura a grani di un materiale metallico policristallino.…”

Section: Generazione DI Microstrutture Statisticamente Equivalentiunclassified

La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

Collini

2010

Frattura Ed Integrità Strutturale

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sono facilmente risolvibili con gli approcci tradizionali. Oltre allo studio delle proprietà effettive dei solidi eterogenei, vi è la crescente necessità di incorporare un maggiore numero di informazioni sui meccanismi di deformazione e danneggiamento generati alla microscala, anche per i materiali abitualmente considerati omogenei. Micromeccanismi di cavitazione e concentrazioni locali di tensione e deformazione, sono indispensabili per spiegare fenomeni non-lineari come la rottura di fatica o il cedimento duttile, altrimenti non inquadrabili con approcci classici di tensioni e deformazioni medie. La micromeccanica si occupa della determinazione precisa, o di una stima accurata, di grandezze di campo microstrutturali locali. In questo lavoro sono illustrati i princìpi che sono alla base dell'approccio micromeccanico, come i concetti di multiscala, di distribuzione statistica delle fasi, di descrizione mediante volumi di riferimento e di omogeneizzazione e localizzazione, e, attraverso alcune applicazioni pratiche delle principali tecniche di modellazione, sono illustrati e discussi criticamente i risultati della ricerca effettuata su varie strutture di ghisa nodulare. ABSTRACT.There are many problems in Solid Mechanics, Physics of Solids and Materials Science that can not been solved using conventional approaches. Besides the effective properties of non-homogeneous bodies, there is an increasing need for incorporating more physical information about small-scale mechanisms of deformation and damage into phenomenological models of plasticity and rupture of materials which are usually considered homogeneous. Cavitation, local stress or strain concentrations at small scale are essential to explain nonlinear phenomena, such as fatigue or ductile rupture, which are not understandable from the simple point of view of average stresses or strains. Precise determination or accurate estimation of local fields is the domain of micromechanics. This work treats the basic concepts of the micromechanics in a simple way, with some practical suggestion on the most commonly used modelling techniques and some applications made by the author on various nodular cast iron microstructures. KEYWORDS.Modellazione micromeccanica; Materiali a struttura eterogenea; Compositi; Comportamento elasto-plastico. INTRODUZIONE ALLA MECCANICA DEI MATERIALI MICROSTRUTTURATIMateriali microstrutturati e concetto di scala di osservazione a Micro-e Meso-Meccanica del Continuo è una branca relativamente giovane della Meccanica dei Materiali, che studia il comportamento meccanico dei materiali a livello microstrutturale. Molti dei materiali di interesse industriale ed ingegneristico, e la maggior parte dei materiali "naturali", presentano una struttura eterogenea, formata cioè da più costituenti o "fasi", distinguibili ad una certa (ridotta) scala di osservazione. In altre parole, ciò che al L

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Centroidal Voronoi Tessellations: Applications and Algorithms

Cited by 1,875 publications

References 50 publications

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

On Combining Multi-robot Coverage and Reciprocal Collision Avoidance

La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

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