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Voronoi Diagrams from (Possibly Discontinuous) Embeddings

Mario Kapl, Franz Aurenhammer, Bert Juttler
2013 2013 10th International Symposium on Voronoi Diagrams in Science and Engineering  
We present different possible applications of these Voronoi diagrams with several examples of generated diagrams.  ...  The framework is used to construct a new type of generalized Voronoi diagrams in [0, 1] 2 , which is possibly anisotropic.  ...  Acknowledgment: This work has been supported by the ESF EUROCORES Programme EuroGIGA -Voronoi, Austrian Science Foundation (FWF).  ... 
doi:10.1109/isvd.2013.13 dblp:conf/isvd/KaplAJ13 fatcat:q7pluxcpeve5fmmllzejl7fwbi

Self-Triggered and Team-Triggered Control of Networked Cyber-Physical Systems [chapter]

Cameron Nowzari, Jorge Cortés
2015 Embedded Systems  
diagram is contained in the Voronoi partition, i.e., gV i ⊂ V i , i ∈ {1, . . . , N }.  ...  The guaranteed Voronoi diagram is not a partition of S, see Figure 1.2(a) . The for some j = i. Note that ∆ g ij = ∆ g ji .  ... 
doi:10.1201/b19013-12 fatcat:b5mf5c37xnh6lcniui4wneclg4

Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model

Mijo Nikolić, Xuan Nam Do, Adnan Ibrahimbegovic, Željana Nikolić
2018 Computer Methods in Applied Mechanics and Engineering  
In both models, propagation of cracks activates enhancements in the displacement field leading to embedded strong discontinuities.  ...  Both models are based on embedded strong discontinuities for localized cohesive type crack description and both provide the advantage to not to require tracking algorithms.  ...  (a) Structure of discrete lattice model with Voronoi cells as units of heterogeneous material and cohesive links between them (b) neighboring Voronoi cells-h is extracted from Voronoi diagram and represents  ... 
doi:10.1016/j.cma.2018.06.012 fatcat:rekpajwqmneqrphvrhu2vhlnpi

Failure of heterogeneous materials: 3D meso-scale FE models with embedded discontinuities

N. Benkemoun, M. Hautefeuille, J.-B. Colliat, A. Ibrahimbegovic
2010 International Journal for Numerical Methods in Engineering  
To that respect both weak and strong discontinuities are embedded into those elements using the Incompatible Mode Method and a dedicated local solution procedure based on the operator split is described  ...  Several macroscopic loading paths are then considered, showing quite complex macroscopic responses though the mesoscopic failure criterion is voluntary chosen as simple as possible.  ...  Such task is carried out by using Qhull ( [26] ) which is a general dimension code for computing convex hulls, Delaunay triangulations and Voronoi diagrams.  ... 
doi:10.1002/nme.2816 fatcat:t4atbf63ezcwlb5opfwq72u6ku

Quad Layout Embedding via Aligned Parameterization

M. Campen, L. Kobbelt
2014 Computer graphics forum (Print)  
Quad layouting, i.e. the partitioning of a surface into a coarse network of quadrilateral patches, is a fundamental step in application scenarios ranging from animation and simulation to reverse engineering  ...  This process involves determining the layout's combinatorial structure as well as its geometric embedding in the surface.  ...  Models have been obtained from the AIM@SHAPE repository, the Stanford 3D Scanning Repository, and the Image-based 3D Models Archive, Télécom Paris.  ... 
doi:10.1111/cgf.12401 fatcat:czqntlvuejcanc3devd3ziuyy4

Embedding minimal dynamical systems into Hilbert cubes [article]

Yonatan Gutman, Masaki Tsukamoto
2015 arXiv   pre-print
Lindenstrauss proved that minimal systems of mean dimension less than N/36 can be embedded into ([0,1]^N)^Z, and he proposed the problem of finding the optimal value of the mean dimension for the embedding  ...  We study the problem of embedding minimal dynamical systems into the shift action on the Hilbert cube ([0,1]^N)^Z.  ...  Figure 6 . 1 . 61 Voronoi diagram and I(x, n). ( Of course, ∂[a, b] = {a, b}.) For r > 0 we set ∂ r [a, b] = [a − r, a + r] ∪ [b − r, b + r]. (∂ r ∅ = ∅.)  ... 
arXiv:1511.01802v1 fatcat:ttc5ljqgwzg2ziqwkggx3bgjii

Surface modelling with guaranteed consistency — An object-based approach [chapter]

Christopher M. Gold, Thomas Roos
1994 Lecture Notes in Computer Science  
The methods described here use the Voronoi diagram to generate surfaces which pass precisely through all data objects (points and line segments) and have no inadvertent surface or slope discontinuities  ...  In addition, discontinuities in the slope or the surface itself may be assigned to the line segment objects; and measures of surface consistency may be derived from the values of nearby data objects.  ...  François Anton helped greatly with some aspects of the mathematics and diagram preparation, and his assistance is gratefully acknowledged.  ... 
doi:10.1007/3-540-58795-0_36 fatcat:oj6jtpa6hbez3kmeo3zwwomucq

Density anomaly in a fluid of softly repulsive particles embedded in a spherical surface

Santi Prestipino, Cristina Speranza, Paolo V. Giaquinta
2012 Soft Matter  
We investigated the volumetric anomaly of a two-dimensional system of particles embedded in the surface of an inert sphere.  ...  The phase diagram of the model exhibits one single fluid phase since the absence of an attractive term in the potential rules out a liquid-vapour phase transition while the curved geometry inhibits the  ...  Under spherical boundary conditions, no extended crystalline order is possible though, at low temperatures, local particle arrangements can hardly be distinguished from those found in the solid.  ... 
doi:10.1039/c2sm26706c fatcat:xp6htd6w45h7zj67vk7o3tsi6q

Constraining the Infalling Envelope Models of Embedded Protostars: BHR 71 and Its Hot Corino

Yao-Lun Yang, Neal J. Evans, Aaron Smith, Jeong-Eun Lee, John J. Tobin, Susan Terebey, Hannah Calcutt, Jes K. Jørgensen, Joel D. Green, Tyler L. Bourke
2020 Astrophysical Journal  
We present unambiguous signatures of infall, probed by optically thick molecular lines, toward an isolated embedded protostar, BHR 71 IRS1.  ...  We further exclude possible optically thick emission from the optimization, based on the line profile, such as significant deviations from Gaussianity and absorption.  ...  However, discontinuities, such as the cavities, in models often lead to unrealistic cell structure in the gridding.  ... 
doi:10.3847/1538-4357/ab7201 fatcat:4qgx3lbqpza5hck37yzpubuq5u

Combining Truncated Binary Search Tree and Direct Search for Flexible Piecewise Function Evaluation for Explicit MPC in Embedded Microcontrollers

Farhad Bayat, Tor A. Johansen, Ali A. Jalali
2011 IFAC Proceedings Volumes  
In the case of linear cost-function in Jones et al. (2006) the point location problem was posed as a weighted Voronoi diagram, which can be solved using an approximate nearest neighbor algorithm.  ...  The idea is to use these HPs as separating variables in the nodes of the tree to split the partitioned space in a way that the number of candidate functions decreases as much as possible from the current  ... 
doi:10.3182/20110828-6-it-1002.00332 fatcat:swvh3s6re5hydjq3fcwlmx3alq

Enforcing essential boundary conditions on domains defined by point clouds [article]

Frank Hartmann, Stefan Kollmannsberger
2021 arXiv   pre-print
Instead of reconstructing a CAD model from point clouds via surface reconstruction and a subsequent boundary conforming mesh generation, a direct analysis without pre-processing is possible using embedded  ...  The computation of domain integrals is circumvented by an implicit approximation of corresponding Voronoi diagrams of higher order and the resulting sharp approximation avoids the side-effects of diffuse  ...  From now on we will refer to Voronoi diagrams and Voronoi regions and imply that they are generalized of order k for simplicity.  ... 
arXiv:2111.06502v1 fatcat:jasyj4uneff4znmqauz3ilde64

A weighted difference barrier method in landscape genetics

Lan Mu, John Radke
2009 Journal of Geographical Systems  
The spatial formation is caused by possible multi-parts and discontinued areas of a weighted Voronoi polygon as described earlier.  ...  Furthermore, embedded within a GIS environment, we explore the correlation of genetic discontinuities detected based on our weighted method and landscape features.  ... 
doi:10.1007/s10109-009-0079-7 fatcat:rjaw4wntznfendci3imq5hstvm

Subset Warping: Rubber Sheeting with Cuts

P Landau
1994 Graphical Models and Image Processing  
To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities and concavities in the range image, using a technique based on generalized Voronoi diagrams.  ...  The Voronoi diagram ¥ £ obtained from the edges is in a sense the dual of that obtained from the vertices of the polygon ¥ ¡ (see figure 2).  ...  To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities and concavities in the range image, using a technique based on generalized Voronoi diagrams.  ... 
doi:10.1006/gmip.1994.1023 fatcat:zecutke67fbdvasjxezji2d4he

Subset Warping: Rubber Sheeting with Cuts

P. Landau, E. Schwartz
1994 CVGIP: Graphical Models and Image Processing  
To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities and concavities in the range image, using a technique based on generalized Voronoi diagrams.  ...  The Voronoi diagram ¥ £ obtained from the edges is in a sense the dual of that obtained from the vertices of the polygon ¥ ¡ (see figure 2).  ...  To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities and concavities in the range image, using a technique based on generalized Voronoi diagrams.  ... 
doi:10.1006/cgip.1994.1022 fatcat:euadveoxavdarikpol5hox7g3y

Deep Learning on Attributed Graphs: A Journey from Graphs to Their Embeddings and Back [article]

Martin Simonovsky
2019 arXiv   pre-print
We concentrate on two important primitives: embedding graphs or their nodes into a continuous vector space representation (encoding) and, conversely, generating graphs from such vectors back (decoding)  ...  Arguably, a powerful embedding network should be able to exploit as much information as possible.  ...  On one hand, generated graphs can be easily visualized in standardized structural diagrams.  ... 
arXiv:1901.08296v1 fatcat:vp6uzgasnrgzpoaqv2dni5bega
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