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Distance computation between non-convex polyhedra at short range based on discrete Voronoi regions

K. Kawachi, H. Suzuki
2000 Proceedings Geometric Modeling and Processing 2000. Theory and Applications  
In our algorithm discrete Voronoi regions are prepared as voxels around a non-convex polyhedron.  ...  The algorithm has been implemented, and the results of distance computations show that it can calculate the minimum distance between non-convex polyhedra composed of a thousand of triangles at interactive  ...  Results Based on the algorithm of the discrete Voronoi regions we have implemented a program for calculating the minimum distance between non-convex polyhedra.  ... 
doi:10.1109/gmap.2000.838244 dblp:conf/gmp/KawachiS00 fatcat:lsvvn4t2bvdg7ghehgdbodvww4

Ionic association in electrolyte solutions: A Voronoi polyhedra analysis

J. C. Gil Montoro, F. Bresme, J. L. F. Abascal
1994 Journal of Chemical Physics  
Voronoi polyhedra (VP) analysis of ionic solutions generated via Monte Carlo simulations for a wide range of concentrations and ionic charges are reported.  ...  The degree of separation between these forms is strongly determined by the charge of the ions.  ...  It is quite deep at concentrations over 1 M meaning that the short-range forces play an important role in the structure at these concentrations.  ... 
doi:10.1063/1.467839 fatcat:v6sp36aiqbaf5irwtjbu3wwnei

High-Dimensional Power Diagrams for Semi-Discrete Optimal Transport

Philip Claude Caplan
2021 Zenodo  
Efficient algorithms for solving optimal transport problems are important for measuring and optimizing distances between functions.  ...  distance as the cost function.  ...  increasing the distance between sites and requiring several more (possibly non-contributing) bisectors to be clipped against.  ... 
doi:10.5281/zenodo.5559221 fatcat:cvfb5ssxene6rd67fjggpesjg4

Contact Detection Algorithms

S. Kockara, T. Halic, C. Bayrak, K. Iqbal, R. A. Rowe
2009 Journal of Computers  
A process that determines whether two or more bodies make contact at one or more points is called contact detection or collision detection.  ...  Contact detection is inseparable part of the computer graphics, surgical simulations, and robotics etc. There are large of methods that are used for collision detection.  ...  The GJK algorithm based on the fact that separation distance between two convex polyhedra A and B is equal to the distance between Minkowski sum and the origin as shown in Figure 2 [3] below.  ... 
doi:10.4304/jcp.4.10.1053-1063 fatcat:ofcoskpnfjdbpmcead423ufeuu

Unsupervised landmark analysis for jump detection in molecular dynamics simulations

Leonid Kahle, Albert Musaelian, Nicola Marzari, Boris Kozinsky
2019 PHYSICAL REVIEW MATERIALS  
Subsequent clustering in landmark space enables a discretization of any trajectory into a sequence of distinct states.  ...  As a final step, the use of the smooth overlap of atomic positions descriptor allows distinguishing between different environments in a straightforward way.  ...  host structure and possible Li sites, mobile ions can also be automatically assigned to sites based on convex-hull analysis of site polyhedra. 10, 33 This topology-based method deals with arbitrary  ... 
doi:10.1103/physrevmaterials.3.055404 fatcat:m5fqffvhrzg7ppnyuvxw5tcgfi

Voronoi-based similarity distances between arbitrary crystal lattices [article]

Marco Michele Mosca, Dr. Vitaliy Kurlin
2020 arXiv   pre-print
Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the prediction of many target properties of crystal structures is computationally  ...  The proposed distances between arbitrary periodic lattices of crystal structures are invariant under all rigid motions, satisfy the metric axioms and continuity under atomic perturbations.  ...  The extended Hausdorff distance d H between lattices is based on the Voronoi cells, which are defined in terms of distances to lattice nodes, hence are independent of a linear bases of a lattice.  ... 
arXiv:2002.11165v1 fatcat:ig7wx4ng5veutmj7wqilslippe

Computational Geometry (Dagstuhl Seminar 17171)

Orfried Cheong, Anne Driemel, Jeff Erickson, Marc Herbstritt
2017 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17171 "Computational Geometry".  ...  Recent advances in computational geometry were presented and new challenges were identified. The report collects the abstracts of talks and open problems presented in the seminar.  ...  distance, discrete biharmonic distance [5] and diffusion distance [2] ).  ... 
doi:10.4230/dagrep.7.4.107 dblp:journals/dagstuhl-reports/CheongD017 fatcat:2dkkuzjgqvgwpfw363tm5st4pe

Learning a Safety Verifiable Adaptive Cruise Controller from Human Driving Data [article]

Qin Lin, Sicco Verwer, John Dolan
2019 arXiv   pre-print
By adding a safety state based on headway in time, a rule that human drivers should follow anyway, we do obtain a provably safe cruise control.  ...  Fig. 3 : 3 Polyhedra obtained by Voronoi diagram linearization. Discrete events are illustrated by different colors.  ...  Therefore, 10 polyhedra are obtained by the Voronoi diagram.  ... 
arXiv:1910.13526v1 fatcat:vyxkylpr2jfxnlhpc4jlthszpa

Bregman Voronoi Diagrams

Jean-Daniel Boissonnat, Frank Nielsen, Richard Nock
2010 Discrete & Computational Geometry  
Accordingly, Bregman Voronoi diagrams allow one to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions.  ...  Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions.  ...  Acknowledgements Frédéric Chazal, David Cohen-Steiner and Mariette Yvinec are gratefully acknowledged for their comments on this paper.  ... 
doi:10.1007/s00454-010-9256-1 fatcat:lik3travqzdfhbm2md3p2t5mfi

Reducing feasible contacts between polyhedral models to red–blue intersections on the sphere

P. Jiménez, C. Torras
2003 Computer-Aided Design  
First, a dual spherical representation of polyhedra is introduced, which reduces the contact detection above to nding intersections between two sets of spherical polygons.  ...  Orientation-related problems in geometric design can be naturally expressed on the spherical surface S 2 .  ...  Aknowledgments This research has been partially supported by the Spanish Science and Technology Commission (CICYT) under contract TAP99-1086-C03-01 (project \Constraint-based computation in robotics and  ... 
doi:10.1016/s0010-4485(02)00099-4 fatcat:76adfkkj7fdnlmw26vmljuxjlu

Refinement of polygonal grids using Convolutional Neural Networks with applications to polygonal Discontinuous Galerkin and Virtual Element methods [article]

P. F. Antonietti, E. Manuzzi
2021 arXiv   pre-print
We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs).  ...  We propose two refinement strategies that exploit the use of CNNs to classify elements' shape, at a low computational cost.  ...  In Figure 12 we show the computed quality metrics described in Section 3.3 on the grids of Figure 11 (triangles, Voronoi, smoothed Voronoi, non-convex).  ... 
arXiv:2102.05738v2 fatcat:6m3l6psxuvbrnfav7abpki47re

Chapter 7 A survey of computational geometry [chapter]

Joseph S.B. Mitchell, Subhash Suri
1995 Handbooks in Operations Research and Management Science  
The topic of path planning is a vast one, with problems ranging from nding shortest paths in a discrete graph to deciding the feasible motion of a complex robot in an environment full of complex obstacles  ...  The structures covered are convex hulls, arrangements, geometric duality, Voronoi diagram, and point location data structures.  ...  In d dimensions, the Voronoi diagram of a set of points S is a tessellation of E d by convex polyhedra.  ... 
doi:10.1016/s0927-0507(05)80124-0 fatcat:nogmdqmv6bflni3waox5dxrsiy

Matching fluid simulation elements to surface geometry and topology

Tyson Brochu, Christopher Batty, Robert Bridson
2010 ACM Transactions on Graphics  
the simulation and the surface-and allowing a precise inclusion of surface tension based directly on and at the same resolution as the surface mesh.  ...  Abstract We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples.  ...  In 3D, Voronoi faces are convex polygons, so determining non-solid weights involves computing polygon areas.  ... 
doi:10.1145/1833351.1778784 fatcat:xnzumwxerzfxvf2btjxfkk3x24

Matching fluid simulation elements to surface geometry and topology

Tyson Brochu, Christopher Batty, Robert Bridson
2010 ACM SIGGRAPH 2010 papers on - SIGGRAPH '10  
the simulation and the surface-and allowing a precise inclusion of surface tension based directly on and at the same resolution as the surface mesh.  ...  Abstract We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples.  ...  In 3D, Voronoi faces are convex polygons, so determining non-solid weights involves computing polygon areas.  ... 
doi:10.1145/1833349.1778784 fatcat:2w32f4nkofhbdk25jx7bh7mvw4

Saddle vertex graph (SVG)

Xiang Ying, Xiaoning Wang, Ying He
2013 ACM Transactions on Graphics  
Exact polyhedral distance: ICH 127s; MMP 144s Our result: 1.96s, max err. 0.11%, rms err. 0.05%, mean err. 0.04%  ...  Qian Sun for her help on the figures. This project was supported by an MOE Tier1 Grant.  ...  Shreiber and Sharir [2006] presented an optimal time O(n log n) algorithm to compute the single source geodesic on convex polyhedra.  ... 
doi:10.1145/2508363.2508379 fatcat:3ppvd7b6ifevvkibw5hmhqsqi4
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