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Regular triangulations of dynamic sets of points

Marc Vigo, Núria Pla, Josep Cotrina
2002 Computer Aided Geometric Design  
In this paper a simple data structure is presented that allows regular triangulations of sets of points to be dynamically updated, that is, new points can be incrementally inserted in the set and old points  ...  The Delaunay triangulations of a set of points are a class of triangulations which play an important role in a variety of different disciplines of science.  ...  Voronoi diagrams -A survey of a fundamental geometric data  ... 
doi:10.1016/s0167-8396(01)00082-6 fatcat:u7rukq77uzegdf6g3xn2btn3qe

Constrained paths in the flip-graph of regular triangulations

L. Pournin, Th.M. Liebling
2007 Computational geometry  
As a consequence, we obtain the connectivity of the flip-graph of regular triangulations that share the same vertex set.  ...  We describe particular paths in the flip-graph of regular triangulations in any dimension.  ...  Up to now it was only known that there is an incremental flip-algorithm exclusively visiting regular triangulations to find any given regular triangulation of a point set [4] .  ... 
doi:10.1016/j.comgeo.2006.07.001 fatcat:gbcb6vo7erdjpbfpofzyswh36e

Making the Case for Causal Dynamical Triangulations

Joshua H. Cooperman
2015 Foundations of physics  
The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry.  ...  My aim in this paper is to give a concise yet comprehensive, impartial yet personal presentation of the causal dynamical triangulations approach.  ...  When invoking this regularization, one implicitly assumes that the set of causal triangulations is in some sense sufficiently dense within the set of causal spacetimes. 3 If a continuum limit does not  ... 
doi:10.1007/s10701-015-9972-8 fatcat:kpydkg5fsjdxti5y7ufd3yhzpa

Finite-Element methods with local triangulation refinement for continuous reinforcement learning problems [chapter]

Rémi Munos
1997 Lecture Notes in Computer Science  
It is composed of two dynamics : the learning dynamics, called Finite-Element Reinforcement Learning, which estimates the values at the vertices of a triangulation defined upon the state space, and the  ...  structural dynamics, which refines the triangulation inside regions where the value function is irregular.  ...  the exit point x(~-) is updated with : = Fig. 3 . 3 Addition of a new point (the square dot) to the set of vertices and the resulting Delaunay triangulation For a given triangulation, we have to distinguish  ... 
doi:10.1007/3-540-62858-4_82 fatcat:3rjaqnkutva3llnmjznu2xg2au

Mixed-volume computation by dynamic lifting applied to polynomial system solving

J. Verschelde, K. Gatermann, R. Cools
1996 Discrete & Computational Geometry  
Mixed-Volume Computation by Dynamic Lifting Applied to Polynomial System Solving 71 Dynamic Construction of Regular Triangulations This part describes the dynamic lifting algorithm applied to one polytope  ...  Regular Triangulations For completeness we start with some well-known definitions [34] . We assume the points to be vectors in Euclidean space E", equipped with the standard inner product (-, .).  ...  Acknowledgments The authors are grateful to Birkett Huber for explaining the Cayley trick and to Paul Pedersen for introducing the connectivity property by means of fans.  ... 
doi:10.1007/bf02711134 fatcat:wsbnzecc4jcbxkjgbssq7b6pjy

On the transition from crystalline to dynamically triangulated random surfaces

Neil Ferguson, J.F. Wheater
1993 Physics Letters B  
We consider methods of interpolating between the crystalline and dynamically triangulated random surface models.  ...  Two simplified models, one of which has a phase transition and the other of which does not, are discussed.  ...  equation for the restricted set of three point graphs. 5) A larger set of graphs constructed from tree graphs.  ... 
doi:10.1016/0370-2693(93)90788-j fatcat:53lo3pv67bhbfbr3ip2vz4iiyi

Mesh Processing Using On-the-Fly Connectivity Reconstruction Given by Regular Triangulations

F B Pires, C A Dietrich, J L D Comba, L G Nonato
2010 2010 23rd SIBGRAPI Conference on Graphics, Patterns and Images  
The connectivity retrieval is accomplished by assigning weights to the vertices of the triangulation, converting it in a regular triangulation.  ...  Once weights have been computed, the connectivity can be rebuild by algorithms devoted to construct regular triangulation.  ...  ACKNOWLEDGMENT This work was supported by grants Fapesp-Brazil (#2008/03349-6), CNPq-NSF (#491034/2008-3) in the framework of Instituto Nacional de Ciłncia e Tecnologia em Medicina Assistida por Computao  ... 
doi:10.1109/sibgrapi.2010.20 dblp:conf/sibgrapi/PiresDCN10 fatcat:j4mvmcm62jed5burqsw4yftbb4

Page 6222 of Mathematical Reviews Vol. , Issue 96j [page]

1996 Mathematical Reviews  
A set of weighted points in general position in R¢ defines a unique regular triangulation. When the weights are the same, this regular triangulation is the Delaunay triangulation.  ...  Summary: “An efficient algorithm for Delaunay triangulation of a given set of points in three dimensions based on the point in- sertion technique is presented.  ... 

Triangulations in CGAL

Jean-Daniel Boissonnat, Olivier Devillers, Sylvain Pion, Monique Teillaud, Mariette Yvinec
2002 Computational geometry  
This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library CGAL.   ...  Acknowledgements The authors would like to thank Carine Bonetto, Hervé Brönnimann, Frank Da, Andreas Fabri, Frédéric Fichel and François Rebufat for contributing to the CGAL triangulation package.  ...  Then the regular triangulation of a set of weighted points can be defined as the dual of the power diagram of the associated spheres.  ... 
doi:10.1016/s0925-7721(01)00054-2 fatcat:bgfipdphuzdytlcvjwabwhyumm

Parallel dynamic and kinetic regular triangulation in three dimensions

Tilo Beyer, Gernot Schaller, Andreas Deutsch, Michael Meyer-Hermann
2005 Computer Physics Communications  
A parallel algorithm for regular triangulations is presented. For the purpose of fully dynamic and kinetic particle simulations it allows vertex insertion, deletion, movement, and weight changes.  ...  We focus on the use of regular triangulations in order to account for the influence of various particles sizes on the neighborhood topology.  ...  as flips) of sets of five points.  ... 
doi:10.1016/j.cpc.2005.06.009 fatcat:7fyggi4ox5frtn45tjhk5mnnua

Comparison of Point Clouds Acquired by 3D Scanner [chapter]

Natalia Dyshkant
2013 Lecture Notes in Computer Science  
We consider a problem of measure introducing for comparing of point clouds acquired by different scanning acts and types of scanners and designing of computationally efficient algorithms for their computing  ...  The algorithm for efficient localization of mesh nodes in a Delaunay triangulation is proposed. As the applications several problems of 3D face model analysis were considered.  ...  After such transformation the approaches of surface comparison and matching for regular sets of nodes [5] can be applied.  ... 
doi:10.1007/978-3-642-37067-0_5 fatcat:gxn6lov3tng6ldrxz55sjrru44

Perturbations for Delaunay and weighted Delaunay 3D triangulations

Olivier Devillers, Monique Teillaud
2011 Computational geometry  
The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate.  ...  We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar.  ...  RT (S) can now be defined as the set of all PP-regular tetrahedra: Theorem 1. The set of PP-regular tetrahedra RT (S) defines a triangulation. Proof.  ... 
doi:10.1016/j.comgeo.2010.09.010 fatcat:smqmruiy5ja3njqrgnmfyky5fm

Robust and Efficient Delaunay Triangulations of Points on Or Close to a Sphere [chapter]

Manuel Caroli, Pedro M. M. de Castro, Sébastien Loriot, Olivier Rouiller, Monique Teillaud, Camille Wormser
2010 Lecture Notes in Computer Science  
We propose two ways to compute the Delaunay triangulation of points on a sphere, or of rounded points close to a sphere, both based on the classic incremental algorithm initially designed for the plane  ...  The eciency of the implementation is established by benchmarks.  ...  through three points; the regular triangulation of the circles is the Delaunay triangulation DT of their centers.  ... 
doi:10.1007/978-3-642-13193-6_39 fatcat:f6l2d2prtfb47gzfxo4q7fhdrq

Quantum Spacetime, from a Practitioner's Point of View [article]

J. Ambjorn, S. Jordan, J. Jurkiewicz, R. Loll
2013 arXiv   pre-print
In the physically relevant case of four spacetime dimensions, the ansatz of Causal Dynamical Triangulations produces - from a fairly minimal set of quantum field-theoretic inputs - an emergent spacetime  ...  We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime.  ...  QUANTUM SPACETIME FROM CAUSAL DYNAMICAL TRIANGULATIONS Tools and ingredients "Quantum gravity from CDT" relies on few ingredients and a minimal set of prior assumptions.  ... 
arXiv:1302.2181v1 fatcat:oyszhcvjufb73mi4ng2j2d3hym

Causal Dynamical Triangulations without preferred foliation

S. Jordan, R. Loll
2013 Physics Letters B  
We introduce a generalized version of the Causal Dynamical Triangulations (CDT) formulation of quantum gravity, in which the regularized, triangulated path integral histories retain their causal properties  ...  a key feature of CDT quantum gravity.  ...  Acknowledgements The authors' contributions are part of the research programme of the Foundation for Fundamental Research on Matter (FOM),  ... 
doi:10.1016/j.physletb.2013.06.007 fatcat:xp5ri5c7pvfuzk4wuquljugrta
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