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Regular triangulations of dynamic sets of points

2002
*
Computer Aided Geometric Design
*

In this paper a simple data structure is presented that allows

doi:10.1016/s0167-8396(01)00082-6
fatcat:u7rukq77uzegdf6g3xn2btn3qe
*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 ...##
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Constrained paths in the flip-graph of regular triangulations

2007
*
Computational geometry
*

As a consequence, we obtain the connectivity

doi:10.1016/j.comgeo.2006.07.001
fatcat:gbcb6vo7erdjpbfpofzyswh36e
*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] . ...##
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Making the Case for Causal Dynamical Triangulations

2015
*
Foundations of physics
*

The aim

doi:10.1007/s10701-015-9972-8
fatcat:kpydkg5fsjdxti5y7ufd3yhzpa
*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 ...##
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Finite-Element methods with local triangulation refinement for continuous reinforcement learning problems
[chapter]

1997
*
Lecture Notes in Computer Science
*

It is composed

doi:10.1007/3-540-62858-4_82
fatcat:3rjaqnkutva3llnmjznu2xg2au
*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 ...##
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Mixed-volume computation by dynamic lifting applied to polynomial system solving

1996
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Discrete & Computational Geometry
*

Mixed-Volume Computation by

doi:10.1007/bf02711134
fatcat:wsbnzecc4jcbxkjgbssq7b6pjy
*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. ...##
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On the transition from crystalline to dynamically triangulated random surfaces

1993
*
Physics Letters B
*

We consider methods

doi:10.1016/0370-2693(93)90788-j
fatcat:53lo3pv67bhbfbr3ip2vz4iiyi
*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. ...##
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Mesh Processing Using On-the-Fly Connectivity Reconstruction Given by Regular Triangulations

2010
*
2010 23rd SIBGRAPI Conference on Graphics, Patterns and Images
*

The connectivity retrieval is accomplished by assigning weights to the vertices

doi:10.1109/sibgrapi.2010.20
dblp:conf/sibgrapi/PiresDCN10
fatcat:j4mvmcm62jed5burqsw4yftbb4
*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 ...##
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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. ...##
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Triangulations in CGAL

2002
*
Computational geometry
*

This paper presents the main algorithmic and design choices that have been made to implement

doi:10.1016/s0925-7721(01)00054-2
fatcat:bgfipdphuzdytlcvjwabwhyumm
*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. ...##
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Parallel dynamic and kinetic regular triangulation in three dimensions

2005
*
Computer Physics Communications
*

A parallel algorithm for

doi:10.1016/j.cpc.2005.06.009
fatcat:7fyggi4ox5frtn45tjhk5mnnua
*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*. ...##
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Comparison of Point Clouds Acquired by 3D Scanner
[chapter]

2013
*
Lecture Notes in Computer Science
*

We consider a problem

doi:10.1007/978-3-642-37067-0_5
fatcat:gxn6lov3tng6ldrxz55sjrru44
*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. ...##
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Perturbations for Delaunay and weighted Delaunay 3D triangulations

2011
*
Computational geometry
*

The Delaunay

doi:10.1016/j.comgeo.2010.09.010
fatcat:smqmruiy5ja3njqrgnmfyky5fm
*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. ...##
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Robust and Efficient Delaunay Triangulations of Points on Or Close to a Sphere
[chapter]

2010
*
Lecture Notes in Computer Science
*

We propose two ways to compute the Delaunay

doi:10.1007/978-3-642-13193-6_39
fatcat:f6l2d2prtfb47gzfxo4q7fhdrq
*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. ...##
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Quantum Spacetime, from a Practitioner's Point of View
[article]

2013
*
arXiv
*
pre-print

In the physically relevant case

arXiv:1302.2181v1
fatcat:oyszhcvjufb73mi4ng2j2d3hym
*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. ...##
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Causal Dynamical Triangulations without preferred foliation

2013
*
Physics Letters B
*

We introduce a generalized version

doi:10.1016/j.physletb.2013.06.007
fatcat:xp5ri5c7pvfuzk4wuquljugrta
*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), ...
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