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Curved optimal delaunay triangulation

Leman Feng, Pierre Alliez, Laurent Busé, Hervé Delingette, Mathieu Desbrun
2018 ACM Transactions on Graphics  
In this paper, we propose an extension of Optimal Delaunay Triangulations (ODT) to curved and graded isotropic meshes.  ...  By exploiting a continuum mechanics interpretation of ODT instead of the usual approximation theoretical foundations, we formulate a very robust geometry and topology optimization of Bézier meshes based  ...  CURVED OPTIMAL DELAUNAY TRIANGULATION We are ready to delve into our extension of ODT for high-order meshes.  ... 
doi:10.1145/3197517.3201358 fatcat:uw474x7zrrgopo3tcoipkl7fzy

Page 3650 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
One approach to meeting this requirement, while maintaining the desirable properties of Delaunay triangu- lation, has been to enforce the empty circumcircle property of Delaunay triangulation, subject  ...  This motivates us to ask whether it is possible to triangulate a 68 COMPUTER SCIENCE 3650 domain by introducing additional points in such a manner that the Delaunay triangulation of the points includes  ... 

Image compression with anisotropic triangulations

Sebastien Bougleux, Gabriel Peyre, Laurent D. Cohen
2009 2009 IEEE 12th International Conference on Computer Vision  
We propose a new image compression method based on geodesic Delaunay triangulations.  ...  The compression is achieved by coding both the coefficients of the spline approximation and the deviation of the geodesic triangulation from an Euclidean Delaunay triangulation.  ...  Using an Euclidean metric might be problematic in highly anisotropic regions where an optimal triangulation deviates from an Euclidean Delaunay triangulation. Triangulation refinement.  ... 
doi:10.1109/iccv.2009.5459425 dblp:conf/iccv/BougleuxPC09 fatcat:zy6kc5garzdyrerdndfvhovlzq

Triangulations of Line Segment Sets in the Plane [chapter]

Mathieu Brévilliers, Nicolas Chevallier, Dominique Schmitt
2007 Lecture Notes in Computer Science  
The main result of this paper is that the local optimality which characterizes point set Delaunay triangulations [10] extends to segment Delaunay triangulations.  ...  This triangulation, called segment Delaunay triangulation, is dual to the segment Voronoi diagram.  ...  Among all the triangulations of S, the Delaunay diagram of S has many optimality properties, some of them extending in any dimension [15] , [17] .  ... 
doi:10.1007/978-3-540-77050-3_32 fatcat:ltz6rtz7afhyldbqh2orkqghlu

Page 535 of Mathematical Reviews Vol. , Issue 2003A [page]

2003 Mathematical Reviews  
The classical Delaunay triangulation is a 0-order Delaunay triangulation in this classification.  ...  The authors also consider first-order Delaunay triangulations in detail.  ... 

Nonlinear dynamics isolated by delaunay triangulation criteria

D. Lindgren, L. Ljung
2004 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)  
We show that Delaunay triangulation of data points sampled from a system with an additive non-linearity gives a criterion by which a linear projection can be found that isolates the non-linear dependence  ...  The criterion is however complex to compute and non-convex, which makes it difficult to optimize globally.  ...  Delaunay Triangulation Delaunay triangulation is a way to connect points with straight lines.  ... 
doi:10.1109/cdc.2004.1429340 fatcat:wo4lebkuufdgxfpkip66hqw2j4

One machine, one minute, three billion tetrahedra [article]

Célestin Marot, Jeanne Pellerin, Jean-François Remacle
2018 arXiv   pre-print
We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to  ...  This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points.  ...  We optimized both the sequential and the parallel algorithm by specifying them exclusively for Delaunay triangulation purposes.  ... 
arXiv:1805.08831v2 fatcat:2jmr3m47yfhbtemrnawqurmvey

Energy-Based Hierarchical Edge Clustering of Graphs

Hong Zhou, Xiaoru Yuan, Weiwei Cui, Huamin Qu, Baoquan Chen
2008 2008 IEEE Pacific Visualization Symposium  
by energy-based optimization.  ...  Taking into the consideration of the graph topology, our method first samples graph edges into segments using Delaunay triangulation to generate the control points, which are then hierarchically clustered  ...  The GPU-accelerated Delaunay triangulation methods [8] and local optimization constraints can be applied to speed up the performance.  ... 
doi:10.1109/pacificvis.2008.4475459 dblp:conf/apvis/ZhouYCQC08 fatcat:ijynuimnsfhh7dr4jb7qrtdcae

Graph-Based Clustering of Random Point Set [chapter]

Atsushi Imiya, Ken Tatara
2004 Lecture Notes in Computer Science  
In this paper, we define clusters and the boundary curves of clusters in a random point set using the Delaunay triangulation and the principal curve analysis.  ...  The principal curve analysis is a generalization of principal axis analysis, which is a standard method for data analysis in pattern recognition.  ...  The construction of the Delaunay triangulation using all points in V is in practice an time-consuming process for a large number of points even if we use an optimal algorithm.  ... 
doi:10.1007/978-3-540-27868-9_104 fatcat:niivtgllczgzndnfye4duq7hn4

Filtering Relocations on a Delaunay Triangulation

Pedro Machado Manhães de Castro, Jane Tournois, Pierre Alliez, Olivier Devillers
2009 Computer graphics forum (Print)  
Updating a Delaunay triangulation when its vertices move is a bottleneck in several domains of application.  ...  This can be explained by several recent advances in efficient construction of Delaunay triangulations.  ...  Mesh optimization based on Optimal Delaunay Triangulation.  ... 
doi:10.1111/j.1467-8659.2009.01523.x fatcat:fq5zywsjazgybic6api7ecqt64

Optimal $N$-term approximation by linear splines over anisotropic Delaunay triangulations

Laurent Demaret, Armin Iske
2014 Mathematics of Computation  
In this paper, we prove asymptotically optimal N -term approximation rates for linear splines over anisotropic Delaunay triangulations, where our analysis applies to relevant classes of target functions  ...  In previous work, we have proposed a locally adaptive method for efficient image approximation, called adaptive thinning, which relies on linear splines over anisotropic Delaunay triangulations.  ...  of vertices Q ± and Q N .3.2.Optimal Decay Rates on Delaunay Triangulations.  ... 
doi:10.1090/s0025-5718-2014-02908-6 fatcat:nb5hjejmprg47hncxsolquwtju

Delaunay Triangulation and Randomized Constructions [chapter]

Olivier Devillers
2016 Encyclopedia of Algorithms  
In higher dimensions, the optimal worst case construction of Delaunay triangulation and convex hulls was solved in the 1990s.  ...  The Delaunay triangulation D(S) is the geometric dual of V(S).  ... 
doi:10.1007/978-1-4939-2864-4_711 fatcat:vc6kqohqyrf67iwakgz5cmuj5e

Page 5488 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
Put another way, if the points are uniformly distributed in a cube or a ball, the expected complexity of the Delaunay triangulation is only linear.  ...  Summary: “It is well known that the complexity of the Delaunay triangulation of n points in R“, i.e., the number of its simplices, can be Q(n'4/?!). In particular, in R?  ... 

Delaunay Triangulation and Randomized Constructions [chapter]

Olivier Devillers
2014 Encyclopedia of Algorithms  
In higher dimensions, the optimal worst case construction of Delaunay triangulation and convex hulls was solved in the 1990s.  ...  The Delaunay triangulation D(S) is the geometric dual of V(S).  ... 
doi:10.1007/978-3-642-27848-8_711-1 fatcat:eo5otjqg4jftvmut7pky7nry7q

Incremental construction of the delaunay triangulation and the delaunay graph in medium dimension

Jean-Daniel Boissonnat, Olivier Devillers, Samuel Hornus
2009 Proceedings of the 25th annual symposium on Computational geometry - SCG '09  
We describe a new implementation of the well-known incremental algorithm for constructing Delaunay triangulations in any dimension.  ...  To circumvent prohibitive memory usage, we also propose a modication of the algorithm that uses and stores only the Delaunay graph (the edges of the full triangulation).  ...  Thus, by storing only the bare Delaunay triangulation, New_DT is more ecient space-wise, since much less simplices are stored, but the theoretical complexity of the localiza-tion step becomes non-optimal  ... 
doi:10.1145/1542362.1542403 dblp:conf/compgeom/BoissonnatDH09 fatcat:rmm62kvcxbfclfsuz2dwbiw274
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