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Curved optimal delaunay triangulation
2018
ACM Transactions on Graphics
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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
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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
2009
2009 IEEE 12th International Conference on Computer Vision
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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]
2007
Lecture Notes in Computer Science
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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
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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
2004
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601)
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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]
2018
arXiv
pre-print
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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
2008
2008 IEEE Pacific Visualization Symposium
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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]
2004
Lecture Notes in Computer Science
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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
2009
Computer graphics forum (Print)
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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
2014
Mathematics of Computation
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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]
2016
Encyclopedia of Algorithms
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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
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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]
2014
Encyclopedia of Algorithms
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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
2009
Proceedings of the 25th annual symposium on Computational geometry - SCG '09
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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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