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On the average length of Delaunay triangulations
1984
BIT Numerical Mathematics
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We shall show that on the average, the total length of a Delaunay triangulation is of the same order as that of a minimum triangulation, under the assumption that our points are drawn from a homogeneous ...
planar Poisson point distribution. ...
This means that the expected number of points in each domain X 1 ..... X m is a random variable depending only on the area IX~l (Lebesgue measure), neither on the shape nor the position of the X[s. ...
doi:10.1007/bf02136025
fatcat:cjbps7sqnjbsdfj2dh755bsvum
Page 5720 of Mathematical Reviews Vol. , Issue 92j
[page]
1992
Mathematical Reviews
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Summary: “An algorithm is presented for constructing a domain Delaunay triangulation (DDT) of an arbitrarily shaped, multiply connected (manifold or nonmanifold), planar domain. ...
shaped planar domains. ...
Large mesh generation from boundary models with parametric face representation
1995
Proceedings of the third ACM symposium on Solid modeling and applications - SMA '95
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Instead of triangulating each face seperately, the faces of the solid are glued and triangulated together according to the neighbourhood information of the BRep. ...
We therefore turn our attention to a new incremental algorithm for the accurate triangulation of meshes of trimmed parametric surfaces. ...
Hüttner for his efforts on all the major implementation issues and the fruitful discussions that led to the realization of this algorithm. ...
doi:10.1145/218013.218097
dblp:conf/sma/KleinS95
fatcat:5sbgllvptjcanhyguolztsegha
Unstructured Mesh Generation
[chapter]
2012
Combinatorial Scientific Computing
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(In that case, the Delaunay triangulation is the planar dual of the well-known Voronoi diagram.) ...
A conforming Delaunay triangulation is a Delaunay mesh such that every domain edge is a union of mesh edges, and every domain face is a union of mesh faces. ...
An algorithm by Labelle [67] is a true hybrid of the Delaunay and octree methods: it refines a Delaunay triangulation by inserting vertices at lattice points near the circumcenters of skinny tetrahedra ...
doi:10.1201/b11644-11
fatcat:zjfel6436jhwlidqrtkvjt3ezy
CAD Tools for Creating Space-filing 3D Escher Tiles
2009
Computer-Aided Design and Applications
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Delaunay triangulation library and a mesh-cutting algorithm used in layering extruded tiles to create more intricate designs. ...
Starting with the simplest case of extruded 2D tilings, we describe geometric algorithms used for maintaining boundary representations of 3D tiles, including a Java implementation of an interactive constrained ...
Such tilings can also be created in non-planar domains. ...
doi:10.3722/cadaps.2009.737-748
fatcat:gd4sqn6d45eidobmidszjjlana
Effective Gouge-Free Tool Selection for Free-Form Surface Machining
2009
Computer-Aided Design and Applications
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Delaunay triangulation library and a mesh-cutting algorithm used in layering extruded tiles to create more intricate designs. ...
Starting with the simplest case of extruded 2D tilings, we describe geometric algorithms used for maintaining boundary representations of 3D tiles, including a Java implementation of an interactive constrained ...
Such tilings can also be created in non-planar domains. ...
doi:10.3722/cadaps.2009.839-849
fatcat:zbjcz2fxkraktg25hyjpfs3yg4
ANISOTROPIC TRIANGULATION OF PARAMETRIC SURFACES VIA CLOSE PACKING OF ELLIPSOIDS
2000
International journal of computational geometry and applications
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The centers of the ellipsoids are then connected by anisotropic Delaunay triangulation for a complete mesh topology. ...
This paper describes a new computational method of fully automated anisotropic triangulation of a trimmed parametric surface. ...
However, there are several unique characteristics that make this method particularly suitable for FEM mesh generation: • A bubble system can triangulate a curved domain, a planar domain, a surface domain ...
doi:10.1142/s0218195900000243
fatcat:7ckd2uobcbb7vphux7nzwi7eai
MESH GENERATION AND OPTIMAL TRIANGULATION
[chapter]
1992
Lecture Notes Series on Computing
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An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. ...
We especially focus on optimal triangulations of geometric domains in two-and three-dimensions. ...
This material spans a spectrum from purely theoretical results (for example, Chazelle's linear-time triangulation algorithm), through a middle ground (our own work on Steiner triangulations), to practical ...
doi:10.1142/9789814355858_0002
fatcat:zjlfgakee5df7nihosmpeuhco4
MESH GENERATION AND OPTIMAL TRIANGULATION
[chapter]
1995
Lecture Notes Series on Computing
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An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. ...
We especially focus on optimal triangulations of geometric domains in two-and three-dimensions. ...
This material spans a spectrum from purely theoretical results (for example, Chazelle's linear-time triangulation algorithm), through a middle ground (our own work on Steiner triangulations), to practical ...
doi:10.1142/9789812831699_0003
fatcat:ec6436f5i5bszheuiherz452ae
Delaunay Mesh Construction
[article]
2007
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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We further examine the usefulness of trading off the geometry-preserving feature of our algorithm with the ability to create fewer triangles. ...
We demonstrate the performance of our algorithms through several experiments. ...
Acknowledgments: We are grateful to John Li for providing the implementation of his nonobtuse decimation algorithm, which we modified to produce Delaunay meshes. ...
doi:10.2312/sgp/sgp07/273-282
fatcat:v7ovrydo6rd65juc7cuf2eceny
Well-Centered Triangulation
2010
SIAM Journal on Scientific Computing
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We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. ...
We also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method. ...
Lastly, we thank the reviewers; their comments led to improvement of the paper. ...
doi:10.1137/090748214
fatcat:35lftukgqjhm5m2ikc2dhaetoy
Delaunay Quadrangulation by Two-coloring Vertices
2014
Procedia Engineering
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We introduce a bichromatic Delaunay quadrangulation principle by assigning the vertices of a Delaunay triangulation one of two colors, then discarding edges between vertices of the same color. ...
We present two new sphere-packing algorithms for generating the colored triangulation, and we may also take as input a Delaunay refinement mesh and color it arbitrarily. ...
Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. ...
doi:10.1016/j.proeng.2014.10.397
fatcat:zsaeqhuqjfbpdl44nksijs5i4m
From Segmented Images to Good Quality Meshes Using Delaunay Refinement
[chapter]
2009
Lecture Notes in Computer Science
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Moreover, it offers extensive control over the size and shape of mesh elements, for instance through a (possibly non-uniform) sizing field. ...
This paper surveys Delaunay-based meshing techniques for curved objects, and their application in medical imaging and in computer vision to the extraction of geometric models from segmented images. ...
Fig. 3 . 3 The medial axis of a planar curve (only the portion inside the domain bounded by the curve is shown). The thin curves are parallel to the boundary of the domain. ...
doi:10.1007/978-3-642-00826-9_2
fatcat:raeabxptmfhhpis3irgby5d4ri
Variational Delaunay approach to the generation of tetrahedral finite element meshes
2001
International Journal for Numerical Methods in Engineering
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To determine if a constraining facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear ...
The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. ...
Acknowledgements We are grateful for support from the Department of Energy through Caltech's ASCI Center of Excellence for Simulating Dynamic Response of Materials. ...
doi:10.1002/nme.91
fatcat:2mhfj64seneodg742vc7udyfnm
On the number of higher order Delaunay triangulations
2011
Theoretical Computer Science
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Higher order Delaunay triangulations are a generalization of the Delaunay triangulation that provides a class of well-shaped triangulations, over which extra criteria can be optimized. ...
We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for first order Delaunay triangulations, the maximum number is 2 n−3 . ...
Acknowledgements We are grateful to Nick Wormald for his help on dealing with the integrals of Section 4. We would also like to thank Christiane Schmidt and Kevin Verbeek for helpful discussions. ...
doi:10.1016/j.tcs.2011.03.005
fatcat:iflyhd4tqnbi3gpbgd7pochsyi
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