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Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

D. W. Jacobsen, M. Gunzburger, T. Ringler, J. Burkardt, J. Peterson
2013 Geoscientific Model Development  
</strong> A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed.  ...  This combination of overlapping domain decompositions with stereographic projections provides a unique algorithm for the construction of spherical meshes that can be used in climate simulations.  ...  circumsphere of the i-th triangle in the local Delaunay tessellation of P k .  ... 
doi:10.5194/gmd-6-1353-2013 fatcat:koaytvybgvhrzlbkfq4qjbydtm

Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

D. W. Jacobsen, M. Gunzburger, T. Ringler, J. Burkardt, J. Peterson
2013 Geoscientific Model Development Discussions  
A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed.  ...  This combination of overlapping domain decompositions with stereographic projections provides a unique algorithm for the construction of spherical meshes that can be used in climate simulations.  ...  circumsphere of the i-th triangle in the local Delaunay tessellation of P k .  ... 
doi:10.5194/gmdd-6-1427-2013 fatcat:ui2tar27kzhnzghnxoxyymdcdm

An implementation of Watson's algorithm for computing 2-dimensional delaunay triangulations

S.W. Sloan, G.T. Houlsby
1984 Advances in Engineering Software (1978)  
THEORY Except in special cases, which are known as degeneracies, the vertices of the Dlrlchlet tessellation occur at points Ftgure 1 angulatzon The Dtnchlet tessellation and Delaunay trt-0141-1195/84]040192  ...  A FORTRAN 77 implementation of Watson's algorithm for computing two-dimensional Delaunay triangulations is described.  ...  may be avoided by pre-sorting all of the points in ascending sequence of one co-ordinate, say their x-co-ordinate In order to test whether a new point hes reside the cIrcumcIrcle of an existing triangle  ... 
doi:10.1016/0141-1195(84)90003-2 fatcat:ftnuayhr2fhzfiz3mqawp3n5wa

Plane-Sweep Incremental Algorithm: Computing Delaunay Tessellations of Large Datasets [article]

Márton Trencséni, István Csabai
2012 arXiv   pre-print
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer's main memory.  ...  The procedure is to first sort the point set along the first principal component and then to sequentially insert the points into the tessellation, essentially simulating a sweeping plane.  ...  Given the current trend in computing to pack many cores into a processor we will comment on the effect of memory- serialization on processor parallelism in the context of Delaunay tessellation.  ... 
arXiv:1210.3595v1 fatcat:o4ltwbgiu5axjawxhs4w57hlly

A fast algorithm for constructing Delaunay triangulations in the plane

S.W. Sloan
1987 Advances in Engineering Software (1978)  
This paper describes an algorithm for computing Delaunay triangulations of arbitrary collections of points in the plane. A FORTRAN 77 implementation of the scheme is given.  ...  The efficiency of the proposed algorithm is verified by comparing its performance with other Delaunay triangulation procedures.  ...  By definition, each vertex of a Dirichlet tessellation a equidistant from each of the three data points forming the Delaunay triangle.  ... 
doi:10.1016/0141-1195(87)90043-x fatcat:ir6enkxkdbgb7navjntljipzhm

Page 190 of Journal of Research and Practice in Information Technology Vol. 17, Issue 4 [page]

1985 Journal of Research and Practice in Information Technology  
A Delaunay triangulation (see Figure 2) of bivariate data is a network of triangles, each formed from three data that lie on an empty circle.  ...  Voronoi vertices each lie on three lines that perpendicularly bisect the edges of the Delaunay triangulation.  ... 

Page 370 of Astronomy and Astrophysics Vol. 283, Issue 2 [page]

1994 Astronomy and Astrophysics  
R; plays a role when checking whether it is sufficient to merely consider the nuclei in S; when search- ing for a triangle with minimum circumradius or for a new Delaunay tetrahedron.  ...  C) or a triangle with minimum circumradius (Appendix A).  ... 

View-dependent adaptive tessellation of spline surfaces

Jatin Chhugani, Subodh Kumar
2001 Proceedings of the 2001 symposium on Interactive 3D graphics - SI3D '01  
Our algorithm pre-computes a prioritized list of important samples on the surface. At rendering time, it adds these points in the specified order to the triangulation.  ...  The algorithm works well in practice and has a low memory footprint.  ...  It stores these domain points in a topologically sorted order so the points that reduce more the deviation between the resulting triangles and the surface appear first.  ... 
doi:10.1145/364338.364349 fatcat:lko2mzyozfdrvp5kpatfffs56e

On shape Delaunay tessellations

Franz Aurenhammer, Günter Paulini
2014 Information Processing Letters  
Shape Delaunay tessellations are a generalization of the classical Delaunay triangulation of a finite set of points in the plane, where the empty circle condition is replaced by emptiness of an arbitrary  ...  We present some new and basic properties of shape Delaunay tessellations, concerning flipping, subgraph structures, and recognition.  ...  Skyum [15] constructs the shape Delaunay tessellation, based on a smooth and strictly convex distance function, using the sweep line approach, in O(n log n) many steps.  ... 
doi:10.1016/j.ipl.2014.04.007 fatcat:qizm2auzwvcsfaxhlf2d5ifymi

The prioritized-layered projection algorithm for visible set estimation

J.T. Klosowski, C.T. Silva
2000 IEEE Transactions on Visualization and Computer Graphics  
We also provide experimental evidence of its performance, including results on two types of spatial tessellation (using octree-and Delaunay-based tessellations), and several datasets.  ...  cell of the tessellation a solidity value, which is used to compute a special ordering on how primitives get projected.  ...  occlusion-culling capabilities of the HP fx series accelerators, the Geometry Center of the University of Minnesota for qhull and geomview, and the University of California, Berkeley for the SODA Hall model used in  ... 
doi:10.1109/2945.856993 fatcat:i6jms27vl5bhpc6opck7exokfa

The Medusa of Spatial Sorting: 3D Kinetic Alpha Complexes and Implementation [article]

Michael Kerber, Herbert Edelsbrunner
2012 arXiv   pre-print
Motivated by an application in cell biology, we consider spatial sorting processes defined by particles moving from an initial to a final configuration.  ...  We describe an algorithm for constructing a cell complex in space-time, called the medusa, that measures topological properties of the sorting process.  ...  Acknowledgments The authors thank Viktoriia Sharmanska for discussions and help with a 2-dimensional prototype of our implementation.  ... 
arXiv:1209.5434v1 fatcat:uh2ya6gkrndkrct5h37mvxfrva

On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane [article]

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian
2022 arXiv   pre-print
For such a set, the distribution of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order  ...  As an example, a stationary Poisson point process in ℝ^2 is locally finite, coarsely dense, and generic with probability one.  ...  Acknowledgements The first author thanks Robert Adler and Anton Nikitenko for discussions on Poisson point processes, and for pointing out the formula for the angle distribution in [10] .  ... 
arXiv:2204.01076v1 fatcat:6qubk3frf5dctpuccfogc5xtxu

Ka-me: a Voronoi image analyzer

N. Khiripet, W. Khantuwan, J. R. Jungck
2012 Bioinformatics  
Ka-me is a Voronoi image analyzer that allows users to analyze any image with a convex polygonal tessellation or any spatial point distribution by fitting Voronoi polygons and their dual, Delaunay triangulations  ...  The analytical tools include a variety of graph theoretic and geometric tools that summarize the distribution of the numbers of edges per face, areas, perimeters, angles of Delaunay triangle edges (anglograms  ...  Rindfleisch, Brian Maunze, Yang Yang, Sijia Liang, Jourdan Posner Erika Moen and Trisha Rettig performed numerous analyses of biological images to test the robustness of Ka-me' in a wide variety of contexts  ... 
doi:10.1093/bioinformatics/bts253 pmid:22556369 pmcid:PMC3381968 fatcat:ztfo25low5erxlgo5szpgjftmu

Two algorithms for constructing a Delaunay triangulation

D. T. Lee, B. J. Schachter
1980 International Journal of Computer & Information Sciences  
This paper provides a unified discussion of the Delaunay triangulation. Its geometric properties are reviewed and several applications are discussed.  ...  It runs in O(Nlog N) time, which is asymptotically optimal. The second algorithm is iterative and requires O(N 2) time in the worst case.  ...  Stearns, and one of the reviewers for their thoughtful comments on this paper.  ... 
doi:10.1007/bf00977785 fatcat:mokjghbfv5cd3nyhnkhqeuqx5y

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

Darren Engwirda
2017 Geoscientific Model Development  
It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape.  ...  Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced.  ...  This work was carried out at the NASA Goddard Institute for Space Studies, the Massachusetts Institute of Technology, and the University of Sydney with the support of a NASA-MIT cooperative agreement and  ... 
doi:10.5194/gmd-10-2117-2017 fatcat:j7vzzbggsbg3nlcr5hinz74jr4
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