delaunay tessellations
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2021 ◽  
Vol 4 ◽  
pp. 121-153
Author(s):  
Anna Gusakova ◽  
Christoph Thäle

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Konstantin T. Matchev ◽  
Alexander Roman ◽  
Prasanth Shyamsundar

Abstract We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.


10.37236/8298 ◽  
2020 ◽  
Vol 27 (2) ◽  
Author(s):  
Mathieu Dutour Sikirić ◽  
Alexey Garber

We consider in this work triangulations of $\mathbb{Z}^n$ that are periodic along $\mathbb{Z}^n$. They generalize the triangulations obtained from Delaunay tessellations of lattices. In certain cases we impose additional restrictions on such triangulations such as regularity or invariance under central symmetry with respect to the origin; both properties hold for Delaunay tessellations of lattices. Full enumeration of such periodic triangulations is obtained for dimension at most $4$. In dimension $5$ several new phenomena happen: there are centrally-symmetric triangulations that are not Delaunay, there are non-regular triangulations (it could happen in dimension $4$) and a given simplex has a priori infinitely many possible adjacent simplices. We found $950$ periodic triangulations in dimension $5$ but finiteness of the whole family is unknown.


Author(s):  
Sanderson L. Gonzaga de Oliveira ◽  
Diogo T. Robaina ◽  
Diego N. Brandão ◽  
Mauricio Kischinhevsky ◽  
Gabriel Oliveira

2016 ◽  
Vol 37 (1) ◽  
pp. 641-674 ◽  
Author(s):  
Sanderson L. Gonzaga de Oliveira ◽  
Jéssica Renata Nogueira

2014 ◽  
Vol 114 (10) ◽  
pp. 535-541 ◽  
Author(s):  
Franz Aurenhammer ◽  
Günter Paulini

2013 ◽  
Vol 6 (4) ◽  
pp. 1353-1365 ◽  
Author(s):  
D. W. Jacobsen ◽  
M. Gunzburger ◽  
T. Ringler ◽  
J. Burkardt ◽  
J. Peterson

Abstract. A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construction of spherical Delaunay and Voronoi tessellations. The algorithms are then embedded into algorithms for the parallel construction of planar and spherical centroidal Voronoi tessellations that require multiple constructions of Delaunay tessellations. 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. Computational tests are used to demonstrate the efficiency and scalability of the algorithms for spherical Delaunay and centroidal Voronoi tessellations. Compared to serial versions of the algorithm and to STRIPACK-based approaches, the new parallel algorithm results in speedups for the construction of spherical centroidal Voronoi tessellations and spherical Delaunay triangulations.


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