scholarly journals Approximate order-k Voronoi cells over positional streams

Author(s):  
Kostas Patroumpas ◽  
Theofanis Minogiannis ◽  
Timos Sellis
Optimization ◽  
2021 ◽  
pp. 1-11
Author(s):  
Juan Enrique Martínez-Legaz ◽  
Maryam Tamadoni Jahromi ◽  
Eskandar Naraghirad
Keyword(s):  

Author(s):  
Dennis R. Bukenberger ◽  
Hendrik P. A. Lensch

Abstract We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve $$L_{2|\infty }$$ L 2 | ∞ Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations. Graphic abstract


2000 ◽  
Vol 32 (01) ◽  
pp. 1-18 ◽  
Author(s):  
F. Baccelli ◽  
K. Tchoumatchenko ◽  
S. Zuyev

Consider the Delaunay graph and the Voronoi tessellation constructed with respect to a Poisson point process. The sequence of nuclei of the Voronoi cells that are crossed by a line defines a path on the Delaunay graph. We show that the evolution of this path is governed by a Markov chain. We study the ergodic properties of the chain and find its stationary distribution. As a corollary, we obtain the ratio of the mean path length to the Euclidean distance between the end points, and hence a bound for the mean asymptotic length of the shortest path. We apply these results to define a family of simple incremental algorithms for constructing short paths on the Delaunay graph and discuss potential applications to routeing in mobile communication networks.


2015 ◽  
Vol 150 ◽  
pp. 30-36 ◽  
Author(s):  
P. Felfer ◽  
A.V. Ceguerra ◽  
S.P. Ringer ◽  
J.M. Cairney

2021 ◽  
Vol 38 (2) ◽  
pp. 73-80
Author(s):  
Yu.N. Slepenok ◽  
◽  
G.V. Stankevich ◽  
L.P. Stepanova ◽  
◽  
...  

The article discusses the particular conditions of holding medical organizations accountable for causing harm to the health of patients. The conditions of civil liability, as well as the degree of responsibility of a medical organization in the provision of medical services, are analyzed. The authors are of the opinion that medical care should be organized in accordance with the procedures, conditions and standards for the provision of such care, however, the standards cannot cover all the options that may arise during the provision of medical care, therefore they are aimed at creating an average “sample”, to determine the approximate order of possible actions carried out by medical personnel. Attention is also paid to the consideration of the features of causing harm to the patient’s health, depending on whether the harm was caused in the provision of medical care or medical services. In conclusion, it was concluded that the conditions for bringing medical organizations to justice should include: unlawful action (inaction), harm, a causal relationship between unlawful action and harm, as well as the fault of the injurer.


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