Filters








13,114 Hits in 4.0 sec

Estimating the number of vertices of a polyhedron

David Avis, Luc Devroye
2000 Information Processing Letters  
Given a polyhedron P by a list of inequalities we develop unbiased estimates of the number of vertices and bases of P .  ...  The method can be applied to estimate the output size of other enumeration problems solvable by reverse search.  ...  In this paper we give a method for estimating the number of vertices and bases of a polytope, and for estimating the running time of the reverse search method.  ... 
doi:10.1016/s0020-0190(00)00011-9 fatcat:7gtt2ksatbfslegcveddv7e63i

Volume estimates for right-angled hyperbolic polyhedra [article]

A. Egorov, A. Vesnin
2020 arXiv   pre-print
For a class of compact right-angled polyhedra and a class of ideal right-angled polyhedra estimates of volumes in terms of the number of vertices were obtained by Atkinson in 2009.  ...  In the present paper upper estimates for both classes are improved.  ...  Two-sided volume estimates for ideal right-angled hyperbolic polyhedra in terms of the number of vertices were obtained by Atkinson [2] .  ... 
arXiv:2010.11147v1 fatcat:abcspzti2rgthbg2durezruliq

Optimization of the Hausdorff distance between convex polyhedrons in R3**This work was supported by the Russian Science Foundation(project no. 15-11-10018)

V.N. Ushakov, P.D. Lebedev, A.M. Tarasyev, A.V. Ushakov
2015 IFAC-PapersOnLine  
In the problem statement, it is necessary to find such disposition of two given polyhedrons A and B that the Hausdorff distance between them obtains the minimal value.  ...  In the problem statement, it is necessary to find such disposition of two given polyhedrons A and B that the Hausdorff distance between them obtains the minimal value.  ...  The index J B (x) of numbers for vertices of the polyhedron B + {x} is defined in the analogous way.  ... 
doi:10.1016/j.ifacol.2015.11.084 fatcat:km6qrsfblve7llssigjs6en4aa

A Geometric Approach for Computing the Kernel of a Polyhedron [article]

Tommaso Sorgente, Silvia Biasotti, Michela Spagnuolo
2021 arXiv   pre-print
We present a geometric algorithm to compute the geometric kernel of a generic polyhedron.  ...  Currently, the principal implementation of the kernel estimation is based on the solution of a linear programming problem.  ...  Manzini for the precious discussions and suggestions, and all the people from IMATI institute involved in the CHANGE project.  ... 
arXiv:2110.11054v2 fatcat:waoxmwtub5flnlgsvi5vh626bu

Two-sided bounds for the volume of right-angled hyperbolic polyhedra [article]

Dušan Repovš, Andrei Vesnin
2011 arXiv   pre-print
For a compact right-angled polyhedron R in H^3 denote by vol (R) the volume and by vert (R) the number of vertices. Upper and lower bounds for vol (R) in terms of vert (R) were obtained in A09.  ...  Constructing a 2-parameter family of polyhedra, we show that the asymptotic upper bound 5 v_3 / 8, where v_3 is the volume of the ideal regular tetrahedron in H^3, is a double limit point for ratios vol  ...  Let us denote by vert(R) the number of vertices of a right-angled polyhedron R.  ... 
arXiv:1104.3437v1 fatcat:bmnoyovtcncn5iztz7d6seo4zi

Polygonal and Polyhedral Contour Reconstruction in Computed Tomography

C. Soussen, A. Mohammad-Djafari
2004 IEEE Transactions on Image Processing  
We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation.  ...  We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Vertice estimation is done without using a voxel approximation of the 3-D image.  ...  ACKNOWLEDGMENT The authors would like to thank Drs. J. Idier and P. Ciuciu for their constant support and precious advice with this paper.  ... 
doi:10.1109/tip.2004.836159 pmid:15540458 fatcat:wjitokti6fcgvjkzrwn65shomm

2-toroids and their 3-triangulation

Milica Stojanovic
2017 Kragujevac Journal of Mathematics  
Here we discuss possibilities and properties of 3-triangulation of 2-toroids, i.e. polyhedra topologically equivalent to sphere with 2 handles, and develop the concepts of piecewise convex polyhedra and  ...  graph of connection.  ...  The estimation of T min was made by substituting t i min with n i −3 (n i is number of vertices of P i ), since t i min ≥ n i − 3.  ... 
doi:10.5937/kgjmath1702203s fatcat:4v56kz2qmjc2valeccn7jn7qpq

Statistical mechanical model of the energetics of coated vesicle formation

M.H. Fagan, T.G. Dewey
1984 Biophysical Journal  
Adsorptive endocytosis is mediated by a structural transformation of a two-dimensional hexagonal lattice to a polyhedron or coated vesicle.  ...  In determining the configurational partition functions required for equilibrium constant calculations, the polyhedron is represented as a planar graph with no surfaces.  ...  The dependence on total number of vertices is shown. FIGURE 5 A plot of log Kq vs. N, the number of vertices in the polyhedron. The total number of vertices is 1,000.  ... 
doi:10.1016/s0006-3495(84)84162-4 pmid:6141814 pmcid:PMC1434869 fatcat:rpqwfsoynngtpdz55n32ggqlhu

Page 564 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
This generally yields a nondegenerate polyhedron, but the number of vertices in this polyhedron may increase.  ...  Using this, he gives a lower and an upper bound on the number of the broken vertices of a degenerate vertex. He also shows that these bounds can be attained.  ... 

Polyhedron Kernel Computation Using a Geometric Approach [article]

Tommaso Sorgente, Silvia Biasotti, Michela Spagnuolo
2022 arXiv   pre-print
The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible.  ...  The most acknowledged solution for the kernel estimation is to solve a linear programming problem.  ...  Manzini for the precious discussions and suggestions, and all the people from IMATI institute involved in the CHANGE project.  ... 
arXiv:2202.06625v1 fatcat:w2m26r4tajbflhrf43qqika6y4

The Number of Vertices of a Polyhedron

T. L. Saaty
1955 The American mathematical monthly  
THE NUMBER OF VERTICES OF A POLYHEDRON T. L. SAATY, Takoma Park, Maryland 1. Introduction.  ...  Unfortunately, so far, this number is only known to be dominated by Casm.n and as will be seen below this is an unsatisfactory estimate of the number of vertices of the convex sets of this problem.  ... 
doi:10.2307/2307037 fatcat:tkpobvpdfzb6bewhzaftgpgsw4

Living with lrs [chapter]

David Avis
2000 Lecture Notes in Computer Science  
Experience gained while trying to solvet hese problems lead to a number of improvements to the original implementation.  ...  This paper describes the development of lrs,a nimplementation of the reverse search method to the vertexe numeration/convex hull problem for convex polyhedra.  ...  This motivated the search for a way to estimate the number of vertices and bases of a polyhedron without computing them all.  ... 
doi:10.1007/978-3-540-46515-7_4 fatcat:pnw2ehq3q5bijmozrcr3rk6is4

Volume estimates for equiangular hyperbolic Coxeter polyhedra

Christopher K Atkinson
2009 Algebraic and Geometric Topology  
It is a consequence of Andreev's theorem that either n=3 and the polyhedron has all ideal vertices or that n=2. Volume estimates are given for all equiangular hyperbolic Coxeter polyhedra.  ...  An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to \pi/n for some fixed integer n at least 2.  ...  Hence the area of a single face is n 1 C n F 2 2 Á ; where n 1 is the number of ideal vertices of the face.  ... 
doi:10.2140/agt.2009.9.1225 fatcat:3z35aczdnzeazjku6b2rrkh23q

On the number of vertices in integer linear programming problems [article]

Nikolai Yu. Zolotykh
2006 arXiv   pre-print
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of these.  ...  From the upper bound (12) on the number of vertices in P I and from the inequality [McM70] , estimating the number of facets in a polyhedron with v vertices, follows that the number of facets in P I is  ...  [CHKM92] generalized this approach for the estimate of the number of vertices N (A, b) if A ∈ Q m×n and b ∈ Q m are arbitrary.  ... 
arXiv:math/0611356v1 fatcat:thbiakponnb5rdy6ekixgrdvja

A New Quantitative Approach to Tree Attributes Estimation Based on LiDAR Point Clouds

Guangpeng Fan, Liangliang Nan, Feixiang Chen, Yanqi Dong, Zhiming Wang, Hao Li, Danyu Chen
2020 Remote Sensing  
Then, the end of the stem or all branches were closed. The tree model changed from a cylinder to a closed convex hull polyhedron, which was to reconstruct a 3D model of the tree.  ...  First, the Adtree method was used to approximate the geometry of the tree stem and branches by fitting a series of cylinders. Trees were represented as a broad set of cylinders.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/rs12111779 fatcat:ivr3betuandbxaj5524koyzyva
« Previous Showing results 1 — 15 out of 13,114 results