A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2010; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Estimating the number of vertices of a polyhedron

2000
*
Information Processing Letters
*

Given

doi:10.1016/s0020-0190(00)00011-9
fatcat:7gtt2ksatbfslegcveddv7e63i
*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. ...##
###
Volume estimates for right-angled hyperbolic polyhedra
[article]

2020
*
arXiv
*
pre-print

For

arXiv:2010.11147v1
fatcat:abcspzti2rgthbg2durezruliq
*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] . ...##
###
Optimization of the Hausdorff distance between convex polyhedrons in R3**This work was supported by the Russian Science Foundation(project no. 15-11-10018)

2015
*
IFAC-PapersOnLine
*

In

doi:10.1016/j.ifacol.2015.11.084
fatcat:km6qrsfblve7llssigjs6en4aa
*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. ...##
###
A Geometric Approach for Computing the Kernel of a Polyhedron
[article]

2021
*
arXiv
*
pre-print

We present

arXiv:2110.11054v2
fatcat:waoxmwtub5flnlgsvi5vh626bu
*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. ...##
###
Two-sided bounds for the volume of right-angled hyperbolic polyhedra
[article]

2011
*
arXiv
*
pre-print

For

arXiv:1104.3437v1
fatcat:bmnoyovtcncn5iztz7d6seo4zi
*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. ...##
###
Polygonal and Polyhedral Contour Reconstruction in Computed Tomography

2004
*
IEEE Transactions on Image Processing
*

We study

doi:10.1109/tip.2004.836159
pmid:15540458
fatcat:wjitokti6fcgvjkzrwn65shomm
*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. ...##
###
2-toroids and their 3-triangulation

2017
*
Kragujevac Journal of Mathematics
*

Here we discuss possibilities and properties

doi:10.5937/kgjmath1702203s
fatcat:4v56kz2qmjc2valeccn7jn7qpq
*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. ...##
###
Statistical mechanical model of the energetics of coated vesicle formation

1984
*
Biophysical Journal
*

Adsorptive endocytosis is mediated by

doi:10.1016/s0006-3495(84)84162-4
pmid:6141814
pmcid:PMC1434869
fatcat:rpqwfsoynngtpdz55n32ggqlhu
*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. ...##
###
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]

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. ...

##
###
The Number of Vertices of a Polyhedron

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. ...

##
###
Living with lrs
[chapter]

2000
*
Lecture Notes in Computer Science
*

Experience gained while trying to solvet hese problems lead to

doi:10.1007/978-3-540-46515-7_4
fatcat:pnw2ehq3q5bijmozrcr3rk6is4
*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. ...##
###
Volume estimates for equiangular hyperbolic Coxeter polyhedra

2009
*
Algebraic and Geometric Topology
*

It is

doi:10.2140/agt.2009.9.1225
fatcat:3z35aczdnzeazjku6b2rrkh23q
*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. ...##
###
On the number of vertices in integer linear programming problems
[article]

2006
*
arXiv
*
pre-print

We give

arXiv:math/0611356v1
fatcat:thbiakponnb5rdy6ekixgrdvja
*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. ...##
###
A New Quantitative Approach to Tree Attributes Estimation Based on LiDAR Point Clouds

2020
*
Remote Sensing
*

Then,

doi:10.3390/rs12111779
fatcat:ivr3betuandbxaj5524koyzyva
*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. ...
« Previous

*Showing results 1 — 15 out of 13,114 results*