Line Transversals of Convex Polyhedra in $\mathbb{R}^3$

2010 ◽  
Vol 39 (7) ◽  
pp. 3283-3310 ◽  
Author(s):  
Haim Kaplan ◽  
Natan Rubin ◽  
Micha Sharir
Keyword(s):  
Convex Polyhedra ◽  
Line Transversals

Line transversals to blown up closed balls

2011 ◽  
Vol 100 (1-2) ◽  
pp. 79-84
Author(s):  
Jesús Jerónimo-Castro ◽  
Edgardo Roldán-Pensado
Keyword(s):  
Line Transversals

scholarly journals Data-based polyhedron model for optimization of engineering structures involving uncertainties

2021 ◽  
Vol 2 ◽  
Author(s):  
Zhiping Qiu ◽  
Han Wu ◽  
Isaac Elishakoff ◽  
Dongliang Liu
Keyword(s):  
Linear Programming ◽  
Convex Polyhedron ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Composite Plates ◽  
Convex Polyhedra ◽  
Chebyshev Inequality ◽  
Engineering Structures ◽  
Load Bearing ◽  
Polyhedron Model

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

Convex polyhedra in hyperbolic space and interpolation of functions

2011 ◽  
Vol 84 (3) ◽  
pp. 850-853
Author(s):  
O. P. Gladunova ◽  
E. D. Rodionov ◽  
V. V. Slavskii
Keyword(s):  
Hyperbolic Space ◽  
Convex Polyhedra ◽  
Interpolation Of Functions

Pseudo minimum translational distance between convex polyhedra (II)

2001 ◽  
Vol 44 (4) ◽  
pp. 337-344 ◽  
Author(s):  
Xiangyang Zhu ◽  
Han Ding ◽  
Youlun Xiong
Keyword(s):  
Convex Polyhedra ◽  
Pseudo Minimum Translational Distance

High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

2012 ◽  
Vol 12 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Level Set ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
High Order ◽  
Convex Polyhedra ◽  
Two Phase ◽  
High Order Schemes ◽  
Flow Problems ◽  
Mixed Element ◽  
Areas Of Interest

AbstractIn this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

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