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About the algebraic solutions of smallest enclosing cylinders problems

Michel Petitjean
2012 Applicable Algebra in Engineering, Communication and Computing  
The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.  ...  For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6.  ...  Bounds for the radius of minimal enclosing d-simplices have been given [3] , and the complexity of the smallest enclosing cylinder problem has been investigated for metrology applications [11] .  ... 
doi:10.1007/s00200-012-0171-y fatcat:ndg4cclubfdjhhfec3fmpxk4v4

Page 10051 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
Philippe Gimenez (E-VALDS-AGT; Valladolid) 2004m:52019 52A40 68U05 Brandenberg, René (D-MUTU-ZM; Munich); Theobald, Thorsten (D-MUTU-ZM; Munich) Algebraic methods for computing smallest enclosing and circumscribing  ...  The authors investigate the problem of computing the cylinder of smallest radius that circumscribes a given simplex. In E* they im- prove results of [O. Devillers et al., Discrete Comput.  ... 

Efficient algorithms for geometric optimization

Pankaj K. Agarwal, Micha Sharir
1998 ACM Computing Surveys  
Whenever A s reaches a branching point that depends on some comparison with an associated polynomial p(λ), it computes all the roots λ 1 , λ 2 , . . . of p and computes P(λ i ) by running (the standard  ...  , placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.  ...  1) n)-time algorithm for finding a smallest cylinder enclosing S; see e.g  ... 
doi:10.1145/299917.299918 fatcat:qfqiikacgvhtxpikdjyvjrdnhm

Multipole fast algorithm for the least-squares approach of the method of fundamental solutions for three-dimensional harmonic problems

I. Saavedra, H. Power
2003 Numerical Methods for Partial Differential Equations  
In this article we describe an improvement in the speed of computation for the least-squares method of fundamental solutions (MFS) by means of Greengard and Rokhlin's FMA.  ...  The results of applying the method to test problems from potential theory with a number of boundary points in the order of 80,000 show that the method can achieve fast solutions for the potential and its  ...  An approximately uniform distribution of N ϭ 64H ϩ 128 sources on a curved surface which encloses the cylinder at a distance from the cylinder surface varying between 2 at the sides and (H/4) ϩ 3 at the  ... 
doi:10.1002/num.10071 fatcat:qiedmt3eynerzfpjlyhsy3isai

The polarizability and the capacitance change of a bounded object in a parallel plate capacitor

Gerhard Kristensson
2012 Physica Scripta  
Here a is the radius of the smallest circumscribing sphere of the object. The formulation of the problem The geometry of the problem is shown in Figure 1 .  ...  The polarizability and the capacitance change of a bounded object in a parallel plate capacitor Kristensson, Gerhard Abstract A method to solve the change in capacitance (or charge), if an object is introduced  ...  Here a is the radius of the smallest circumscribing sphere of the body, and R > a is the radius of a spherical surface not enclosing the domain of excitation V app . P nn = N nn (l + l )!  ... 
doi:10.1088/0031-8949/86/03/035405 fatcat:7zaxb6jc55forin7mwl6hstshe

Investigation on polynomial integrators for time-domain electromagnetics using a high-order discontinuous Galerkin method

H. Fahs
2012 Applied Mathematical Modelling  
In this work, we investigate the application of polynomial integrators in a high-order discontinuous Galerkin method for solving the time-domain Maxwell equations.  ...  This family of expansions is suitable for non-Hermitian matrices, and consequently the proposed integrators can handle absorbing media and conductive materials.  ...  Christophe Guiffaut (XLIM institute, Limoges, France) for his assistance during the process of this work.  ... 
doi:10.1016/j.apm.2011.12.055 fatcat:xb3iscejfrbbro26hj56h3jpse

AUTOMATIC RECONSTRUCTION OF 3D CAD MODELS FROM DIGITAL SCANS

FAUSTO BERNARDINI, CHANDRAJIT L. BAJAJ, JINDONG CHEN, DANIEL R. SCHIKORE
1999 International journal of computational geometry and applications  
Applications include rapid reverse engineering of existing objects for use in a synthetic computer environment, including computer aided design and manufacturing.  ...  We present an approach for the reconstruction and approximation of 3D CAD models from an unorganized collection of points.  ...  Thanks to the Computer Graphics Group, University o f W ashington and the Stanford University Computer Graphics Laboratory, for making some of the range data used in this paper publicly available.  ... 
doi:10.1142/s0218195999000236 fatcat:e6dugdyssrhuxk4zh2ykdv2one

Robust Geometric Computation [chapter]

Chee K. Yap, Vikram Sharma
2008 Encyclopedia of Algorithms  
(iii) An interesting domain is optimization problems such as linear and quadratic programming [Gae99, GS00] and smallest enclosing cylinder problem [SSTY00] .  ...  The first work in this area is the SoS ("simulation of simplicity") technique of Edelsbrunner and Mücke [EM90] . The method amounts to adding powers of an indeterminate ǫ to each input parameter.  ... 
doi:10.1007/978-0-387-30162-4_349 fatcat:h3xf7abcyzdazhvqpwszvkd7ca

Why is a soap bubble like a railway? [article]

David Wakeham
2020 arXiv   pre-print
The only prerequisites are high school geometry, some algebra, and a spirit of adventure. These notes should therefore be suitable for high school enrichment and bedside reading.  ...  Along the way, we touch on algorithms and complexity, the physics of computation, curvature, chemistry, space-filling polyhedra, and bees from other dimensions.  ...  smallest-area) way to enclose some air pockets.  ... 
arXiv:2008.09611v1 fatcat:q2xipjqlvrdcfa463lhbw3ctyq

Anisotropic triangulations via discrete Riemannian Voronoi diagrams [article]

Jean-Daniel Boissonnat, Mael Rouxel-Labbé, Mathijs Wintraecken
2017 arXiv   pre-print
The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics.  ...  Furthermore, we show that, under similar conditions, the simplices of this triangulation can be straightened.  ...  The first and third authors have received funding from the European Research Council under the European Union's ERC Grant Agreement number 339025 GUDHI (Algorithmic Foundations of Geometric Understanding  ... 
arXiv:1703.06487v1 fatcat:dabg76qhxveudgrsl3wn6ihf3q

Throwing a Sofa Through the Window [article]

Dan Halperin, Micha Sharir, Itay Yehuda
2021 arXiv   pre-print
can slide through a gate of width equal to the diameter of W. ∙ We study the case of a circular window W, and show that, for the regular tetrahedron K of edge length 1, there are two thresholds 1 > δ_1  ...  setup, where we want to plan a general motion (with all six degrees of freedom) for K through a rectangular window W, and present an efficient algorithm for this problem, with running time close to O(  ...  The intersection of K and Ω p is a tiny convex polygon, which we denote by ω p , with a vertex for each edge of E p .  ... 
arXiv:2102.04262v2 fatcat:m74j67y2jzatjgaytupatizg4e

Exponentially small asymptotic formulas for the length spectrum in some billiard tables [article]

Pau Martín, Anna Tamarit-Sariol, Rafael Ramírez-Ros
2015 arXiv   pre-print
Our computations require a multiple-precision arithmetic and have been programmed in PARI/GP.  ...  the exponent r is half of the radius of convergence of the Borel transform of the well-known asymptotic series for the lengths of the (1,q)-periodic trajectories.  ...  Seara and C. Simó for very useful remarks and comments. We also appreciate the assistance of A. Granados and P. Roldán in the use of the UPC Applied Math cluster for our experiments.  ... 
arXiv:1504.08243v1 fatcat:rky3qrcpcfdj7b6igirwlf2a6y

MESH GENERATION AND OPTIMAL TRIANGULATION [chapter]

MARSHALL BERN, DAVID EPPSTEIN
1992 Lecture Notes Series on Computing  
We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices (Steiner points).  ...  We survey the computational geometry relevant to nite element mesh generation. We especially focus on optimal triangulations of geometric domains in two-and three-dimensions.  ...  Frances Yao for various helpful suggestions.  ... 
doi:10.1142/9789814355858_0002 fatcat:zjlfgakee5df7nihosmpeuhco4

MESH GENERATION AND OPTIMAL TRIANGULATION [chapter]

MARSHALL BERN, DAVID EPPSTEIN
1995 Lecture Notes Series on Computing  
We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices (Steiner points).  ...  We survey the computational geometry relevant to nite element mesh generation. We especially focus on optimal triangulations of geometric domains in two-and three-dimensions.  ...  Frances Yao for various helpful suggestions.  ... 
doi:10.1142/9789812831699_0003 fatcat:ec6436f5i5bszheuiherz452ae

Exponentially Small Asymptotic Formulas for the Length Spectrum in Some Billiard Tables

P. Martín, R. Ramírez-Ros, A. Tamarit-Sariol
2016 Experimental Mathematics  
We also detect some non-generic behaviors due to the presence of extra symmetries. Our computations require a multiple-precision arithmetic and have been programmed in PARI/GP.  ...  the exponent r is half of the radius of convergence of the Borel transform of the well-known asymptotic series for the lengths of the (1, q)-periodic trajectories.  ...  Seara and C. Simó for very useful remarks and comments. We also appreciate the assistance of A. Granados and P. Roldán in the use of the UPC Applied Math cluster for our experiments.  ... 
doi:10.1080/10586458.2015.1076361 fatcat:jm7l7nwit5hphntxvnchc33ui4
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