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Titre du document / Document title

Derivations of the solid angle subtended at a point by first- and second-order surfaces and volumes as a function of elliptic integrals

Auteur(s) / Author(s)

CRAMER S. N. (1) ;

Affiliation(s) du ou des auteurs / Author(s) Affiliation(s)

(1) Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6362, ETATS-UNIS

Résumé / Abstract

An analytic study of the solid angle subtended at a point by objects of first and second algebraic order has been made. It is shown that the derived solid angle for all such objects is in the form of a general elliptic integral, which can be written as a linear combination of elliptic integrals of the first and third kind and elementary functions. Many common surfaces and volumes have been investigated, including the conic sections and their volumes of revolution. The principal feature of the study is the manipulation of solid-angle equations into integral forms that can be matched with those found in handbook tables. These integrals are amenable to computer special function library routine analysis requiring no direct interaction with elliptic integrals by the user. The general case requires the solution of a fourth-order equation before specific solid-angle formulation can be made, but for many common geometric objects this equation can be solved by elementary means. Methods for the testing and application of solid-angle equations with Monte Carlo rejection and estimation techniques are presented. Approximate and degenerate forms of the equations are shown, and methods for the evaluation of the solid angle of a torus are outlined.

Revue / Journal Title

Nuclear science and engineering    ISSN  0029-5639   CODEN NSENAO 

Source / Source

1999, vol. 132, no2, pp. 217-258 (16 ref.)

Langue / Language

Anglais

Editeur / Publisher

American Nuclear Society, La Grange Park, IL, ETATS-UNIS  (1956) (Revue)

Mots-clés anglais / English Keywords

Surfaces

;

Volume

;

Elliptic integral

;

Solid angle

;

Special function

;

Monte Carlo methods

;

Spheres

;

Hemisphere

;

Circle

;

Cylinders

;

Mots-clés français / French Keywords

Surface

;

Volume

;

Intégrale elliptique

;

Angle solide

;

Fonction spéciale

;

Méthode Monte Carlo

;

Sphère

;

Hémisphère

;

Cercle

;

Cylindre

;

Mots-clés espagnols / Spanish Keywords

Integral elíptica

;

Angulo sólido

;

Función especial

;

Hemisferio

;

Circulo

;

Localisation / Location

INIST-CNRS, Cote INIST : 8020, 35400008464357.0050

Nº notice refdoc (ud4) : 1930292



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