Computing a front-facing ellipse that subtends the same solid angle as an arbitrarily oriented ellipse

Abstract : A front-facing ellipse, with respect to an observation point, is an ellipse that is perpendicular to the line that goes through the origin and the center of the ellipse. Front-facing ellipses are more convenient than arbitrarily oriented ellipses for solid-angle computations. In this report, we present an algebraic method for computing a front-facing ellipse that covers the same solid angle as an arbitrarily oriented ellipse. A previous approach was described by Conway [Con10] but it is involved, in terms of trigonometric derivations and computations. Our formulation shows that this problem is equivalent to computing the eigenvectors of a 3×3 matrix, which is simpler to derive and compute.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01561624
Contributeur : Eric Heitz <>
Soumis le : jeudi 13 juillet 2017 - 10:41:27
Dernière modification le : lundi 24 juillet 2017 - 14:14:20

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solidAngleEllipse.pdf
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  • HAL Id : hal-01561624, version 1

Citation

Eric Heitz. Computing a front-facing ellipse that subtends the same solid angle as an arbitrarily oriented ellipse. 2017. 〈hal-01561624〉

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