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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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01561624
Contributor : Eric Heitz <>
Submitted on : Thursday, July 13, 2017 - 10:41:27 AM
Last modification on : Monday, July 24, 2017 - 2:14:20 PM
Long-term archiving on: : Thursday, January 25, 2018 - 2:17:26 AM

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  • HAL Id : hal-01561624, version 1

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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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