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Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid

Abstract : We present a geometric method for computing an ellipse that subtends the same solid-angle domain as an arbitrarily positioned ellipsoid. With this method we can extend existing analytical solid-angle calculations of ellipses to ellipsoids. Our idea consists of applying a linear transformation on the ellipsoid such that it is transformed into a sphere from which a disk that covers the same solid-angle domain can be computed. We demonstrate that by applying the inverse linear transformation on this disk we obtain an ellipse that subtends the same solid-angle domain as the ellipsoid. We provide a MATLAB implementation of our algorithm and we validate it numerically.
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https://hal.archives-ouvertes.fr/hal-01402302
Contributor : Eric Heitz Connect in order to contact the contributor
Submitted on : Thursday, November 24, 2016 - 3:02:31 PM
Last modification on : Saturday, December 24, 2016 - 1:04:13 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 12:31:41 AM

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solidAngleEllipsoid.pdf
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  • HAL Id : hal-01402302, version 1

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Eric Heitz. Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid. [Research Report] Unity Technologies. 2016. ⟨hal-01402302v1⟩

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