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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Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Elsevier, 2017, 〈http://www.sciencedirect.com/science/article/pii/S0168900217301857〉
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Dernière modification le : jeudi 9 février 2017 - 01:01:25
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Eric Heitz. Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Elsevier, 2017, 〈http://www.sciencedirect.com/science/article/pii/S0168900217301857〉. 〈hal-01402302v3〉

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