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Journal Articles Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment Year : 2017

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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Dates and versions

hal-01402302 , version 1 (24-11-2016)
hal-01402302 , version 2 (20-12-2016)
hal-01402302 , version 3 (05-02-2017)

Identifiers

  • HAL Id : hal-01402302 , version 3

Cite

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, 2017. ⟨hal-01402302v3⟩

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