https://hal.archives-ouvertes.fr/hal-01402302v3Heitz, EricEricHeitzUnity Technologies [San Francisco]Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoidHAL CCSD2017solid angle ellipsoid[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Heitz, Eric2017-02-05 17:12:362017-02-09 01:01:252017-02-08 14:59:13enJournal articleshttps://hal.archives-ouvertes.fr/hal-01402302v2application/pdf3We 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.