%0 Report
%T Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid
%+ Unity Technologies [San Francisco]
%A Heitz, Eric
%I Unity Technologies
%8 2016-11-24
%D 2016
%K solid angle
%K ellipsoid
%Z Mathematics [math]/General Mathematics [math.GM]Reports
%X 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.
%G English
%2 https://hal.science/hal-01402302v1/document
%2 https://hal.science/hal-01402302v1/file/solidAngleEllipsoid.pdf
%L hal-01402302
%U https://hal.science/hal-01402302