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.
Описание
Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid to a point source - ScienceDirect
%0 Journal Article
%1 HEITZ201710
%A Heitz, Eric
%D 2017
%J Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
%K 2017 3D ellipse games geometry
%P 10 - 14
%R https://doi.org/10.1016/j.nima.2017.02.004
%T Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid to a point source
%U http://www.sciencedirect.com/science/article/pii/S0168900217301857
%V 852
%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.
@article{HEITZ201710,
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.},
added-at = {2018-03-30T18:46:34.000+0200},
author = {Heitz, Eric},
biburl = {https://www.bibsonomy.org/bibtex/28857ba1c3d7e2e64f8599baa4fbdefd0/achakraborty},
description = {Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid to a point source - ScienceDirect},
doi = {https://doi.org/10.1016/j.nima.2017.02.004},
interhash = {5308b4edd0b85b215436b625016d0700},
intrahash = {8857ba1c3d7e2e64f8599baa4fbdefd0},
issn = {0168-9002},
journal = {Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment},
keywords = {2017 3D ellipse games geometry},
pages = {10 - 14},
timestamp = {2018-03-30T18:46:34.000+0200},
title = {Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid to a point source},
url = {http://www.sciencedirect.com/science/article/pii/S0168900217301857},
volume = 852,
year = 2017
}