Integrates an S2Fun on the region of all vector3d's that are close to a specified vector3d (center) by a tolerance (radius), i.e.
\[ \int_{\angle(g,c)<r} f(g) \, dg.\]
Description
The function 'volume' returns the ratio of the volume of an S2Fun on the region (of all vector3d's that are close to a specified vector3d (center) by a tolerance (radius)) to the volume of the entire spherical function.
Note that if the S2Fun \(f\) is 'antipodal' the volume in any center with radius 90° will return the mean value of the S2Fun, which is infact the volume of the whole sphere.
Syntax
v = volume(sF,center,radius)Input
| sF | S2FunTri |
| center | vector3d |
| radius | double |
Options
| resolution | resolution of discretization |
See also
Citing this page.
This page is part of the documentation of
MTEX, a free and open
source MATLAB toolbox for analyzing and modeling crystallographic textures.
It was written by The MTEX Developers and is published at
https://mtex-toolbox.github.io/S2FunTri.volume.html.
If you use MTEX, or reuse text or figures from this page, in your research,
please cite
F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63
BibTeX
@article{bachmann2010mtex,
author = {F. Bachmann and R. Hielscher and H. Schaeben},
title = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
journal = {Solid State Phenomena},
volume = {160},
pages = {63-68},
year = {2010},
doi = {10.4028/www.scientific.net/SSP.160.63},
url = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.