the moments of the polygon of every outline: the area, the first and the second moments about the origin, summed over its loops

Syntax

ar, cx, cy, ixx, iyy, ixy = polygonMoments(grains.V, grains.loops, grains.size)

Per grain.

ar, cx, cy, ixx, iyy, ixy = polygonMoments(grains.V, grains.loops[0])

One outline.

Description

The integrals over the area of 1, x, y, x^2, y^2 and xy, from the loops by Green’s theorem; an inner loop, stored the other way round, subtracts. The centroid is (cx, cy) / ar.

Input

V (m, 2) array of the vertices
loops per outline a list of loops of vertex indices, or the loops of one outline

Keywords

keyword default description
size None the number of outlines; without it loops is one outline

Output

ar, cx, cy, ixx, iyy, ixy arrays, one value per outline, or numbers for one

See also

grain2d.area, grain2d.centroid, grain2d.principalComponents

source

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/polygonMoments_py.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.