A method of grainBoundary.

the signed curvature of every segment: the Menger curvature through the midpoints of a segment and its two neighbours along the chain, smoothed by a binomial filter along it; positive where the boundary bulges into grainId[:, 1]; MATLAB’s grainBoundary.curvature

Syntax

kappa = gB.curvature()

Smoothed 50 times.

kappa = gB.curvature(2)

Smoothed twice.

Description

The segments are stored in walk order with the grain grainId[:, 0] on the left, so the sign says into which grain the boundary bulges. To read it as convex or concave with respect to one grain, put that grain first throughout, gB.flip(gB.grainId[:, 1] == id). A segment at the end of an open chain has a neighbour on one side only and is NaN, as is a chain of one segment; a closed chain wraps around.

Input

gB grainBoundary

Keywords

keyword default description
n 50 the number of passes of the binomial filter along the chain

Output

kappa one over the radius of the fitted circle, in the units of the map, per segment

See also

grainBoundary.flip, grainBoundary.calcMeanDirection

MATLAB’s grainBoundary.curvature

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/grainBoundary.curvature_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.