Description

confidence ellipse for the mean direction based on Tanaka / asymptotic covariance of the maximum eigenvector (1999) https://doi.org/10.1186/BF03351601

Syntax

BS2 = S2FunBingham.fit(v)
[BS2, ab, rot] = S2FunBingham.fit(v,'p',0.95)

Input

`v`	`vector3d`

Output

`BS2`	`S2FunBingham`
`ab`	`semi axes length of the confidence ellipse (in radian)`
`rot`	`orientation of the confidence ellipse, to be used with \|ellipse\|`

Options

`p`	`confidence level p of the ellipse computed (default at 0.95)`

Example

simulate some directions

odf = unimodalODF(quaternion.id,'halfwidth',10*degree);
N = 100;
v = odf.discreteSample(N) .* ...
rotation.byAxisAngle(vector3d.X,rand(N,1)*2*pi) * vector3d.Y;

fit a Bingham distribution

[S2F, ab, rot] = S2FunBingham.fit(v)

S2F = S2FunBingham (y↓→x)
ab =
    0.0507    2.1552
 
rot = rotation
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  165.975 11.1085 195.629

visualization

plot(S2F)
mtexColorMap LaboTeX
hold on
plot(v,'Markercolor','k','MarkerSize',3)
ellipse(rot,ab(1),ab(2))
hold off

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/S2FunBingham.fit.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.