a displacement that varies polynomially across the frame
Degree 1 is an affine and could equally be a spatialTransformShift - inv converts to one, since a matrix has an exact inverse where a polynomial does not. Degree 2 is what mops up the residual curvature a projective stage leaves behind.
The coefficients describe the DISPLACEMENT, not the mapped position, so the identity is c = 0.
Syntax
T = spatialTransformPoly(c,degree)
T = spatialTransformPoly.fit(posA,posB,'degree',2)
T = spatialTransformPoly.fit(posA,posB,'degree',2,'weights',w)Input
| c | m × 2 coefficients, one column per displacement component |
| degree | 1 or 2 |
| posA, posB | vector3d, the same points in the two frames |
| w | double, one weight per point |
Output
| T | spatialTransformPoly |
Class Properties
| c | m x 2 coefficients against [1 x y] or [1 x y x^2 xy y^2] |
| degree | 1 or 2 |
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/spatialTransformPoly.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.