a displacement measured at scattered points and interpolated between them
The free form transform: no model, just where things moved. Used to mop up whatever structure a fitted model leaves in its residual, and as the common currency any chain can be collapsed into by discretize.
The sample points need not lie on a grid and the query points need not either, so a field fitted on one data set can be evaluated on another. Interpolation is natural neighbour, extrapolation linear.
Coordinates are normalised before interpolating, because natural neighbour weights come from a Delaunay triangulation and that is not scale invariant - a frame far wider than it is tall would otherwise get sliver triangles. The displacements themselves need no normalising: the weights do not depend on them.
Syntax
T = spatialTransformField(pos,u)
T = spatialTransformField.fit(posA,posB)Input
| pos | vector3d, where the displacement was measured |
| u | vector3d, the displacement there |
| posA, posB | vector3d, the same points in the two frames |
Output
| T | spatialTransformField |
| There is deliberately no smooth: tools/math_tools/smoothn is for gridded data, and applying it to scattered samples in storage order smooths along the index rather than across the frame, which collapses the field to its mean. Smoothing a scattered field needs a regularised scattered fit. | |
Class Properties
| pos | vector3d, the sample points |
| u | vector3d, the displacement at each |
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/spatialTransformField.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.