a scan distortion described by a polynomial displacement in x and y

Syntax

T = spatialTransformPoly(c, 2)
T = spatialTransformPoly.fit(posA, posB, degree=2)
pos2 = T * pos

Description

The output is the input position plus the polynomial displacement. Rows of c multiply the terms [1, x, y] for degree 1, or [1, x, y, x**2, x*y, y**2] for degree 2. Its two columns give the x and y displacements. The z coordinate is unchanged. A degree-1 displacement is an affine map and has an exact matrix inverse; degree 2 uses a numerical inverse. With no coefficients the transform is the identity.

Input

`c`	coefficient array of shape (3, 2) or (6, 2)
`degree`	1 or 2; inferred from the number of coefficient rows when omitted

Output

`T`	spatialTransformPoly

Properties

`c`	displacement coefficients
`degree`	polynomial degree

Members

eval	the positions moved by the polynomial displacement
fit	the polynomial displacement best mapping the positions posA onto posB
fitOptions	the degree, the keyword a refit keeps
inv	the inverse: the inverse affine map at degree 1, the fixed point inverse at degree 2
isid	whether every coefficient vanishes
paramChar	the size of the coefficients as a line of text
shiftMatrix	the affine map a degree 1 displacement is
shortChar	the name in the display, poly11 or poly22 by the degree

Used on

EBSDSpatialTransform

MATLAB’s spatialTransformPoly

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/spatialTransformPoly_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.

The class spatialTransformPoly