Lattices, measurement planes and grid variants used to locate and index measurements in maps and volumes.

Class or function Description
lattice the lattice an EBSD map is measured on: the basis of the two shortest translations, the cell shape ‘square’ or ‘hex’, the plane and the integer index of every position, inferred from the positions or fitted to a known basis
mapPlane the plane of a set of positions with an orthonormal frame: the normal fitted and pointing up, e1 the given direction projected into the plane, the origin the specimen origin’s foot on it
voxelLattice the lattice a volume is measured on: the origin, the translations d1, d2, d3 as the rows of D and the integer index of every voxel, voxel n at origin + ijk[n] @ D
cellComplex the spatial decomposition of a map, one cell per site: the vertices V, the vertex pair F and the site pair of every face, the sites and the lattice
latticeBasis the basis, the stencil and the spacing a cell polygon of four or six corners describes
EBSDsquare a map on a square grid from arrays in map shape, the rows of the array its rows of pixels
EBSD3square a volume on its (n1, n2, n3) array of voxels, on a rectangular lattice
hex2cube the cube coordinates x, y, z of cells of a hexagonal grid, given by their row and column (counted from 0) or by their flat index
cube2hex the row and column (counted from 0) of the cells with cube coordinates x, y, z, NaN for a cell outside the grid

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/latticeHelpers_index_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.