Function Reference
Classes representing Geometry
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Specimen Directions (The Class @vector3d)
SchmidTensor |
computes the Schmidt tensor |
TSP |
traveling salesman problem on the 2 dimensional unit-sphere |
abs |
length of vector |
angle |
angle between two vectors Input v1, v2 - @vector3d |
angle_outer |
angle between two vectors |
arrow3d |
plot three dimensional arrows |
calcDelaunay |
compute the Delaynay triangulation for a spherical grid |
calcQuadratureWeights |
compute the area of the Voronoi decomposition |
calcVoronoi |
compute the area of the Voronoi decomposition |
calcVoronoiArea |
compute the area of the Voronoi decomposition |
cat |
|
char |
convert to char |
circle |
annotated a circle |
contour |
spherical contour plot |
contourf |
spherical filled contour plot |
cross |
pointwise cross product of two vector3d |
cross_outer |
pointwise cross product of two vector3d |
ctranspose |
transpose vector |
display |
standard output |
dot |
pointwise inner product |
dot_outer |
outer dot product |
double |
converts vector3d to double |
end |
overloaded end function |
eq |
? v1 == v2 |
export |
|
find |
return index of all points in a epsilon neighborhood of a vector |
horzcat |
overloads [v1,v2,v3..] |
interp |
dirty spherical interpolation - including some smoothing |
isPerp |
check whether v1 and v2 are orthogonal |
isempty |
overloads isempty |
kernelDensityEstimation |
calculates a density function out of (weighted) unit vectors |
length |
overloads length |
line |
|
mean |
computes the mean vector |
minus |
overload minus |
mtimes |
scalar multiplication |
ne |
? v1 == v2 |
norm |
vector norm |
normalize |
normalize a vector |
orth |
an arbitrary orthogonal vector |
patchPatala |
Syntax |
pcolor |
spherical contour plot |
perp |
conmpute an vector best orthogonal to a list of directions |
plot |
plot three dimensional vector |
plot3d |
plot spherical data |
plotCustom |
Syntax plotcustom(v,@(x,y) drawCommand(x,y)) % |
plus |
poitwise addition |
polar |
cartesian to spherical coordinates Input v - @vector3d Output theta - polar angle rho - azimuthal angle r - radius |
project2FundamentalRegion |
projects vectors to the fundamental sector of the inverse pole figure |
quiver |
Syntax quiver(v,d) |
rdivide |
scalar division |
refine |
refine vectors |
region |
|
repmat |
overloads repmat |
reshape |
overloads reshape |
rotate |
rotate vector3d by quaternion |
scatter |
Syntax scatter(v) % scatter(v,data) % scatter(v,text) |
scatter3d |
plot spherical data |
size |
overloads size |
smooth |
Syntax |
subSet |
subindex vector3d |
subsasgn |
overloads subsasgn |
subsref |
overloads subsref |
sum |
sum of vectors |
surf |
Syntax |
symmetrise |
symmetrcially equivalent directions and its multiple |
text |
display a text in a spherical plot |
text3 |
plot three dimensional arrows |
times |
.* - componenwtise multiplication |
transpose |
transpose vector |
uminus |
overloads unitary minus |
unique |
disjoint list of vectors |
vector3d |
|
vertcat |
overloads [v1,v2,v3..] |
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Crystal Directions (The Class @Miller)
Miller |
(InferiorClasses = {?vector3d,?S2Grid}) |
cat |
concatenate lists of Miller indices to one list |
char |
Miller indece to string |
checkFundamentalRegion |
checks Miller indice to be within the fundamental region |
display |
standard output |
dot |
inner product between two Miller indece |
dot_outer |
inner product between two Miller indece |
dspacing |
space between crystal planes |
project2FundamentalRegion |
projects vectors to the fundamental sector of the inverse pole figure |
region |
return spherical region associated to a set of crystal directions |
rotate |
rotate crystal directions |
round |
tries to round miller indizes to greatest common divisor |
scatter |
plot Miller indece |
smooth |
plot Miller indece |
symmetrise |
directions symmetrically equivalent to m |
text |
plot Miller indece |
transformReferenceFrame |
change reference frame |
unique |
disjoint list of Miller indices |
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Discretisation of 1-Sphere (The Class @S1Grid)
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Discretisation of 2 - Sphere (The Class @S2Grid)
S2Grid |
Syntax S2Grid(theta,rho) % fills a Sphere with N--nodes regularS2Grid(...) % construct regular polar and azimuthal
spacing equispacedS2Grid(...) % construct equispaced nodes
|
cat |
|
copy |
copy certain condition from grid |
delete |
elilinates points from grid |
display |
standard output |
find |
return index of all points in a epsilon neighborhood of a vector |
getdata |
return index of all points in a epsilon neighborhood of a vector |
polar |
polar coordinates of S2Grid |
refine |
refine S2Grid |
subGrid |
subgrid |
subsasgn |
overloads subsasgn |
subsref |
overloads subsref |
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Quaternions (The Class @quaternion)
Euler |
quaternion to euler angle |
Rodrigues |
quaternion to rodrigues representation |
angle |
calcualtes the rotational angle between rotations q1 and q2 |
angle_outer |
calcualtes the rotational angle between all rotations q1 and q2 |
axis |
rotational axis of the quaternion |
calcVoronoi |
compute the the Voronoi decomposition for unit quaternions |
cat |
|
char |
quaternion to char |
cross |
pointwise cross product of three quaternions |
ctranspose |
transpose quaternion |
display |
standart output |
dot |
inner product of quaternions g1 and g2 |
dot_angle |
compute minimum q1 . q2 modulo rotation about zaxis and angle omega |
dot_outer |
outer inner product between two quaternions |
double |
quaternion to double |
end |
overloads end function |
eq |
? q1 == q2 |
export |
export quaternions to a ascii file |
find |
return indece and distance of all nodes within a eps neighborhood |
horzcat |
implements [q1,q2,q3..] |
inv |
quaternion of the inverse roation |
isempty |
overloads isempty |
length |
overloads length |
matrix |
quaternion to direction cosine matrix conversion converts direction cosine matrix to quaternion |
mean |
mean of a list of quaternions, principle axes and moments of inertia |
mean_CS |
fast mean of |
minus |
overloads minus |
mldivide |
|
mpower |
q^n |
mrdivide |
scalar division |
mtimes |
quaternionen multiplication q1 * q2 |
ndims |
overloads ndims |
ne |
q1 ~= q2 ? |
norm |
quaternion norm sqrt(a^2+b^2+c^2+c^2) |
normalize |
normalize quaternion |
permute |
overloads permute |
pertube |
pertube data randomly by epsilon |
perturbe |
pertube data randomly by epsilon |
plot |
|
plus |
pointwise addition |
power |
q.^n |
prod |
overloads q1 * q2 * q3 |
project2EulerFR |
projects quaternions to a fundamental region |
project2FundamentalRegion |
projects quaternions to a fundamental region |
qmatrix |
returns the quaternion multiplication matrix |
qq |
returns w * q' * q |
quaternion |
|
rdivide |
scalar division |
real |
real-part of of quaternion |
repmat |
overloads repmat |
reshape |
overloads reshape |
scatter |
plot function |
setSubSet |
indexing of quaternions |
size |
overloads size |
subSet |
indexing of quaternions |
subsasgn |
overloads subsasgn |
subsref |
overloads subsref |
sum |
overloads sum |
symmetrise |
symmetrcially equivalent orientations |
times |
implements quaternion .* quaternion and quaternion .* vector3d |
transpose |
transpose array of quaternions |
uminus |
overload unitary minus |
unique |
disjoint list of quaternions |
vertcat |
implements [q1;q2;q3..] |
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Rotations (The Class @rotation)
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Crystal and Specimen Symmetries (The Class @symmetry)
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Crystal Orientations (The Class @orientation)
BCV |
biased cross validation |
KLCV |
Kullback Leibler cross validation for optimal kernel estimation |
LSCV |
least squares cross valiadation |
angle |
calculates rotational angle between orientations |
axis |
rotational axis of the orientation or misorientation |
bingham_test |
bingham test for spherical/prolat/oblat case |
calcAngleDistribution |
calculate angle distribution |
calcBinghamODF |
calculate ODF from individuel orientations via kernel density estimation |
calcFourierODF |
calculate ODF from individuel orientations via kernel density estimation |
calcKernel |
compute an optimal kernel function for ODF estimation |
calcKernelODF |
calculate ODF from individuel orientations via kernel density estimation |
calcODF |
computes an ODF from individuel orientations |
calcTensor |
compute the average tensor for a vector of orientations |
checkFundamentalRegion |
checks whether a orientation sits within the fundamental region |
crossCorrelation |
computes the cross correlation for the kernel density estimator |
display |
standart output |
dot |
compute minimum dot(o1,o2) modulo symmetry |
dot_outer |
dot_outer |
fibreVolume |
ratio of orientations close to a certain fibre |
getFundamentalRegion |
projects orientations to a fundamental region |
inv |
inverse of an orientation |
isMisorientation |
check whether o is a misorientation |
ldivide |
o .\ v |
mean |
mean of a list of orientations, principle axes and moments of inertia |
mldivide |
o \ v |
mtimes |
orientation times Miller and orientation times orientation |
niceEuler |
orientation to euler angle |
orientation |
orientation - class representing orientations |
plot |
annotate a orientation to an existing plot |
plotAngleDistribution |
plot the angle distribution |
plotAxisDistribution |
plot uncorrelated axis distribution |
plotIPDF |
plot orientations into inverse pole figures |
plotODF |
Plot EBSD data at ODF sections |
plotPDF |
plot orientations into pole figures |
project2EulerFR |
projects orientation to a fundamental region |
project2FundamentalRegion |
projects orientation to a fundamental region |
project2ODFsection |
project orientation to ODF sections used by plotODF |
qqplot |
quantile-quantile of misorientation angle against random angular misorientation |
scatter |
plots ebsd data as scatter plot |
sphereVolume |
ratio of orientations with a certain orientation |
symmetrise |
all crystallographically equivalent orientations |
times |
vec = ori .* Miller |
transformReferenceFrame |
only applicable for crystal symmetry |
unique |
disjoint list of quaternions |
volume |
ratio of orientations with a certain orientation |
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Discretisation of Orientation Space (The Class SO3Grid)
SO3Grid |
Syntax S3G = SO3Grid(nodes,CS,SS) S3G = SO3Grid(points,CS,SS) S3G = SO3Grid(resolution,CS,SS) |
char |
convert to char |
copy |
copy nodes by indece |
delete |
clear nodes by indece Input SOG - @SO3Grid indece - int32 |
display |
standard output |
dot_outer |
return outer inner product of all nodes within a eps neighborhood |
find |
return indece and distance of all nodes within a eps neighborhood |
mtimes |
outer quaternion multiplication |
spy |
spy distance matrix |
subGrid |
sub-SO3Grid as epsilon neigborhood of a node |
subsasgn |
overloads subsasgn |
subsref |
overloads subsref |
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Classes for Quantitative Texture Analysis
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Orientation Density Functions (The Class @ODF)
MDFAnalysis |
Misorientation Distribution Function Explains how to compute and analyze misorientation distribution functions. |
ModelODFs |
Model ODFs Describes how to define model ODFs in MTEX, i.e., uniform ODFs, unimodal ODFs, fibre ODFs, Bingham ODFs and ODFs
defined by its Fourier coefficients.
|
ODFAnalysis |
ODF Analysis Explains how to import and export ODFs, how to define model ODFs and how to analyze ODFs, e.g., with respect
to modalorientations, textureindex, volumeportions. Pole figure simulation and single orientation simulation is explained
as well.
|
ODFCalculations |
First Steps Indroduction to analysis of ODFs |
ODFCharacteristics |
Characterizing ODFs Explains how to analyze ODFs, i.e. how to compute modal orientations, texture index, volume portions,
Fourier coefficients and pole figures.
|
ODFImportExport |
Importing and Exporting ODF Data Explains how to read and write ODFs to a data file |
ODFPlot |
Visualizing ODFs Explains all possibilities to visualize ODfs, i.e. pole figure plots, inverse pole figure plots, ODF sections,
fibre sections.
|
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Standard ODFs
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ODF Shapes (The class @kernel)
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Pole Figure Data (The Class @PoleFigure)
ImportPoleFigureData |
Importing Pole Figure Data How to import Pole Figure Data |
ModifyPoleFigureData |
Modify Pole Figure Data Explains how to manipulate pole figure data in MTEX. |
PlotPoleFigures |
Plotting of Pole Figures Described various possibilities to visualize pole figure data. |
PoleFigure2odf |
ODF Estimation from Pole Figure Data This page describes how to use MTEX to estimate an ODF from pole figure data. |
PoleFigureAnalysis |
Pole Figure Analysis Explains how to import pole figure data, how to correct them, and how to recover an ODF. |
PoleFigureAnalysisIntro |
First Steps Get in touch with PoleFigure Data in MTEX. |
PoleFigureSimulation_demo |
Simulating Pole Figure data Simulate arbitary pole figure data |
ghost_demo |
Ghost Effect Analysis Explains the ghost effect to ODF reconstruction and the MTEX option ghostcorrection. |
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Electron Backscatter Diffraction Data (The Class @EBSD)
AliginingEBSDData |
Aligning EBSD data to a reference frame How to align EBSD correctly to certain reference frames |
AnalyzeEBSDData |
Analyze EBSD Data |
EBSD2odf |
ODF Estimation from EBSD data How to estimate an ODF from single orientation measurements. |
EBSDAnalysis |
EBSD Data Analysis Data Import of Electron Backscatter Diffraction Data, Correct Data, Estimate Orientation Density Functions
out of EBSD Data, Model Grains and Misorientation Density Functions
|
EBSDAnalysisIntro |
First Steps Get in touch with EBSD Data in MTEX |
EBSDBingham |
Bingham distribution and EBSD data testing rotational symmetry of individual orientations |
EBSDModifyData |
Modify EBSD Data How to correct EBSD data for measurement errors. |
EBSDOrientationPlots |
Plotting Individual Orientations Basics to the plot types for individual orientations data |
EBSDSharpPlot |
Visualizing EBSD data with sharp textures Using spezialized orientation mappings is particularly usefull when visualizing
sharp data. Let us consider the following data set which restrict to the calcite phase
|
EBSDSimulation_demo |
Simulating EBSD data How to simulate an arbitrary number of individual orientations data from any ODF. |
EBSDSpatialPlots |
Plotting spatially indexed EBSD data How to visualize EBSD data |
ImportEBSDData |
Importing EBSD Data How to import EBSD Data |
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Material Tensors (The Class @tensor)
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Auxiliary Functions
Plotting Tools
| Below you find a list of tools to work with data given in the Dubna format |
Geometry Tools
| This section of geometry tools especialy contains methods to convert
directions and rotations from one paramterization into another.
Additionlly some basic geometrical objects are predefined.
|
Statistics
| Below you find a list of statistical tools included in the MTEX toolbox. |
Plotting
| Below you find a list of plotting tools inlcuded in the MTEX toolbox. Of
special importance is the command [[savefigure.html,savefigure]] which
allows to save plots in any kinds of image files.
|
docopt |
DOCOPT Web browser for UNIX platforms. DOCOPT is an M-file that you or your system manager can edit to specify the Web browser
to use with MATLAB. It is used for the WEB function with the -BROWSER option. It is also used for links to external Web sites
from the the Help browser and from Web menu items. DOCOPT applies only to non-Macintosh UNIX platforms.
|
dynOption |
class to add dynamic options to a static class Detailed explanation goes here |
dynProp |
class to add dynamic properties to a static class Detailed explanation goes here |
mtexdata |
load of data provided with mtex and often used in documentation |
mtexdegchar |
returns the degree character |
zip_mtex |
zip mtex for publishing (on website) |
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Plotting Tools
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Geometry Tools
CSL |
coincidence site lattice misorientations for cubic symmetry |
EulerAngleConvention |
|
Miller2quat |
calculate quaternion from Miller indece |
axis2quat |
rotational axis, roational angle to Quaternion |
axis2quat_outer |
rotational axis, roational angle to Quaternion |
brassOrientation |
returns the cube orientation |
checkEulerAngleConvention |
|
cubeOrientation |
returns the cube orientation |
equispacedS2Grid |
defines an equispaced spherical grid |
equispacedSO3Grid |
defines a equispaced grid in the orientation space |
euler2quat |
converts euler angle to quaternion |
fibre2quat |
arbitrary quaternion q with q * h = r |
gossOrientation |
returns the cube orientation |
guessfibre |
try to find the fibre of to given rotations by finding the eigenvector of g_1*h = g_2*h -> (g_2^-1)*g_1* h = h -> R*h = (lambda)*h |
hr2quat |
arbitrary quaternion q with q * h = r |
idRotation |
the identical rotation |
idquaternion |
the identical rotation - quaternion(1,0,0,0) |
inversion |
the inversion - reflection at the origin |
loadCIF |
import crystal symmetry from cif file |
loadPHL |
|
localOrientationGrid |
define a equispaced grid localized to a center orientation |
mat2quat |
converts direction cosine matrix to quaternion |
plotS2Grid |
create a regular S2Grid for plotting |
plotSO3Grid |
give a regular grid in orientation space |
randq |
returns random quaternions |
randv |
|
reflection |
defines a reflection at plane with normal n |
regularS2Grid |
Syntax regularS2Grid('points',[72 19]) regularS2Grid('resolution',[5*degree 2.5*degree]) regularS2Grid('theta',theta,'rho',rho) |
regularSO3Grid |
give a regular grid in orientation space |
rodrigues2quat |
|
vec42quat |
returns a quaternion q with q u_1 = v1 and q u2 = v2 |
xvector |
vector (1,0,0) |
yvector |
vector (0,1,0) |
zvector |
vector (0,0,1) |
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Statistics
c_hat |
return the second moments for bingham test |
discretesample |
Samples from a discrete distribution |
quantile |
n percent quantile of x |
randp |
randp(lambda) returns Poisson distributed Vector with mean lambda |
range |
RANGE Sample range. Y = RANGE(X) returns the range of the values in X. For a vector input, Y is the difference between the
maximum and minimum values. For a matrix input, Y is a vector containing the range for each column. For N-D arrays, RANGE
operates along the first non-singleton dimension.
|
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Plotting
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