Function Reference
Classes representing Geometry
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Specimen Directions (The Class @vector3d)
SchmidTensor |
computes the Schmidt tensor |
abs |
length of vector |
angle |
angle between two vectors |
angle_outer |
angle between two vectors Input v1, v2 - @vector3d |
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 Input v - @vector3d Output x, y, z - double |
end |
overloaded end function |
eq |
? v1 == v2 |
export |
export quaternions to a ascii file |
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 |
orthProj |
|
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) % plot the directions v scatter(v,data) % colorize directions according to data scatter(v,'label',text)
% plot text below markers scatter(v,'label',text,'textaboveMarker') % plot text above markers
|
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..] |
Back to Top of Section
Crystal Directions (The Class @Miller)
Miller |
(InferiorClasses = {?vector3d,?S2Grid}) |
cat |
concatenate lists of Miller indices to one list |
char |
Miller indece to string |
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 |
surf |
Syntax |
symmetrise |
directions symmetrically equivalent to m |
text |
plot Miller indece |
transformReferenceFrame |
change reference frame while keeping hkl or uvw |
unique |
disjoint list of Miller indices |
Back to Top of Section
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 |
log |
project a quaternion into the tangential space |
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..] |
Back to Top of Section
Rotations (The Class @rotation)
Back to Top of Section
Crystal and Specimen Symmetries (The Class @symmetry)
Laue |
return the corresponding Laue group |
LaueName |
get Laue name |
alignment |
return alignment of the reference frame as string, e.g. x||a, y||b* |
calcAngleDistribution |
compute the angle distribution of a uniform ODF for a crystal symmetry |
calcAxisDistribution |
compute the axis distribution of an uniform ODF or MDF |
calcQuat |
calculate quaternions for Laue groups |
check |
check symmetry |
disjoint |
returns the disjoint of two symmetry groups |
ensureCS |
ensures that an obj has the right crystal symmetry |
eq |
check S1 == S2 |
factor |
factorizes s1 and s2 into l, d, r such that s1 = l * d and s2 = d * r |
fundamentalRegion |
get the fundamental sector for a symmetry in the inverse pole figure |
fundamentalRegionEuler |
get the fundamental region in Euler angles |
fundamentalSector |
get the fundamental sector for a symmetry in the inverse pole figure |
length |
number of symmetry elements |
maxAngle |
get the maximum angle of the fundamental region |
multiplicityPerpZ |
maximum angle rho |
multiplicityZ |
maximum angle rho |
nfold |
maximal n-fold of symmetry axes |
plot |
visualize symmetry elements according to international table |
properGroup |
return the corresponding Laue group |
properSubGroup |
return the corresponding Laue group |
rotation_special |
returns symmetry elements different from rotation about c-axis |
subsref |
overloads subsref |
symmetry |
Supported Symmetries |
union |
returns the union of two symmetry groups |
Back to Top of Section
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 an misorientation or two orientations |
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 |
calcMDF |
computes an MDF from individuel orientations or misorientations |
calcMIndex |
TODO!!! |
calcODF |
computes an ODF from individuel orientations |
calcTensor |
compute the average tensor for a vector of orientations |
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 |
export_VPSC |
export individual orientations to the VPSC format |
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 |
log |
Syntax v = log(ori) v = log(ori,ori_ref) |
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 |
plotIPDF |
plot orientations into inverse pole figures |
plotPDF |
plot orientations into pole figures |
plotSection |
plot orientations to ODF sections |
project2EulerFR |
projects orientation to a fundamental region |
project2FundamentalRegion |
projects orientation to a fundamental region |
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 |
Back to Top of Section
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)
FourierODF |
compute FourierODF from another ODF |
ODF |
|
bandwidth |
bandwidth of the ODF |
calcAngleDistribution |
compute the angle distribution of an ODF or an MDF |
calcAxisDistribution |
compute the axis distribution of an ODF or MDF |
calcAxisVolume |
compute the axis distribution of an ODF or MDF |
calcError |
calculate approximation error between two ODFs |
calcFourier |
compute Fourier coefficients of odf |
calcMDF |
calculate the uncorrelated misorientation distribution function (MDF) from one or two ODF |
calcMIndex |
M-index of Skemer et al.(2005) based on the difference between uncorrelated and uniform misorientation angle distributions |
calcModes |
heuristic to find modal orientations |
calcOrientations |
draw random orientations from ODF |
calcPDF |
calculate pdf |
calcPoleFigure |
simulate pole figures from an ODF |
calcTensor |
compute the average tensor for an ODF |
calcpdf_special3 |
compute the pdf for h = (theta,rhoh), r = (theta,rhor) |
centerSpecimen |
rotatates an odf with specimen symmetry into its symmetry axes |
concentration |
not yet implemeted |
conv |
convolute ODF with kernel psi |
discreteSample |
draw a random sample |
display |
standard output |
entropy |
caclulate entropy of ODF |
eval |
evaluate an odf at orientation g |
export |
export an ODF to an ASCII file |
export_VPSC |
export an ODF to the VPSC format |
export_generic |
export an ODF to an ASCII file |
export_mtex |
export an ODF into the MTEX format |
fibreVolume |
ratio of orientations with a certain orientation |
hist |
calcualtes a histogram of ODF |
isFourier |
check whether odf is given by Fourier coefficients |
max |
heuristic to find local modal orientations |
maxpdf |
returns the maximum orientation in a polefigure |
mean |
returns mean, kappas |
minus |
superposeing two ODFs |
mrdivide |
scaling of the ODF |
mtimes |
scaling of the ODF |
neuralgas |
attempt to distribute measure-sites equally according to invers polefigure density (experimental) |
norm |
caclulate texture index of ODF |
plot |
plots odf |
plot3d |
plots odf |
plotDiff |
difference plot between two odfs or an odf and a pole figure |
plotFibre |
plot odf along a fibre |
plotFourier |
plots Fourier coefficients of the odf |
plotIPDF |
plot inverse pole figures |
plotPDF |
plot pole figures |
plotSection |
plot ODF sections |
plus |
superposeing two ODFs |
quantile |
quantile orientations of an ODF |
rdivide |
scaling of the ODF |
rotate |
rotate ODF |
slope |
| grad(r) | |
smooth |
smooth ODF |
textureindex |
caclulate texture index of ODF |
times |
scaling of the ODF |
uminus |
superposeing two ODFs |
volume |
ratio of orientations with a certain orientation |
Back to Top of Section
Standard ODFs
Back to Top of Section
ODF Shapes (The class @kernel)
Back to Top of Section
Pole Figure Data (The Class @PoleFigure)
PoleFigure |
|
calcError |
RP and mean square error |
calcErrorPF |
error polefigure between meassured and recalculated pole figures |
calcFEMODF |
PDF to ODF inversion |
calcNormalization |
normalization of a meassured pole figure with respect to a second pole figure |
calcODF |
PDF to ODF inversion |
calcPoleFigure |
simulate pole figure |
cat |
|
char |
standard output |
correct |
corrects polfigures for background and defocussing |
display |
standard output |
export |
export pole figure in an ASCII file |
findOutlier |
find outliers in pole figures |
isOutlier |
find outliers in pole figures |
isempty |
overloads length |
max |
maximum of two pole figures or the maximum of a single polefigure |
mean |
mean of pole figure intensities |
min |
minimum of two pole figures or the minimum of a single polefigure |
minus |
implements pf1 - pf2 |
mrdivide |
implements pf1 ./ b and a ./ pf2 |
mtimes |
scaling of PoleFigures, implements pf1 * b and a * pf2 |
noisepf |
simulate diffraction counts |
normalize |
normalization of a meassured pole figure with respect to an ODF |
plot |
plot pole figure |
plotDiff |
difference plot between two pole figures or an odf and a pole figure |
plot_zero_range |
implements the zero range method |
plus |
implements pf1 + pf2 |
rdivide |
implements pf1 ./ b and a ./ pf2 |
rotate |
rotates pole figures by a certain rotation |
scale |
scale polefigure by a factor |
select |
select PoleFigures |
subsasgn |
overloads subsasgn |
subsref |
|
times |
implements pf1 .* b and a .* pf2 |
uminus |
implements -pf |
union |
crytsallographic direction to one |
unique |
remove dublicated points in a polefigure |
zeroRange |
implements the zero range method |
Back to Top of Section
Electron Backscatter Diffraction Data (The Class @EBSD)
EBSD |
constructor |
KAM |
intragranular average misorientation angle per orientation |
affinetrans |
perform an affine transformation on spatial ebsd data |
calcGrains |
2d and 3d construction of GrainSets from spatially indexed EBSD data |
calcMisorientation |
calculate uncorrelated misorientations between two ebsd phases |
calcTensor |
compute the average tensor for an EBSD data set |
cat |
overloads [ebsd1,ebsd2,ebsd3..] |
char |
ebsd -> char |
display |
standard output |
export |
export EBSD data to a ascii file |
export_h5 |
export EBSD data to a ascii file |
extend |
returns the boundings of spatial EBSD data |
fill |
extrapolate spatial EBSD data by nearest neighbour for tetragonal lattice |
fillByGrainId |
extrapolate spatial EBSD data by nearest neighbour for tetragonal lattice |
findByLocation |
select EBSD data by spatial coordinates |
findByOrientation |
select grains by orientation |
fliplr |
flip spatial ebsd-data from left to right |
flipud |
flip spatial ebsd-data from upside down |
gridify |
extend EBSD data to an grid |
inpolygon |
checks which ebsd data are within given polygon |
mtimes |
rotating the ebsd data by a certain rotation |
plot |
spatial EBSD plot |
quiver |
plot directions at ebsd centers |
reduce |
reduce ebsd data by a factor |
rotate |
rotate EBSD orientations or spatial data around point of origin |
shift |
shift spatial ebsd-data about (x,y) |
smooth |
smooth spatial EBSD |
spatialProfile |
select EBSD data along line segments |
subSet |
indexing of EBSD data |
subsasgn |
overloads subsasgn |
subsind |
subindexing of EBSD data |
subsref |
indexing of EBSD data |
Back to Top of Section
Material Tensors (The Class @tensor)
Back to Top of Section
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.
|
fft_rho |
project rho to interval [-1,1) |
fft_theta |
project theta to interval [0,0.5] |
ar2rgb |
compute rgb values from angle and radius |
contour3s |
contour-slices |
convertFigureRGB2ind |
default resolution |
getCamera |
get xAxis and zAxis position from axis |
getHoldState |
|
hsl2hsv |
|
isRGB |
|
mtexColorbar |
overide buildin Matlab colorbar function |
nextstyle |
NEXTSTYLE Get next plot linespec [L,C,M] = NEXTSTYLE(AX) gets the next line style, color and marker for plotting from the
ColorOrder and LineStyleOrder of axes AX.
|
optiondraw |
apply options to handle |
optionplot |
plot y against x using the options in varargin |
scaleBar |
Inserts a scale bar on the current ebsd or grain map. |
sectionLabels |
|
setCamera |
set Camera according to xAxis and zAxis position |
switchUnit |
returns the closest length to a known unit. For example, 10e3m will give 10km. |
xticklabel_rotate |
hText = xticklabel_rotate(XTick,rot,XTickLabel,varargin) Rotate XTickLabel |
assert_grid |
check for valid grid parameters |
calcUnitCell |
compute the unit cell for an EBSD data set |
check_interfaces |
determine interface from file |
loadHelper |
helps to load data-matrix with ColumnNames restricts also data according to conventions (e.g. >4pi) |
string2Miller |
converts string to Miller indece |
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) |
Back to Top
Plotting Tools
Back to Top of Section
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 |
expquat |
matrix exponential to convert skew symmetric matrices into quaternions |
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 |
nanquaternion |
the identical rotation - quaternion(1,0,0,0) |
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) |
Back to Top of Section
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.
|
Back to Top of Section
Plotting
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