# Function Reference

 Classes representing Geometry Classes for Quantitative Texture Analysis Auxiliary Functions Helper functions making life easier Below you can find a series of powerful all purpose tools provided by the MTEX toolbox.

## Classes representing Geometry

 Specimen Directions (The Class @vector3d) This section describes the class *vector3d* and gives an overview how to deal with specimen directions in MTEX. Crystal Directions (The Class @Miller) This section describes the class *Miller* and gives an overview how to deal with crystal directions in MTEX. specimenSymmetry defines a specimen symmetry Rotations (The Class @rotation) This section describes the class and gives an overview on how to work with rotations in MTEX. Crystal and Specimen Symmetries (The Class @symmetry) This section describes the class *symmetry* and gives an overview how to deal with crystal symmetries in MTEX. Crystal Orientations (The Class @orientation) This sections describes the class *orientation* and gives an overview how to work with crystal orientation in MTEX. Fibres This sections describes the class and gives an overview how to work with fibres in MTEX. Quaternions (The Class @quaternion) class representing orientations Discretisation of 1-Sphere (The Class @S1Grid) S1Grid is a class of purely internal use Discretisation of 2 - Sphere (The Class @S2Grid) represents a grid of nodes on the sphere Discretisation of Orientation Space (The Class SO3Grid) represents a set of orientations
fundamentalRegion get the fundamental zone in orientation space for a symmetry
plotAngleDistribution plot axis distribution
plotAxisDistribution plot axis distribution
strainTensor
stressTensor

## 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
eq ? v1 == v2
export export quaternions to a ascii file
find return index of all points in a epsilon neighborhood of a vector
interp dirty spherical interpolation - including some smoothing
isPerp check whether v1 and v2 are orthogonal
kernelDensityEstimation calculates a density function out of (weighted) unit vectors
line Syntax
mean computes the mean vector
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)) %
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
rotate rotate vector3d by rotation or orientation
rotate_outer 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
smooth Syntax
sparse
subSet subindex vector3d
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
unique disjoint list of vectors
vector3d

## Crystal Directions (The Class @Miller)

Miller define a crystal direction by Miller indice
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
rotate_outer 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

## Rotations (The Class @rotation)

cat
char quaternion to char
display standart output
dot compute rot1 . rot2
dot_outer dot_outer
getMinAxes
isImproper
line draw rotations connected by lines
matrix quaternion to direction cosine matrix conversion converts direction cosine matrix to quaternion
mldivide o \ v
mtimes r = a * b
power r.^n
project2FundamentalRegion projects rotation to a fundamental region
rotation defines an rotation
subSet indexing of rotation
times r = a .* b
transpose transpose array of rotations
uminus implements -rotation
unique disjoint list of rotations

## 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 fundamental region in orientation space for a (pair) of symmetries
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
symmetry Supported Symmetries
union returns the union of two symmetry groups

## Crystal Orientations (The Class @orientation)

BCV biased cross validation
KLCV Kullback Leibler cross validation for optimal kernel estimation
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
calcCluster sort orientations into clusters
calcFourierODF calculate ODF from individuel orientations via kernel density estimation
calcInvTaylor Taylor factor from orientation gradient
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
ctranspose inverse orientation
display standart output
doHClustering sort orientations into clusters
dot compute minimum dot(o1,o2) modulo symmetry
dot_outer dot_outer
exp exponential function
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
isMisorientation check whether o is a misorientation
ldivide o .\ v
log the inverse of the exponential map
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
parents variants of an orientation relationship
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
power ori.^n
project2EulerFR projects orientation to a fundamental region
project2FundamentalRegion projects orientation to a fundamental region
qqplot quantile-quantile of misorientation angle against random angular misorientation
round2Miller find lattice alignements for arbitrary misorientations
scatter plots orientations in 3d
sphereVolume ratio of orientations with a certain orientation
symmetrise all crystallographically equivalent orientations
times vec = ori .* Miller
transformReferenceFrame change reference frame of an orientation
unique disjoint list of quaternions
variants variants of an orientation relationship
volume ratio of orientations with a certain orientation

## Fibres

angle angle fibre to orientation or fibre to fibre
cat
display standard output
eq ? sS1 == sS2
fibre fibre is a class representing a fibre in orientation space. Examples are alpha, beta or gamma fibres. In general a fibre is defined by a crystal direction h of type <Miller_index.html Miller> and a specimen direction of type <vector3d_index.html vector3d>.
ne ? sS1 ~= sS2
orientation generate a list of orientation out of a fibre
plot
plotIPDF plot orientations into inverse pole figures
plotPDF plot a fibre into pole figures
subSet subindex vector3d
symmetrise all crystallographically equivalent fibres
transpose transpose list of slipSystem

## 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
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
isnan check for nan values
log project a quaternion into the tangential space
logm the dislocation tensor for a rotation
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
mldivide
mpower q^n
mrdivide scalar division
mtimes quaternionen multiplication q1 * q2
ne q1 ~= q2 ?
norm quaternion norm sqrt(a^2+b^2+c^2+c^2)
normalize normalize quaternion
perturbe pertube data randomly by epsilon
plot
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
scatter plot function
setSubSet indexing of quaternions
subSet indexing of quaternions
symmetrise symmetrcially equivalent orientations
times quaternion .* quaternion and quaternion .* vector3d
transpose transpose array of quaternions
unique disjoint list of quaternions
vertcat implements [q1;q2;q3..]

## Discretisation of 1-Sphere (The Class @S1Grid)

GridLength return number of points
S1Grid
coarser makes S1Grid more coarse
delete delte points from S1Grid
display standart output
dist distance to all points of S1Grid
dist_outer distance to all points of S1Grid
double convert to double
eq implements G1 == G2
find find close points
max return maximum value
min return maximum value
minus
plot plot grid
plus
refine refine S1Grid
shift shifts S1Grid by delta
subGrid epsilon - neighborhood of a point in the grid

## 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

## 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

## Classes for Quantitative Texture Analysis

 Orientation Density Functions (The Class @ODF) This sections describes the class *ODF* and gives an overview how to work with orientation density functions in MTEX. Standard ODFs predefined ODFs ODF Shapes (The class @kernel) standard distributions on SO(3) Pole Figure Data (The Class @PoleFigure) This section describes the class *PoleFigure* and gives an overview of the functionality MTEX offers to analyze pole figure data. Electron Backscatter Diffraction Data (The Class @EBSD) This section describes the class *EBSD* and gives an overview over the functionality that MTEX offers to analyze EBSD data. Material Tensors (The Class @tensor)

## 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 amount of orientations with a specific misorientation axis
calcComponents heuristic to find modal orientations
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
char odf -> char
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 expected value of an ODF
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
smooth smooth ODF
steepestDescent find maximum with steepest descent
steepestDescentX find maximum with steepest descent
textureindex caclulate texture index of ODF
times scaling of the ODF
uminus superposeing two ODFs
volume ratio of orientations with a certain orientation

## Standard ODFs

BinghamODF defines a Bingham distributed ODF
FourierODF defines an ODF by its Fourier coefficients
SantaFe the SantaFe-sample ODF
femODF defines an ODF by finite elements
fibreODF defines an fibre symmetric ODF
mix2 mix2 sample ODF
uniformODF get crystal and specimen symmetry
unimodalODF define a unimodal ODF

## ODF Shapes (The class @kernel)

K_symmetrised evaluate kernel modulo symmetries
kernel
plot plot the kernel function
plotFourier plot the Chybeyshev coefficients of the kernel function
volume

## 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
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
subsref overide polefigure() and polefigure{}
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

## 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 grains reconstruction from 2d EBSD data
calcMisorientation calculate uncorrelated misorientations between two ebsd phases
calcTensor compute the average tensor for an EBSD data set
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 ebsd data 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
id2ind find ind such that ebsd.id(ind) == id
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
subsind subindexing of EBSD data
subsref indexing of EBSD data
updateUnitCell this function should be called after the spatial coordinates of an EBSD data set have been modified

## Material Tensors (The Class @tensor)

ChristoffelTensor Christoffel tensor of an elasticity tensor for a given direction
EinsteinSum tensor multiplication according to Einstein summation
Fourier compute the Fourier coefficients of the tensor
PoissonRatio computes the Poisson ratio of an elasticity tensor
Voigt
YoungsModulus Young's modulus for an elasticity tensor
antiSym the antisymmetric part A = 0.5(T - T.') of a tensor
calcShearStress shear stress
calcTaylor compute Taylor factor and strain dependent orientation gradient
char tensor to char
checkSymmetry
conj conjugate of a tensor
ctranspose conjugate of a tensor
diag convert rank 1 or rank 0 tensor into diagonal rank 2 tensor
directionalMagnitude magnitude of a tensor in direction v
display standard output
double convert tensor values to matrix
eig compute the eigenvalues and eigenvectors of a tensor
eq checks whether two tensors are equal
expm matrix exponential of a tensor
inv inverse of a tensor
length returns the number of tensors
linearCompressibility computes the linear compressibility of an elasticity tensor
logm matrix logarithm of a tensor
matrix return tensor as a matrix
max
min
mrdivide implements T / S
mtimes implements T1 * T2
ne checks whether two tensors are not equal
numel returns the number of tensors
plot plot a tensor T
plotS2Grid define a plotting grid suitable for tensor plots
quiverGrid
rdivide
real
rotate rotate a tensor by a list of rotations
rotate_outer rotate a tensor by a list of rotations
shearModulus shear modulus for an elasticity tensor
sum sum over all tensors allong dimension 1
sym the symmetric part S = 0.5(T + T.') of a tensor
symmetrise symmetrise a tensor according to its crystal symmetry
tensor
times multiply a tensor by a scalar
trace compute the trace of a rank 2 tensor
transform transform a tensor to a given crystal frame
transformReferenceFrame set properties of a tensor variable
transpose transpose a list of a tensors
velocity computes the elastic wave velocity(km/s) from the elastic stiffness Cijkl tensor and density (g/cm3)
volumeCompressibility computes the volume compressibility of an elasticity tensor

## 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 especially contains methods to convert directions and rotations from one parametrization into another. Additionally, 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 included in the MTEX toolbox. Of special importance is the command [[savefigure.html,savefigure]] which allows saving plots in any kinds of image files.
fft_rho project rho to interval [-1,1)
fft_theta project theta to interval [0,0.5]
annotate annotate to a existing figure
ar2rgb compute rgb values from angle and radius
contour3s contour-slices
convertFigureRGB2ind default resolution
gcm
getCamera get xAxis and zAxis position from axis
getHoldState
hsl2hsv
isRGB
mtexColorMap define an MTEX colormap
mtexColorbar overide buildin Matlab colorbar function
newMapPlot
newMtexFigure
newODFSectionPlot generate a new ODF section plot
newSphericalPlot split plot in upper and lower hemisphere
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
plotEllipse plot multiple ellipses
plota2east set the default plot direction of the x-axis
plota2north set the default plot direction of the x-axis
plota2south set the default plot direction of the x-axis
plota2west set the default plot direction of the x-axis
plotb2east set the default plot direction of the x-axis
plotb2north set the default plot direction of the x-axis
plotb2south set the default plot direction of the x-axis
plotb2west set the default plot direction of the x-axis
plotx2east set the default plot direction of the x-axis
plotx2north set the default plot direction of the x-axis
plotx2south set the default plot direction of the x-axis
plotx2west set the default plot direction of the x-axis
plotzIntoPlane set the default plot direction of the z-axis
plotzOutOfPlane set the default plot direction of the z-axis
saveFigure save figure as graphics file
sectionLabels
selectPolygon select a polygon by mouse
setCamera set Camera according to xAxis and zAxis position
setColorRange set color range for figures
switchUnit returns the closest length to a known unit. For example, 10e3m will give 10km.
xticklabel_rotate 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)

## 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
fit_ellipse fit_ellipse - finds the best fit to an ellipse for the given set of points.
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
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 regular grid in Euler 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)

## 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.