ebsd_Orientation.Orientation Class Reference

Detailed Description

Orientation combination of material symmetry and specific rotation.

Public Member Functions
def	__copy__ (self)
def	__init__ (self, quaternion=Quaternion.fromIdentity(), Rodrigues=None, angleAxis=None, matrix=None, Eulers=None, random=False, symmetry=None)
def	__repr__ (self)
def	asAngleAxis (self, degrees=False)
def	asEulers (self, notation='bunge', degrees=False, standardRange=False)
def	asMatrix (self)
def	asQuaternion (self)
def	asRodrigues (self)
def	equivalentOrientations (self, who=[])
def	equivalentQuaternions (self, who=[])
def	inFZ (self)
	Check whether given Rodrigues vector falls into fundamental zone of own symmetry. More...
def	reduced (self)
	Transform orientation to fall into fundamental zone according to symmetry. More...
MATERIAL SPECIFIC ROUTINES
Disorientation between myself and given other orientation. Rotation axis falls into SST if SST == True. (Currently requires same symmetry for both orientations. Look into A. Heinz and P. Neumann 1991 for cases with differing sym.) Parameters other other orientation SST True (rotation axis falls into SST); False Returns disorientation quaternion, idx of equivalent orientation1, idx of equivalent orientation2, num. of conjugated
def	disorientation (self, other, SST=True)
def	inversePole (self, axis, proper=False, SST=True)
	axis rotated according to orientation (using crystal symmetry to ensure location falls into SST) More...
def	IPFcolor (self, axis, proper=False)
	color of inverse pole figure for given axis More...
def	average (cls, orientations, multiplicity=[])
	Return the average orientation. More...
PLOTTING, PRINTING
down y, -x up -y, x right x,y left -x,-y 3D x,y,z
def	project (self, x, y, z)
def	plotLine (self, ax, start, delta, color='k', lw=1, ls='solid', markerSize=None)
	Plot one line using given projection. More...
def	plotUnit (self, ax, xlabel, ylabel, zlabel, x=0, y=0, z=0, s=1)
	Coordinate see plotLine. More...
def	plot (self, poles=None, unitCell=True, cos=True, annotate=False, plot2D=None, scale=2, fileName=None)
	Plot rotated unit-cell in 3D, and possibly the pole-figure and specific poles. More...
def	toScreen (self, equivalent=True)
	print Euler angles and HKL /UVW More...
MISC
Related Models KS from S. Morito et al./Journal of Alloys and Compounds 5775 (2013) S587-S592 DOES THIS PAPER EXISTS? GT from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81 GT' from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81 NW from H. Kitahara et al./Materials Characterization 54 (2005) 378-386 Pitsch from Y. He et al./Acta Materialia 53 (2005) 1179-1190 Bain from Y. He et al./Journal of Applied Crystallography (2006). 39, 72-81 Parameters relationModel – direction – targetSymmetry – Returns vector
def	related (self, relationModel, direction, targetSymmetry=None)

Properties
	angleAxis = property(asAngleAxis)
	eulers = property(asEulers)
	infz = property(inFZ)
	matrix = property(asMatrix)
	rodrigues = property(asRodrigues)

Constructor & Destructor Documentation

__init__()

def ebsd_Orientation.Orientation.__init__	(		self,
			quaternion = Quaternion.fromIdentity(),
			Rodrigues = None,
			angleAxis = None,
			matrix = None,
			Eulers = None,
			random = False,
			symmetry = None
	)

Member Function Documentation

__copy__()

def ebsd_Orientation.Orientation.__copy__

(

self

)

__repr__()

def ebsd_Orientation.Orientation.__repr__

(

self

)

asAngleAxis()

def ebsd_Orientation.Orientation.asAngleAxis	(		self,
			degrees = False
	)

asEulers()

def ebsd_Orientation.Orientation.asEulers	(		self,
			notation = 'bunge',
			degrees = False,
			standardRange = False
	)

asMatrix()

def ebsd_Orientation.Orientation.asMatrix

(

self

)

asQuaternion()

def ebsd_Orientation.Orientation.asQuaternion

(

self

)

asRodrigues()

def ebsd_Orientation.Orientation.asRodrigues

(

self

)

average()

def ebsd_Orientation.Orientation.average	(		cls,
			orientations,
			multiplicity = []
	)

Return the average orientation.

ref F. Landis Markley, Yang Cheng, John Lucas Crassidis, and Yaakov Oshman, Averaging Quaternions, Journal of Guidance, Control, and Dynamics, Vol. 30, No. 4 (2007), pp. 1193-1197. doi 10.2514/1.28949

Usage

• a = Orientation(Eulers=np.radians([10, 10, 0]), symmetry='hexagonal')
• b = Orientation(Eulers=np.radians([20, 0, 0]), symmetry='hexagonal')
• avg = Orientation.average([a,b])

Parameters

cls	class method (void)
orientations	list of orientations
multiplicity	–

Returns

average orientation (not rotation) in radians

disorientation()

def ebsd_Orientation.Orientation.disorientation	(		self,
			other,
			SST = True
	)

equivalentOrientations()

def ebsd_Orientation.Orientation.equivalentOrientations	(		self,
			who = []
	)

equivalentQuaternions()

def ebsd_Orientation.Orientation.equivalentQuaternions	(		self,
			who = []
	)

inFZ()

def ebsd_Orientation.Orientation.inFZ

(

self

)

Check whether given Rodrigues vector falls into fundamental zone of own symmetry.

inversePole()

def ebsd_Orientation.Orientation.inversePole	(		self,
			axis,
			proper = False,
			SST = True
	)

axis rotated according to orientation (using crystal symmetry to ensure location falls into SST)

Parameters

axis	vector in crystal orientation, e.g. [100]
proper	considers only vectors with z >= 0, hence uses two neighboring SSTs to determine if in SST. i.e. allows more positive results, rgb-value does not depend on this
SST	iterate through all equivalent and find the one in the SST

Returns

vector of axis

IPFcolor()

def ebsd_Orientation.Orientation.IPFcolor	(		self,
			axis,
			proper = False
	)

color of inverse pole figure for given axis

Parameters

axis	axis of pole figure (ND=001)
proper	considers only vectors with z >= 0, hence uses two neighboring SSTs to determine if in SST. i.e. allows more positive results, rgb-value does not depend on this

Returns

vector of color (rgb)

plot()

def ebsd_Orientation.Orientation.plot	(		self,
			poles = None,
			unitCell = True,
			cos = True,
			annotate = False,
			plot2D = None,
			scale = 2,
			fileName = None
	)

Plot rotated unit-cell in 3D, and possibly the pole-figure and specific poles.

Projection onto 2D: cooradinate systems are given as xDirection-yDirection (z follows)

• down-right: [default in text books] RD = x = down; TD = y = right; ND = z = outOfPlane
• up-left: [default in OIM] RD = x = up; TD = y = left; ND = z = outOfPlane

Parameters

poles	if given (e.g. [1,0,0]), plot pole-figure and the corresponding poles
unitCell	plot unit cell
cos	plot coordinate system
annotate	annotate poles in pole figure (requires poles given)
plot2D	do a normal projection onto 2D plane: [down-right, up-left, None]
scale	scale of pole-figure dome over crystal
fileName	fileName for image output (if given, image not shown)

plotLine()

def ebsd_Orientation.Orientation.plotLine	(		self,
			ax,
			start,
			delta,
			color = 'k',
			lw = 1,
			ls = 'solid',
			markerSize = None
	)

Plot one line using given projection.

Parameters

ax	axis to plot into
start	start coordinate
delta	delta cooradinate (end-start)
color	color
lw	line width
ls	line style "solid",'dashed'
markerSize	size of marker (only used for non-lines: delta>0)

plotUnit()

def ebsd_Orientation.Orientation.plotUnit	(		self,
			ax,
			xlabel,
			ylabel,
			zlabel,
			x = 0,
			y = 0,
			z = 0,
			s = 1
	)

Coordinate see plotLine.

Parameters

ax	axis to used for plotting
xlabel	x-label
ylabel	y-label
zlabel	z-label
x	x-coordinate of origin
y	y-coordinate of origin
z	z-coordinate of origin
s	scale

project()

def ebsd_Orientation.Orientation.project	(		self,
			x,
			y,
			z
	)

reduced()

def ebsd_Orientation.Orientation.reduced

(

self

)

Transform orientation to fall into fundamental zone according to symmetry.

related()

def ebsd_Orientation.Orientation.related	(		self,
			relationModel,
			direction,
			targetSymmetry = None
	)

toScreen()

def ebsd_Orientation.Orientation.toScreen	(		self,
			equivalent = True
	)

print Euler angles and HKL /UVW

Parameters

equivalent

print also equivalent orientations

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The documentation for this class was generated from the following file:

• pythonEBSD/ebsd_Orientation.py