ebsd_Quaternion.Quaternion Class Reference

Detailed Description

Quaternion: mathematical rotation description.

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All methods and naming conventions based of http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions
code derived from http://pyeuclid.googlecode.com/svn/trunk/euclid.py
suggested reading: http://web.mit.edu/2.998/www/QuaternionReport1.pdf

w is the real part, (x, y, z) are the imaginary parts

Representation of rotation is in ACTIVE form!
(derived directly or through angleAxis, Euler angles, or active matrix)
vector "a" (defined in coordinate system "A") is actively rotated to new coordinates "b"
b = Q * a
b = np.dot(Q.asMatrix(),a)

Public Member Functions
def	__cmp__ (self, other)
def	__copy__ (self)
def	__eq__ (self, other)
def	__getitem__ (self, item)
def	__init__ (self, quatArray=[1.0)
def	__iter__ (self)
def	__ne__ (self, other)
def	__repr__ (self)
GET ROTATION IN DIFFERENT FORMS
def	normalized (self)
def	conjugated (self)
def	inversed (self)
def	homomorphed (self)
def	asList (self)
def	asM (self)
def	asMatrix (self)
def	asAngleAxis (self, degrees=False)
	Returns tuple(angle,axis) More...
def	asRodrigues (self)
def	asEulers (self, notation='bunge', degrees=False, standardRange=False, round=8)
	conversion of ACTIVE rotation to Euler angles taken from. More...
STATIC CLASS METHODS
def	fromIdentity (cls)
def	fromRandom (cls, randomSeed=None)
def	fromRodrigues (cls, rodrigues)
def	fromAngleAxis (cls, angle, axis)
def	fromEulers (cls, eulers, type='Bunge')
def	fromMatrix (cls, m)
	Modified Method to calculate Quaternion from Orientation Matrix. More...
def	new_interpolate (cls, q1, q2, t)
	Interpolation. More...

MATHEMATICAL SPECIFIC ROUTINES
def	magnitude = __abs__
def	__pow__ (self, exponent)
def	__ipow__ (self, exponent)
def	__mul__ (self, other)
def	__imul__ (self, other)
def	__div__ (self, other)
def	__idiv__ (self, other)
def	__add__ (self, other)
def	__iadd__ (self, other)
def	__sub__ (self, other)
def	__isub__ (self, other)
def	__neg__ (self)
def	__abs__ (self)
def	magnitude_squared (self)
def	identity (self)
def	normalize (self)
def	conjugate (self)
def	inverse (self)
def	homomorph (self)

Constructor & Destructor Documentation

__init__()

def ebsd_Quaternion.Quaternion.__init__	(		self,
			quatArray = [1.0
	)

Member Function Documentation

__abs__()

def ebsd_Quaternion.Quaternion.__abs__

(

self

)

__add__()

def ebsd_Quaternion.Quaternion.__add__	(		self,
			other
	)

__cmp__()

def ebsd_Quaternion.Quaternion.__cmp__	(		self,
			other
	)

__copy__()

def ebsd_Quaternion.Quaternion.__copy__

(

self

)

__div__()

def ebsd_Quaternion.Quaternion.__div__	(		self,
			other
	)

__eq__()

def ebsd_Quaternion.Quaternion.__eq__	(		self,
			other
	)

__getitem__()

def ebsd_Quaternion.Quaternion.__getitem__	(		self,
			item
	)

__iadd__()

def ebsd_Quaternion.Quaternion.__iadd__	(		self,
			other
	)

__idiv__()

def ebsd_Quaternion.Quaternion.__idiv__	(		self,
			other
	)

__imul__()

def ebsd_Quaternion.Quaternion.__imul__	(		self,
			other
	)

__ipow__()

def ebsd_Quaternion.Quaternion.__ipow__	(		self,
			exponent
	)

__isub__()

def ebsd_Quaternion.Quaternion.__isub__	(		self,
			other
	)

__iter__()

def ebsd_Quaternion.Quaternion.__iter__

(

self

)

__mul__()

def ebsd_Quaternion.Quaternion.__mul__	(		self,
			other
	)

__ne__()

def ebsd_Quaternion.Quaternion.__ne__	(		self,
			other
	)

__neg__()

def ebsd_Quaternion.Quaternion.__neg__

(

self

)

__pow__()

def ebsd_Quaternion.Quaternion.__pow__	(		self,
			exponent
	)

__repr__()

def ebsd_Quaternion.Quaternion.__repr__

(

self

)

__sub__()

def ebsd_Quaternion.Quaternion.__sub__	(		self,
			other
	)

asAngleAxis()

def ebsd_Quaternion.Quaternion.asAngleAxis	(		self,
			degrees = False
	)

Returns tuple(angle,axis)

asEulers()

def ebsd_Quaternion.Quaternion.asEulers	(		self,
			notation = 'bunge',
			degrees = False,
			standardRange = False,
			round = 8
	)

conversion of ACTIVE rotation to Euler angles taken from.

Melcher, A.; Unser, A.; Reichhardt, M.; Nestler, B.; Pötschke, M.; Selzer, M. Conversion of EBSD data by a quaternion based algorithm to be used for grain structure simulations Technische Mechanik 30 (2010) pp 401–413

asList()

def ebsd_Quaternion.Quaternion.asList

(

self

)

asM()

def ebsd_Quaternion.Quaternion.asM

(

self

)

asMatrix()

def ebsd_Quaternion.Quaternion.asMatrix

(

self

)

asRodrigues()

def ebsd_Quaternion.Quaternion.asRodrigues

(

self

)

conjugate()

def ebsd_Quaternion.Quaternion.conjugate

(

self

)

conjugated()

def ebsd_Quaternion.Quaternion.conjugated

(

self

)

fromAngleAxis()

def ebsd_Quaternion.Quaternion.fromAngleAxis	(		cls,
			angle,
			axis
	)

fromEulers()

def ebsd_Quaternion.Quaternion.fromEulers	(		cls,
			eulers,
			type = 'Bunge'
	)

fromIdentity()

def ebsd_Quaternion.Quaternion.fromIdentity

(

cls

)

fromMatrix()

def ebsd_Quaternion.Quaternion.fromMatrix	(		cls,
			m
	)

Modified Method to calculate Quaternion from Orientation Matrix.

Source http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/

fromRandom()

def ebsd_Quaternion.Quaternion.fromRandom	(		cls,
			randomSeed = None
	)

fromRodrigues()

def ebsd_Quaternion.Quaternion.fromRodrigues	(		cls,
			rodrigues
	)

homomorph()

def ebsd_Quaternion.Quaternion.homomorph

(

self

)

homomorphed()

def ebsd_Quaternion.Quaternion.homomorphed

(

self

)

identity()

def ebsd_Quaternion.Quaternion.identity

(

self

)

inverse()

def ebsd_Quaternion.Quaternion.inverse

(

self

)

inversed()

def ebsd_Quaternion.Quaternion.inversed

(

self

)

magnitude_squared()

def ebsd_Quaternion.Quaternion.magnitude_squared

(

self

)

new_interpolate()

def ebsd_Quaternion.Quaternion.new_interpolate	(		cls,
			q1,
			q2,
			t
	)

Interpolation.

see http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070017872_2007014421.pdf for (another?) way to interpolate quaternions

normalize()

def ebsd_Quaternion.Quaternion.normalize

(

self

)

normalized()

def ebsd_Quaternion.Quaternion.normalized

(

self

)

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

• pythonEBSD/ebsd_Quaternion.py