gepetto.quaternion.Quaternion Class Reference

Public Member Functions
def	__init__ (self, *args)
def	__str__ (self)
def	__neg__ (self)
def	__add__ (self, other)
def	__sub__ (self, other)
def	__mul__ (self, other)
def	__rmul__ (self, other)
def	__abs__ (self)
def	conjugate (self)
def	inv (self)
def	__div__ (self, other)
def	__pow__ (self, n)
def	normalize (self)
def	normalized (self)
def	toRotationMatrix (self)
def	toRotationVector (self)
def	copy (self)
def	toRPY (self)
def	fromRPY (self, R, P, Y)
def	toTuple (self)
def	fromTwoVectors (self, a, b)

Public Attributes
	array

Detailed Description

Quaternion class :
------------------

A quaternion has a scalar part and a vector part.
In this class the quaternion is represented as an array of 4 elements :
  - the first element is the scalar part
  - the next 3 elements represents the vector part

One can acces to the array directly with the attribute "array"
  e.g. q1=Quaternion(1,0,0,0) --> q1.array

A quaternion can be instanciated with 1, 2 or 4 elements
  (see : __init__() for more information).

It can also return a rotation vector, a rotation matrix, or a SO3
  (see the methods : to...() for more information).

Constructor & Destructor Documentation

__init__()

def gepetto.quaternion.Quaternion.__init__	(		self,
		*	args
	)

Instanciation of the quaternion with 1, 2 or 4 arguments  :
-----------------------------------------------------------
This creates a 4-sized array (self.array) representing the quaternion
with the first element representing the scalar part
and the 3 others the vector part.

With 4 arguments :
------------------
  - the first one is used as the scalar part,
    the other three as the vector part.

With 2 arguments :
------------------
  - the 1-sized argument is used as the scalar part,
    the 3-sized argument is used as the vector part.

With 1 argument :
-----------------
  - if it is a quaternion it will create a copy of this quaternion.
  - if it is a scalar, the scalar will be used as the scalar part
    and the vector part will be set at (0,0,0).
  - if it is an array, matrix, tuple or list of 4 elements,
    the first element is used as the scalar part
    and the rest as the vector part.
  - if it is an array, matrix, tuple or list of 3 elements,
    the 3 elements are interpreted as a rotation vector,
    this creates a quaternion representing the same rotation.
  - if it is a to 2 dimension array convertible array, matrix, tuple
    or list with at least (3*3) elements,
    the upper left (3*3) elements are interpreted as a rotation matrix,
    this creates a quaternion representing the same rotation.
  - if it is an instance of SO3, quaternion is built from rotation
    matrix.

With 0 arguments :
------------------
If no argument is given, than the quaternion will be set by default
to with the scalar part set to 1 and the vector part to (0,0,0).
(this is the neutral element for multiplication in quaternion space)

To create a quaternion from Roll, Pitch, Yaw angles :
-----------------------------------------------------
first instanciate a quaternion and than use the method fromRPY()
to change the values of it to the dezired ones.
  e.g. : quat().fromRPY(R,P,Y)

Member Function Documentation

__abs__()

def gepetto.quaternion.Quaternion.__abs__

(

self

)

Returns the norm of the quaternion.

__add__()

def gepetto.quaternion.Quaternion.__add__	(		self,
			other
	)

If other is not a quaternion it is casted to a quaternion,
the elements are added one to one.

__div__()

def gepetto.quaternion.Quaternion.__div__	(		self,
			other
	)

If other is not a quaternion it is casted to a quaternion,
the result of the quaternion multiplication with the inverse of other
is returned.

__mul__()

def gepetto.quaternion.Quaternion.__mul__	(		self,
			other
	)

If other is not a quaternion it is casted to a quaternion,
the result of the quaternion multiplication is returned.

__neg__()

def gepetto.quaternion.Quaternion.__neg__

(

self

)

Returns a quaternion which elements are the opposite of the original,
(this opposite quaternion represents the same rotation).

__pow__()

def gepetto.quaternion.Quaternion.__pow__	(		self,
			n
	)

Returns quaternion**n with quaternion**0 = Quaternion(1,0,0,0).

__rmul__()

def gepetto.quaternion.Quaternion.__rmul__	(		self,
			other
	)

other is casted to a quaternion,
the result of the quaternion multiplication is returned.

__str__()

def gepetto.quaternion.Quaternion.__str__

(

self

)

String representation of the quaternion.

__sub__()

def gepetto.quaternion.Quaternion.__sub__	(		self,
			other
	)

If other is not a quaternion it is casted to a quaternion,
the elements are substracted one to one.

conjugate()

def gepetto.quaternion.Quaternion.conjugate

(

self

)

Returns the conjugate of the quaternion.

copy()

def gepetto.quaternion.Quaternion.copy

(

self

)

Returns a copy of the quaternion.

fromRPY()

def gepetto.quaternion.Quaternion.fromRPY	(		self,
			R,
			P,
			Y
	)

Set the values of the quaternion to the values of a unit quaternion
representing the same rotation as the one performed by Roll Pitch Yaw :
  - A rotation of R (Roll) about the original x-axis,
    followed by a rotation of P (Pitch) about the original y-axis,
    followed by a rotation of Y (Yaw) about the original z-axis.
  - Or otherwise a rotation of Y about the original z-axis,
    followed by a rotation of P about the new y-axis,
    followed by a rotation of R about the new x-axis.

fromTwoVectors()

def gepetto.quaternion.Quaternion.fromTwoVectors	(		self,
			a,
			b
	)

Return a quaternion build representing the rotation between the two vectors.
In other words, the built rotation represent a rotation sending the line of
direction a to the line of direction b,
both lines passing through the origin.
Equations from:
Eigen https://eigen.tuxfamily.org/dox/classEigen_1_1Quaternion.html#title13

inv()

def gepetto.quaternion.Quaternion.inv

(

self

)

Returns the inverse of the quaternion.

normalize()

def gepetto.quaternion.Quaternion.normalize

(

self

)

Changes the values of the quaternion to make it a unit quaternion
representing the same rotation as the original one
and returns the updated version.

normalized()

def gepetto.quaternion.Quaternion.normalized

(

self

)

Returns the unit quaternion representation of the quaternion
without changing the original.

toRotationMatrix()

def gepetto.quaternion.Quaternion.toRotationMatrix

(

self

)

Returns a (3*3) array (rotation matrix)
representing the same rotation as the (normalized) quaternion.

toRotationVector()

def gepetto.quaternion.Quaternion.toRotationVector

(

self

)

Returns a 3-sized array (rotation vector)
representing the same rotation as the (normalized) quaternion.

toRPY()

def gepetto.quaternion.Quaternion.toRPY

(

self

)

Returns a 3-sized array with representing the same rotation
as the (normalized) quaternion. With :
  - the first element representing the Roll,
  - the second the Pitch
  - the third the Yaw
Where Roll Pitch and Yaw are the angles so that the rotation
with the quaternion represents the same rotation as :
  - A rotation of R (Roll) about the original x-axis,
    followed by a rotation of P (Pitch) about the original y-axis,
    followed by a rotation of Y (Yaw) about the original z-axis.
  - Or otherwise a rotation of Y about the original z-axis,
    followed by a rotation of P about the new y-axis,
    followed by a rotation of R about the new x-axis.

toTuple()

def gepetto.quaternion.Quaternion.toTuple

(

self

)

Return quaternion as a tuple a float starting with real part.

Member Data Documentation

array

gepetto.quaternion.Quaternion.array

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

• src/gepetto/quaternion.py