Orientation_3D Class Reference

This class, introduces a rotation in the three-dimensional space. More...

Inheritance diagram for Orientation_3D:

Public Member Functions
def	clear_acceleration
	private More...
def	clear_velocity
	Clears all velocity properties. More...
def	clear
	Clears all rotation properties. More...
def	is_none
	Use this function to find out if a rotation by any convention is defined for the instance. More...
def	velocity_is_none
	Use this function to find out if a rotation velocity is defined for the instance. More...
def	acceleration_is_none
	private More...
def	__init__
	Class Constructor: More...
def	__str__
def	tensor
def	matrix_velocity
def	angular_velocity
def	quaternion_velocity
def	angle_velocity
def	axis_velocity
def	matrix
def	vector
def	vector_velocity
def	vector_acceleration
def	set_parametrization
	Sets the parametrization for the generating function in vectorial representation of orientation. More...
def	gen_fun
	Returns the value of the generating function for the given angle phi. More...
def	gen_fun_inv
def	gen_fun_derivative
def	noo
def	zeta
def	moo
def	quaternion
def	angle
def	spherical
def	angle_axis
def	axis
def	frame_axis
def	__setitem__
def	__getitem__
def	set_acceleration
def	set_velocity
def	set_acceleration
def	get_velocity
def	__div__
def	__mul__

Public Attributes
	pdd
	A numpy vector of size 3 containing \( \ddot{\p} \) (second derivative of orientation vector \( p \) w.r.t. More...
	Rdd
	A numpy 3x3 rotation matrix: Representation of orientation acceleration as 3x3 numpy rotation matrix second derivative w.r.t. More...
	omega
	A numpy vector of size 3 containing the angular velocity representation of orientation velocity. More...
	Rd
	A numpy 3x3 rotation matrix: Representation of orientation velocity as 3x3 numpy rotation matrix derivative w.r.t. More...
	Qd
	A numpy vector of size 4: Quaternion representation of orientation velocity as a numpy vector ( \( \frac{ dq }{ dt } \)) More...
	phid
	A float containing \( \dot{\phi} \) (derivative of \( \phi \) w.r.t. More...
	ud
	A numpy vector of size 3 containing \( \dot{\u} \) (derivative of unit vector \( u \) w.r.t. More...
	pd
	A numpy vector of size 3 containing \( \dot{\p} \) (derivative of orientation vector \( p \) w.r.t. More...
	R
	A numpy 3x3 rotation matrix: Representation of orientation as 3x3 numpy rotation matrix. More...
	Q
	A numpy vector of size 4: Quaternion representation of orientation as a numpy vector. More...
	p
	A numpy vector of size 3: Representation of orientation as a non-redundant numpy vector (depends on the generator function) More...
	phi
	A float: Angle phi in Angle-Axis representation of orientation. More...
	u
	A numpy vector of size 3: Unit vector u in Angle-Axis representation of orientation. More...
	H
	sa
	A numpy vector of 3 elements: Non-redundant representation of orientation by three Spherical Orientation Angles More...
	representation
	parametrization
	m

Detailed Description

This class, introduces a rotation in the three-dimensional space.

It supports various representations and convensions of orientation. This class also supports computation orientation speed represented by various convensions.

Definition at line 266 of file geometry.py.

Constructor & Destructor Documentation

def __init__	(		self,
			ori,
			representation = 'matrix',
			ori_velocity = None,
			ori_acceleration = None,
			parametrization = 'identity'
	)

Class Constructor:

Parameters

ori	The orientation or rotation defined A tuple or numpy vector of 4 elements if representation = 'quaternion', A 3 X 3 numpy matrix if representation = 'matrix', A tuple or numpy vector of 4 elements if representation = 'angle_axis', A tuple or numpy vector of 3 elements if representation = 'vector',
representation	A string: Must be one of the supported convensions: matrix quaternion angle_axis vector

Definition at line 353 of file geometry.py.

Member Function Documentation

def __div__	(		o1,
			o2
	)

Definition at line 797 of file geometry.py.

def __getitem__	(		self,
			representation
	)

Definition at line 706 of file geometry.py.

def __mul__	(		o1,
			o2
	)

Definition at line 816 of file geometry.py.

def __setitem__	(		self,
			representation,
			value
	)

Definition at line 691 of file geometry.py.

def __str__

(

self

)

Definition at line 368 of file geometry.py.

def acceleration_is_none

(

self

)

private

Definition at line 339 of file geometry.py.

def angle

(

self

)

Definition at line 646 of file geometry.py.

def angle_axis

(

self

)

Definition at line 674 of file geometry.py.

def angle_velocity

(

self

)

Definition at line 450 of file geometry.py.

def angular_velocity

(

self

)

Definition at line 420 of file geometry.py.

def axis

(

self

)

Definition at line 678 of file geometry.py.

def axis_velocity

(

self

)

Definition at line 460 of file geometry.py.

def clear

(

self

)

Clears all rotation properties.

All rotation properties (self.R, self.Q, self.u, self.p, self.phi, self.H, self.sa) will be set to None.

Parameters

None

Returns

None

Definition at line 305 of file geometry.py.

def clear_acceleration

(

self

)

private

Definition at line 269 of file geometry.py.

def clear_velocity

(

self

)

Clears all velocity properties.

All velocity properties (self.omega, self.Rd, self.Qd, self.ud, self.pd, self.phid) will be set to None.

Parameters

None

Returns

None

Definition at line 280 of file geometry.py.

def frame_axis	(		self,
			k
	)

Definition at line 687 of file geometry.py.

def gen_fun	(		self,
			phi
	)

Returns the value of the generating function for the given angle phi.

Parameters

phi	A float variable specifying the angle

Returns

A float containing the value of the generating function for the given phi. The generating function depends on property self.parametrization

Definition at line 553 of file geometry.py.

def gen_fun_derivative	(		self,
			phi
	)

Definition at line 584 of file geometry.py.

def gen_fun_inv	(		self,
			p
	)

Definition at line 570 of file geometry.py.

def get_velocity	(		self,
			representation = None
	)

Definition at line 781 of file geometry.py.

def is_none

(

self

)

Use this function to find out if a rotation by any convention is defined for the instance.

Parameters

None

Returns

A boolean: True if all rotation properties (self.p, self.R, self.u, self.phi, self.Q) are set to None, False, if otherwise.

Definition at line 329 of file geometry.py.

def matrix

(

self

)

Definition at line 475 of file geometry.py.

def matrix_velocity

(

self

)

Definition at line 394 of file geometry.py.

def moo	(		self,
			phi = None
	)

Definition at line 624 of file geometry.py.

def noo	(		self,
			phi = None
	)

Definition at line 604 of file geometry.py.

def quaternion

(

self

)

Definition at line 630 of file geometry.py.

def quaternion_velocity

(

self

)

Definition at line 430 of file geometry.py.

def set_acceleration	(		self,
			ori_dd,
			representation = None
	)

Definition at line 747 of file geometry.py.

def set_acceleration	(		self,
			value,
			representation = None
	)

Definition at line 770 of file geometry.py.

def set_parametrization	(		self,
			parametrization = 'identity'
	)

Sets the parametrization for the generating function in vectorial representation of orientation.

Parameters

parametrization

A string specifying the parametrization. Valid values are: 'identity', 'linear', 'cayley-gibbs-rodrigues', 'bauchau-trainelli', 'exponential'

Returns

None

Definition at line 537 of file geometry.py.

def set_velocity	(		self,
			value,
			representation = None
	)

Definition at line 754 of file geometry.py.

def spherical

(

self

)

Definition at line 664 of file geometry.py.

def tensor

(

self

)

Definition at line 375 of file geometry.py.

def vector

(

self

)

Definition at line 503 of file geometry.py.

def vector_acceleration

(

self

)

Definition at line 530 of file geometry.py.

def vector_velocity

(

self

)

Definition at line 515 of file geometry.py.

def velocity_is_none

(

self

)

Use this function to find out if a rotation velocity is defined for the instance.

Parameters

None

Returns

A boolean: True if all rotation speed properties (self.Rd, self.ud, self.phid, self.Qd, self.pd) are set to None, False, if otherwise.

Definition at line 335 of file geometry.py.

def zeta	(		self,
			phi = None
	)

Definition at line 614 of file geometry.py.

Member Data Documentation

H

Definition at line 321 of file geometry.py.

m

Definition at line 357 of file geometry.py.

omega

A numpy vector of size 3 containing the angular velocity representation of orientation velocity.

Definition at line 282 of file geometry.py.

p

A numpy vector of size 3: Representation of orientation as a non-redundant numpy vector (depends on the generator function)

Definition at line 313 of file geometry.py.

parametrization

Definition at line 355 of file geometry.py.

pd

A numpy vector of size 3 containing \( \dot{\p} \) (derivative of orientation vector \( p \) w.r.t.

time) where \( p \) is the vectorial representation of orientation which is defined according to property self.parametrization

Definition at line 300 of file geometry.py.

pdd

A numpy vector of size 3 containing \( \ddot{\p} \) (second derivative of orientation vector \( p \) w.r.t.

time) where \( p \) is the vectorial representation of orientation which is defined according to property self.parametrization

Definition at line 272 of file geometry.py.

phi

A float: Angle phi in Angle-Axis representation of orientation.

Definition at line 316 of file geometry.py.

phid

A float containing \( \dot{\phi} \) (derivative of \( \phi \) w.r.t.

time), where \( \phi \) is the angle in Angle-Axis representation of orientation

Definition at line 292 of file geometry.py.

Q

A numpy vector of size 4: Quaternion representation of orientation as a numpy vector.

Definition at line 310 of file geometry.py.

Qd

A numpy vector of size 4: Quaternion representation of orientation velocity as a numpy vector ( \( \frac{ dq }{ dt } \))

Definition at line 288 of file geometry.py.

R

A numpy 3x3 rotation matrix: Representation of orientation as 3x3 numpy rotation matrix.

Definition at line 307 of file geometry.py.

Rd

A numpy 3x3 rotation matrix: Representation of orientation velocity as 3x3 numpy rotation matrix derivative w.r.t.

time

Definition at line 285 of file geometry.py.

Rdd

A numpy 3x3 rotation matrix: Representation of orientation acceleration as 3x3 numpy rotation matrix second derivative w.r.t.

time

Definition at line 275 of file geometry.py.

representation

Definition at line 354 of file geometry.py.

sa

A numpy vector of 3 elements: Non-redundant representation of orientation by three Spherical Orientation Angles

Definition at line 324 of file geometry.py.

u

A numpy vector of size 3: Unit vector u in Angle-Axis representation of orientation.

Definition at line 319 of file geometry.py.

ud

A numpy vector of size 3 containing \( \dot{\u} \) (derivative of unit vector \( u \) w.r.t.

time) where \( u \) is the axis in Angle-Axis representation of orientation

Definition at line 296 of file geometry.py.

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

• geometry.py