spatial_casadi.spatial Namespace Reference

Classes
class	Rotation
class	Translation
	A class defining a translation vector. More...
class	Transformation
	A class for representing homogenous transformations. More...

Functions
bool	_iszero (Array a)
CasadiArray	_cross3 (Array a, Array b)
CasadiArray	_make_elementary_quat (str axis, Array angles)
CasadiArray	_dot3 (Array a, Array b)
CasadiArray	_norm3 (Array elems)
CasadiArray	_normalize4 (Array elems)
def	_argmax4 (a)
CasadiArray	_quat_canonical_single (Array q)
CasadiArray	_quat_canonical (Array q)
def	_get_angles (angles, extrinsic, symmetric, sign, lamb, a, b, c, d)
def	_compose_quat (p, q)
def	_elementary_quat_compose (seq, angles, intrinsic)
def	_single_matrix_to_quat (matrix)

Variables
	eps = np.finfo(float).eps
	CasadiArray = cs.MX | cs.SX | cs.DM
	NonSymbolicCasadiArray = cs.DM
	Array = cs.MX | cs.SX | cs.DM | np.ndarray
	NonSymbolicArray = cs.DM | np.ndarray
	_ex = cs.DM([1.0, 0.0, 0.0])
	_ey = cs.DM([0.0, 1.0, 0.0])
	_ez = cs.DM([0.0, 0.0, 1.0])
dictionary	_elementary_basis_vector = {"x": _ex, "y": _ey, "z": _ez}

Function Documentation

_argmax4()

def spatial_casadi.spatial._argmax4 (   a )

private

Index for the element with maximum value.

_compose_quat()

def spatial_casadi.spatial._compose_quat (   p,   q  )

private

Compose two quaternions by performing quaternion multiplication.

Args
    p (array-like): The first quaternion as an array-like object.
    q (array-like): The second quaternion as an array-like object.

Returns
    casadi-array: The resulting quaternion from the multiplication of p and q.

_cross3()

CasadiArray spatial_casadi.spatial._cross3 ( Array  a, Array  b  )

private

Cross product for vectors a and b of length 3.

_dot3()

CasadiArray spatial_casadi.spatial._dot3 ( Array  a, Array  b  )

private

Dot-product with vectors of length 3.

_elementary_quat_compose()

def spatial_casadi.spatial._elementary_quat_compose (   seq,   angles,   intrinsic  )

private

Compose a sequence of elementary quaternions into a single quaternion.

Args
    seq (array-like): A sequence of axes ('x', 'y', 'z') around which to rotate.
    angles (array-like): A sequence of rotation angles in radians corresponding to each axis in `seq`.
    intrinsic (bool): If `True`, applies intrinsic rotations; otherwise, applies extrinsic rotations.

Returns
    casadi-array: The resulting quaternion from composing the sequence of elementary quaternions.

_get_angles()

def spatial_casadi.spatial._get_angles (   angles,   extrinsic,   symmetric,   sign,   lamb,   a,   b,   c,   d  )

private

_iszero()

bool spatial_casadi.spatial._iszero ( Array  a )

private

True when a is numerically zero, False otherwise.

_make_elementary_quat()

CasadiArray spatial_casadi.spatial._make_elementary_quat ( str  axis, Array  angles  )

private

Create an elementary quaternion representing a rotation around a specified axis.

Args
    axis (str): The axis to rotate around. Must be 'x', 'y', or 'z'.
    angles (array-like): The rotation angle(s) in radians.

Returns
    casadi-array: A quaternion representing the rotation.

_norm3()

CasadiArray spatial_casadi.spatial._norm3 ( Array  elems )

private

Euclidean norm for a vector of length 3.

_normalize4()

CasadiArray spatial_casadi.spatial._normalize4 ( Array  elems )

private

Normalize vector of length 4.

_quat_canonical()

CasadiArray spatial_casadi.spatial._quat_canonical ( Array  q )

private

_quat_canonical_single()

CasadiArray spatial_casadi.spatial._quat_canonical_single ( Array  q )

private

Reduce the quaternion double coverage of the rotation group to a unique canonical 'positive' single cover.

_single_matrix_to_quat()

def spatial_casadi.spatial._single_matrix_to_quat (   matrix )

private

Variable Documentation

_elementary_basis_vector

dictionary spatial_casadi.spatial._elementary_basis_vector = {"x": _ex, "y": _ey, "z": _ez}

private

_ex

spatial_casadi.spatial._ex = cs.DM([1.0, 0.0, 0.0])

private

_ey

spatial_casadi.spatial._ey = cs.DM([0.0, 1.0, 0.0])

private

_ez

spatial_casadi.spatial._ez = cs.DM([0.0, 0.0, 1.0])

private

Array

spatial_casadi.spatial.Array = cs.MX | cs.SX | cs.DM | np.ndarray

CasadiArray

spatial_casadi.spatial.CasadiArray = cs.MX | cs.SX | cs.DM

eps

spatial_casadi.spatial.eps = np.finfo(float).eps

NonSymbolicArray

spatial_casadi.spatial.NonSymbolicArray = cs.DM | np.ndarray

NonSymbolicCasadiArray

spatial_casadi.spatial.NonSymbolicCasadiArray = cs.DM