Rotation

class geoteqpy.Rotation(angle: float, axis: ndarray)

Class to perform 3D rotations.

Parameters:

angle (float) – Angle of rotation
axis (numpy.ndarray) – Axis of rotation, expected shape (3,). The vector is expected to be normalized.

Attributes:

angle: float: Angle of rotation

axis: numpy.ndarray: Axis of rotation

Methods:

rotate_referential(self, coor, O, L, ccw=True)

Rotate the referential of the coordinates \(\mathbf{x}\) given the rotation matrix \(\boldsymbol R\). The referential is first translated to be centred on \(\mathbf{0}\), then rotated and finally translated back to its original position.

\[\begin{split}\mathbf x_T &= \mathbf x - \frac{1}{2}(\mathbf L + \mathbf O) \\ \mathbf x_{TR} &= \boldsymbol R \mathbf x_T \\ \mathbf x_R &= \mathbf x_{TR} + \frac{1}{2}(\mathbf L + \mathbf O)\end{split}\]

Parameters:

coor (np.ndarray) – coordinates to be rotated of the shape (npoints,dim)
O (np.ndarray) – origin of the referential of the shape (dim,)
L (np.ndarray) – maximum coordinates of the referential of the shape (dim,)
ccw (bool) – rotate counter-clockwise (default is True)

Returns:

Rotated coordinates of the shape (npoints,dim)

rotate_tensor(R: ndarray, tensor: ndarray, ccw: bool = True) → ndarray

Rotate a tensor such that

\[\boldsymbol{\tau}_R = \boldsymbol{R} \boldsymbol{\tau} \boldsymbol{R}^T\]

Parameters:

R (np.ndarray) – rotation matrix of the shape (dim,dim)
tensor (np.ndarray) – tensor(s) to be rotated of the shape (npoints,dim,dim)
ccw (bool) – rotate counter-clockwise (default is True)

Returns:

Rotated tensor of the shape (npoints,dim,dim)

rotate_vector(R: ndarray, u: ndarray, ccw: bool = True) → ndarray

Rotate vector(s) \(\mathbf u\) given the rotation matrix \(\boldsymbol R\).

Warning

This is not a rotation of the vector field, but a rotation of the vectors themselves.

Parameters:

R (np.ndarray) – rotation matrix of the shape (dim,dim)
u (np.ndarray) – vector(s) to be rotated of the shape (npoints,dim)
ccw (bool) – rotate counter-clockwise (default is True)

Returns:

Rotated vector of the shape (npoints,dim)

rotation_matrix() → ndarray

Construct the 3D rotation matrix for an angle \(\theta\) and a rotation axis \(\mathbf r\).

Returns:: The rotation matrix. Shape (3,3)
Ret type:: numpy.ndarray