euler_matrix

odl.tomo.util.utility.euler_matrix(phi, theta=None, psi=None)

Rotation matrix in 2 and 3 dimensions.

Its rows represent the canonical unit vectors as seen from the rotated system while the columns are the rotated unit vectors as seen from the canonical system.

Parameters:

phifloat or array-like

Either 2D counter-clockwise rotation angle (in radians) or first Euler angle.

theta, psifloat or array-like, optional

Second and third Euler angles in radians. If both are None, a 2D rotation matrix is computed. Otherwise a 3D rotation is computed, where the default None is equivalent to 0.0. The rotation is performed in "ZXZ" rotation order, see the Wikipedia article Euler angles.

Returns:

matnumpy.ndarray

Rotation matrix corresponding to the given angles. The returned array has shape (ndim, ndim) if all angles represent single parameters, with ndim == 2 for phi only and ndim == 3 for 2 or 3 Euler angles. If any of the angle parameters is an array, the shape of the returned array is broadcast(phi, theta, psi).shape + (ndim, ndim).

References