Parallel3dEulerGeometry

class odl.applications.tomo.geometry.parallel.Parallel3dEulerGeometry(apart, dpart, det_pos_init=(0, 1, 0), **kwargs)[source]

Bases: ParallelBeamGeometry

Parallel beam geometry in 3d.

The motion parameters are two or three Euler angles, and the detector is flat and two-dimensional.

In the standard configuration, the detector reference point starts at (0, 1, 0), and the initial detector axes are [(1, 0, 0), (0, 0, 1)].

For details, check the online docs.

__init__(apart, dpart, det_pos_init=(0, 1, 0), **kwargs)[source]

Initialize a new instance.

Parameters

apart2- or 3-dim. RectPartition: Partition of the angle parameter set.
dpart2-dim. RectPartition: Partition of the detector parameter set.
det_pos_initarray-like, shape (3,), optional: Initial position of the detector reference point.

Other Parameters

det_axes_init2-tuple of array-like’s (shape (3,)), optional: Initial axes defining the detector orientation. The default depends on det_pos_init, see Notes.
translationarray-like, shape (3,), optional: Global translation of the geometry. This is added last in any method that computes an absolute vector, e.g., det_refpoint, and also shifts the center of rotation. Default: (0, 0, 0)
check_boundsbool, optional: If True, methods computing vectors check input arguments. Checks are vectorized and add only a small overhead. Default: True

Notes

In the default configuration, the initial detector reference point is (0, 1, 0), and the initial detector axes are [(1, 0, 0), (0, 0, 1)]. If a different det_pos_init is chosen, the new default axes are given as a rotation of the original ones by a matrix that transforms (0, 1, 0) to the new (normalized) det_pos_init. This matrix is calculated with the rotation_matrix_from_to function. Expressed in code, we have

init_rot = rotation_matrix_from_to((0, 1, 0), det_pos_init)
det_axes_init[0] = init_rot.dot((1, 0, 0))
det_axes_init[1] = init_rot.dot((0, 0, 1))

Examples

Initialization with default parameters and 2 Euler angles:

>>> apart = odl.uniform_partition([0, 0], [np.pi, 2 * np.pi],
...                               (10, 20))
>>> dpart = odl.uniform_partition([-1, -1], [1, 1], (20, 20))
>>> geom = Parallel3dEulerGeometry(apart, dpart)
>>> geom.det_refpoint([0, 0])
array([ 0.,  1.,  0.])
>>> geom.det_point_position([0, 0], [-1, 1])
array([-1.,  1.,  1.])

Checking the default orientation:

>>> e_x, e_y, e_z = np.eye(3)  # standard unit vectors
>>> np.allclose(geom.det_pos_init, e_y)
True
>>> np.allclose(geom.det_axes_init, (e_x, e_z))
True

Specifying an initial detector position by default rotates the standard configuration to this position:

>>> geom = Parallel3dEulerGeometry(apart, dpart,
...                                det_pos_init=(1, 0, 0))
>>> np.allclose(geom.det_pos_init, e_x)
True
>>> np.allclose(geom.det_axes_init, (-e_y, e_z))
True
>>> geom = Parallel3dEulerGeometry(apart, dpart,
...                                det_pos_init=(0, 0, 1))
>>> np.allclose(geom.det_pos_init, e_z)
True
>>> np.allclose(geom.det_axes_init, (e_x, -e_y))
True

The initial detector axes can also be set explicitly:

>>> geom = Parallel3dEulerGeometry(
...     apart, dpart, det_pos_init=(-1, 0, 0),
...     det_axes_init=((0, 1, 0), (0, 0, 1)))
>>> np.allclose(geom.det_pos_init, -e_x)
True
>>> np.allclose(geom.det_axes_init, (e_y, e_z))
True