Parallel2dGeometry

class odl.applications.tomo.geometry.parallel.Parallel2dGeometry(apart, dpart, det_pos_init=(0, 1), **kwargs)

Bases: ParallelBeamGeometry

Parallel beam geometry in 2d.

The motion parameter is the counter-clockwise rotation angle around the origin, and the detector is a line detector.

In the standard configuration, the detector is perpendicular to the ray direction, its reference point is initially at (0, 1), and the initial detector axis is (1, 0).

For details, check the online docs.

__init__(apart, dpart, det_pos_init=(0, 1), **kwargs)

Initialize a new instance.

Parameters

apart1-dim. RectPartition

Partition of the angle interval.

dpart1-dim. RectPartition

Partition of the detector parameter interval.

det_pos_initarray-like, shape (2,), optional

Initial position of the detector reference point.

Other Parameters

det_axis_initarray-like (shape (2,)), optional

Initial axis defining the detector orientation. The default depends on det_pos_init, see Notes.

translationarray-like, shape (2,), 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)

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), and the initial detector axis is (1, 0). If a different det_pos_init is chosen, the new default axis is given as a rotation of the original one by a matrix that transforms (0, 1) 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), det_pos_init)
det_axis_init = init_rot.dot((1, 0))

If det_pos_init == (0, 0), no rotation is performed.

Examples

Initialization with default parameters:

>>> apart = odl.uniform_partition(0, np.pi, 10)
>>> dpart = odl.uniform_partition(-1, 1, 20)
>>> geom = Parallel2dGeometry(apart, dpart)
>>> np.allclose(geom.det_refpoint(0), (0, 1))
True
>>> np.allclose(geom.det_point_position(0, 1), (1, 1))
True

Checking the default orientation:

>>> e_x, e_y = np.eye(2)  # standard unit vectors
>>> np.allclose(geom.det_pos_init, e_y)
True
>>> np.allclose(geom.det_axis_init, e_x)
True

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

>>> geom = Parallel2dGeometry(apart, dpart, det_pos_init=(-1, 0))
>>> np.allclose(geom.det_pos_init, -e_x)
True
>>> np.allclose(geom.det_axis_init, e_y)
True
>>> geom = Parallel2dGeometry(apart, dpart, det_pos_init=(0, -1))
>>> np.allclose(geom.det_pos_init, -e_y)
True
>>> np.allclose(geom.det_axis_init, -e_x)
True

The initial detector axis can also be set explicitly:

>>> geom = Parallel2dGeometry(
...     apart, dpart, det_pos_init=(0, -1), det_axis_init=(1, 0))
>>> np.allclose(geom.det_pos_init, -e_y)
True
>>> np.allclose(geom.det_axis_init, e_x)
True