Parallel2dGeometry¶

class odl.tomo.geometry.parallel.Parallel2dGeometry(apart, dpart, det_pos_init=(0, 1), **kwargs)[source]¶

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.

Attributes:

angles: All angles of this geometry as an array.
check_bounds: If True, methods computing vectors check input arguments.
det_axis_init: Detector axis at angle 0.
det_grid: Sampling grid of det_params.
det_params: Continuous detector parameter range, an IntervalProd.
det_partition: Partition of the detector parameter set into subsets.
det_pos_init: Initial position of the detector reference point.
detector: Detector representation of this geometry.
grid: Joined sampling grid for motion and detector.
implementation_cache: Dictionary acting as a cache for this geometry.
motion_grid: Sampling grid of motion_params.
motion_params: Continuous motion parameter range, an IntervalProd.
motion_partition: Partition of the motion parameter set into subsets.
ndim: Number of dimensions of the geometry.
params: Joined parameter set for motion and detector.
partition: Joined parameter set partition for motion and detector.
translation: Shift of the origin of this geometry.

Methods

`det_axis`(angle)	Return the detector axis (axes) at `angle`.
`det_point_position`(mparam, dparam)	Return the detector point at `(mparam, dparam)`.
`det_refpoint`(angle)	Return the position(s) of the detector ref.
`det_to_src`(angle, dparam)	Direction from a detector location to the source.
`frommatrix`(apart, dpart, init_matrix, **kwargs)	Create an instance of `Parallel2dGeometry` using a matrix.
`rotation_matrix`(angle)	Return the rotation matrix to the system state at `angle`.

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

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