Parallel3dAxisGeometry¶

class odl.tomo.geometry.parallel.Parallel3dAxisGeometry(apart, dpart, axis=(0, 0, 1), **kwargs)[source]¶

Bases: ParallelBeamGeometry, AxisOrientedGeometry

Parallel beam geometry in 3d with single rotation axis.

The motion parameter is the rotation angle around the specified axis, and the detector is a flat 2d detector perpendicular to the ray direction.

In the standard configuration, the rotation axis is (0, 0, 1), 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.

Attributes:

angles: All angles of this geometry as an array.
axis: Normalized axis of rotation, a 3d vector.
check_bounds: If True, methods computing vectors check input arguments.
det_axes_init: Initial axes of the detector.
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_axes`(angle)	Return the detector axes tuple 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 `Parallel3dAxisGeometry` using a matrix.
`rotation_matrix`(angle)	Return the rotation matrix to the system state at `angle`.

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

Initialize a new instance.

Parameters:

apart1-dim. RectPartition: Partition of the angle interval.
dpart2-dim. RectPartition: Partition of the detector parameter rectangle.
axisarray-like, shape (3,), optional: Vector defining the fixed rotation axis of this geometry.

Other Parameters:

det_pos_initarray-like, shape (3,), optional: Initial position of the detector reference point. The default depends on axis, see Notes.
det_axes_init2-tuple of array-like's (shape (3,)), optional: Initial axes defining the detector orientation. The default depends on axis, 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 axis 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 rotation axis is (0, 0, 1), the initial detector reference point position is (0, 1, 0), and the default detector axes are [(1, 0, 0), (0, 0, 1)]. If a different axis is provided, the new default initial position and the new default axes are the computed by rotating the original ones by a matrix that transforms (0, 0, 1) to the new (normalized) axis. This matrix is calculated with the rotation_matrix_from_to function. Expressed in code, we have

init_rot = rotation_matrix_from_to((0, 0, 1), axis)
det_pos_init = init_rot.dot((0, 1, 0))
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:

>>> apart = odl.uniform_partition(0, np.pi, 10)
>>> dpart = odl.uniform_partition([-1, -1], [1, 1], (20, 20))
>>> geom = Parallel3dAxisGeometry(apart, dpart)
>>> geom.det_refpoint(0)
array([ 0.,  1.,  0.])
>>> geom.det_point_position(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.axis, e_z)
True
>>> np.allclose(geom.det_pos_init, e_y)
True
>>> np.allclose(geom.det_axes_init, (e_x, e_z))
True

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

>>> geom = Parallel3dAxisGeometry(apart, dpart, axis=(0, 1, 0))
>>> np.allclose(geom.axis, e_y)
True
>>> np.allclose(geom.det_pos_init, -e_z)
True
>>> np.allclose(geom.det_axes_init, (e_x, e_y))
True
>>> geom = Parallel3dAxisGeometry(apart, dpart, axis=(1, 0, 0))
>>> np.allclose(geom.axis, e_x)
True
>>> np.allclose(geom.det_pos_init, e_y)
True
>>> np.allclose(geom.det_axes_init, (-e_z, e_x))
True

The initial detector position and axes can also be set explicitly:

>>> geom = Parallel3dAxisGeometry(
...     apart, dpart, det_pos_init=(-1, 0, 0),
...     det_axes_init=((0, 1, 0), (0, 0, 1)))
>>> np.allclose(geom.axis, e_z)
True
>>> np.allclose(geom.det_pos_init, -e_x)
True
>>> np.allclose(geom.det_axes_init, (e_y, e_z))
True