Parallel3dEulerGeometry.det_point_position

Parallel3dEulerGeometry.det_point_position(self, mparam, dparam)

Return the detector point at (mparam, dparam).

The position is computed as follows:

pos = refpoint(mparam) +
      rotation_matrix(mparam).dot(detector.surface(dparam))

In other words, the motion parameter mparam is used to move the detector reference point, and the detector parameter dparam defines an intrinsic shift that is added to the reference point.

Parameters
mparamarray-like or sequence

Motion parameter(s) at which to evaluate. If motion_params.ndim >= 2, a sequence of that length must be provided.

dparamarray-like or sequence

Detector parameter(s) at which to evaluate. If det_params.ndim >= 2, a sequence of that length must be provided.

Returns
posnumpy.ndarray

Vector(s) pointing from the origin to the detector point. The shape of the returned array is obtained from the (broadcast) shapes of mparam and dparam, and broadcasting is supported within both parameters and between them. The precise definition of the shape is broadcast(bcast_mparam, bcast_dparam).shape + (ndim,), where bcast_mparam is

and bcast_dparam defined analogously.

Examples

The method works with single parameter values, in which case a single vector is returned:

>>> apart = odl.uniform_partition(0, np.pi, 10)
>>> dpart = odl.uniform_partition(-1, 1, 20)
>>> geom = odl.tomo.Parallel2dGeometry(apart, dpart)
>>> geom.det_point_position(0, 0)  # (0, 1) + 0 * (1, 0)
array([ 0.,  1.])
>>> geom.det_point_position(0, 1)  # (0, 1) + 1 * (1, 0)
array([ 1.,  1.])
>>> pt = geom.det_point_position(np.pi / 2, 0)  # (-1, 0) + 0 * (0, 1)
>>> np.allclose(pt, [-1, 0])
True
>>> pt = geom.det_point_position(np.pi / 2, 1)  # (-1, 0) + 1 * (0, 1)
>>> np.allclose(pt, [-1, 1])
True

Both variables support vectorized calls, i.e., stacks of parameters can be provided. The order of axes in the output (left of the ndim axis for the vector dimension) corresponds to the order of arguments:

>>> geom.det_point_position(0, [-1, 0, 0.5, 1])
array([[-1. ,  1. ],
       [ 0. ,  1. ],
       [ 0.5,  1. ],
       [ 1. ,  1. ]])
>>> pts = geom.det_point_position([0, np.pi / 2, np.pi], 0)
>>> np.allclose(pts, [[0, 1],
...                   [-1, 0],
...                   [0, -1]])
True
>>> # Providing 3 pairs of parameters, resulting in 3 vectors
>>> pts = geom.det_point_position([0, np.pi / 2, np.pi],
...                               [-1, 0, 1])
>>> pts[0]  # Corresponds to angle = 0, dparam = -1
array([-1.,  1.])
>>> pts.shape
(3, 2)
>>> # Pairs of parameters arranged in arrays of same size
>>> geom.det_point_position(np.zeros((4, 5)), np.zeros((4, 5))).shape
(4, 5, 2)
>>> # "Outer product" type evaluation using broadcasting
>>> geom.det_point_position(np.zeros((4, 1)), np.zeros((1, 5))).shape
(4, 5, 2)

More complicated 3D geometry with 2 angle variables and 2 detector variables:

>>> apart = odl.uniform_partition([0, 0], [np.pi, 2 * np.pi],
...                               (10, 20))
>>> dpart = odl.uniform_partition([-1, -1], [1, 1], (20, 20))
>>> geom = odl.tomo.Parallel3dEulerGeometry(apart, dpart)
>>> # 2 values for each variable, resulting in 2 vectors
>>> angles = ([0, np.pi / 2], [0, np.pi])
>>> dparams = ([-1, 0], [-1, 0])
>>> pts = geom.det_point_position(angles, dparams)
>>> pts[0]  # Corresponds to angle = (0, 0), dparam = (-1, -1)
array([-1.,  1., -1.])
>>> pts.shape
(2, 3)
>>> # 4 x 5 parameters for both
>>> angles = dparams = (np.zeros((4, 5)), np.zeros((4, 5)))
>>> geom.det_point_position(angles, dparams).shape
(4, 5, 3)
>>> # Broadcasting angles to shape (4, 5, 1, 1)
>>> angles = (np.zeros((4, 1, 1, 1)), np.zeros((1, 5, 1, 1)))
>>> # Broadcasting dparams to shape (1, 1, 6, 7)
>>> dparams = (np.zeros((1, 1, 6, 1)), np.zeros((1, 1, 1, 7)))
>>> # Total broadcast parameter shape is (4, 5, 6, 7)
>>> geom.det_point_position(angles, dparams).shape
(4, 5, 6, 7, 3)