Parallel3dAxisGeometry.det_to_src

Parallel3dAxisGeometry.det_to_src(angle, dparam)

Direction from a detector location to the source.

The direction vector is computed as follows:

dir = rotation_matrix(angle).dot(detector.surface_normal(dparam))

Note that for flat detectors, surface_normal does not depend on the parameter dparam, hence this function is constant in that variable.

Parameters:
anglearray-like or sequence

One or several (Euler) angles in radians 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:
det_to_srcnumpy.ndarray

Vector(s) pointing from a detector point to the source (at infinity). The shape of the returned array is obtained from the (broadcast) shapes of angle and dparam, and broadcasting is supported within both parameters and between them. The precise definition of the shape is broadcast(bcast_angle, bcast_dparam).shape + (ndim,), where bcast_angle 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_to_src(0, 0)
array([ 0., -1.])
>>> geom.det_to_src(0, 1)
array([ 0., -1.])
>>> dir = geom.det_to_src(np.pi / 2, 0)
>>> np.allclose(dir, [1, 0])
True
>>> dir = geom.det_to_src(np.pi / 2, 1)
>>> np.allclose(dir, [1, 0])
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:

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