def zslice(z, x_spec, y_spec, output_space=''):
""" Return a slice through a 3d box with z fixed.
Parameters
----------
z : float
The value at which z is fixed.
x_spec : ([float,float], int)
Tuple representing the x-limits of the bounding
box and the number of points.
y_spec : ([float,float], int)
Tuple representing the y-limits of the bounding
box and the number of points.
output_space : str, optional
Origin of the range CoordinateSystem.
Returns
-------
affine_transform : AffineTransform
An affine transform that describes an plane in
LPS coordinates with z fixed.
Examples
--------
>>> x_spec = ([-92,92], 93) # voxels of size 2 in x, starting at -92, ending at 92
>>> y_spec = ([-114,114], 115) # voxels of size 2 in y, starting at -114, ending at 114
>>> z40 = zslice(40, x_spec, y_spec)
>>> z40
AffineTransform(
function_domain=CoordinateSystem(coord_names=('i_x', 'i_y'), name='slice', coord_dtype=float64),
function_range=CoordinateSystem(coord_names=('x+LR', 'y+PA', 'z+SI'), name='', coord_dtype=float64),
affine=array([[ 2., 0., -92.],
[ 0., 2., -114.],
[ 0., 0., 40.],
[ 0., 0., 1.]])
)
>>>
>>> z40([0,0])
array([ -92., -114., 40.])
>>> z40([92,114])
array([ 92., 114., 40.])
>>> bounding_box(z40, (x_spec[1], y_spec[1]))
([-92.0, 92.0], [-114.0, 114.0], [40.0, 40.0])
"""
xlim = x_spec[0]
ylim = y_spec[0]
shape = (y_spec[1], x_spec[1])
origin = [xlim[0],ylim[0],z]
colvectors = [[(xlim[1]-xlim[0])/(shape[1] - 1.),0,0],
[0,(ylim[1]-ylim[0])/(shape[0] - 1.),0]]
T = from_matrix_vector(np.vstack(colvectors).T, origin)
affine_domain = CoordinateSystem(['i_x', 'i_y'], 'slice')
affine_range = CoordinateSystem(lps_output_coordnames, output_space)
return AffineTransform(affine_domain,
affine_range,
T)
def yslice(y, x_spec, z_spec, output_space=''):
""" Return a slice through a 3d box with y fixed.
Parameters
----------
y : float
The value at which y is fixed.
x_spec : sequence
A sequence with 2 values of form ((float, float), int). The
(float, float) components are the min and max x values; the int
is the number of points.
z_spec : sequence
As for `x_spec` but for z
output_space : str, optional
Origin of the range CoordinateSystem.
Returns
-------
affine_transform : AffineTransform
An affine transform that describes an plane in
LPS coordinates with y fixed.
Examples
--------
>>> x_spec = ([-92,92], 93) # voxels of size 2 in x, starting at -92, ending at 92
>>> z_spec = ([-70,100], 86) # voxels of size 2 in z, starting at -70, ending at 100
>>> y70 = yslice(70, x_spec, z_spec)
>>> y70
AffineTransform(
function_domain=CoordinateSystem(coord_names=('i_x', 'i_z'), name='slice', coord_dtype=float64),
function_range=CoordinateSystem(coord_names=('x+LR', 'y+PA', 'z+SI'), name='', coord_dtype=float64),
affine=array([[ 2., 0., -92.],
[ 0., 0., 70.],
[ 0., 2., -70.],
[ 0., 0., 1.]])
)
>>> y70([0,0])
array([-92., 70., -70.])
>>> y70([92,85])
array([ 92., 70., 100.])
>>>
>>> bounding_box(y70, (x_spec[1], z_spec[1]))
((-92.0, 92.0), (70.0, 70.0), (-70.0, 100.0))
"""
(xmin, xmax), xno = x_spec
x_tick = (xmax-xmin) / (xno - 1.0)
(zmin, zmax), zno = z_spec
z_tick = (zmax-zmin) / (zno - 1.0)
origin = [xmin, y, zmin]
colvectors = np.asarray([[x_tick, 0],
[0, 0],
[0, z_tick]])
T = from_matrix_vector(colvectors, origin)
affine_domain = CoordinateSystem(['i_x', 'i_z'], 'slice')
affine_range = CoordinateSystem(lps_output_coordnames, output_space)
return AffineTransform(affine_domain,
affine_range,
T)
def xslice(x, y_spec, z_spec, output_space=''):
"""
Return an LPS slice through a 3d box with x fixed.
Parameters
----------
x : float
The value at which x is fixed.
y_spec : sequence
A sequence with 2 values of form ((float, float), int). The
(float, float) components are the min and max y values; the int
is the number of points.
z_spec : sequence
As for `y_spec` but for z
output_space : str, optional
Origin of the range CoordinateSystem.
Returns
-------
affine_transform : AffineTransform
An affine transform that describes an plane in
LPS coordinates with x fixed.
Examples
--------
>>> y_spec = ([-114,114], 115) # voxels of size 2 in y, starting at -114, ending at 114
>>> z_spec = ([-70,100], 86) # voxels of size 2 in z, starting at -70, ending at 100
>>> x30 = xslice(30, y_spec, z_spec)
>>> x30([0,0])
array([ 30., -114., -70.])
>>> x30([114,85])
array([ 30., 114., 100.])
>>> x30
AffineTransform(
function_domain=CoordinateSystem(coord_names=('i_y', 'i_z'), name='slice', coord_dtype=float64),
function_range=CoordinateSystem(coord_names=('x+LR', 'y+PA', 'z+SI'), name='', coord_dtype=float64),
affine=array([[ 0., 0., 30.],
[ 2., 0., -114.],
[ 0., 2., -70.],
[ 0., 0., 1.]])
)
>>> bounding_box(x30, (y_spec[1], z_spec[1]))
((30.0, 30.0), (-114.0, 114.0), (-70.0, 100.0))
"""
(ymin, ymax), yno = y_spec
y_tick = (ymax-ymin) / (yno - 1.0)
(zmin, zmax), zno = z_spec
z_tick = (zmax-zmin) / (zno - 1.0)
origin = [x, ymin, zmin]
colvectors = np.asarray([[0, 0],
[y_tick, 0],
[0, z_tick]])
T = from_matrix_vector(colvectors, origin)
affine_domain = CoordinateSystem(['i_y', 'i_z'], 'slice')
affine_range = CoordinateSystem(lps_output_coordnames, output_space)
return AffineTransform(affine_domain,
affine_range,
T)
def xslice(x, y_spec, z_spec, output_space=''):
"""
Return an LPS slice through a 3d box with x fixed.
Parameters
----------
x : float
The value at which x is fixed.
yspec : ([float,float], int)
Tuple representing the y-limits of the bounding
box and the number of points.
zspec : ([float,float], int)
Tuple representing the z-limits of the bounding
box and the number of points.
output_space : str, optional
Origin of the range CoordinateSystem.
Returns
-------
affine_transform : AffineTransform
An affine transform that describes an plane in
LPS coordinates with x fixed.
Examples
--------
>>> y_spec = ([-114,114], 115) # voxels of size 2 in y, starting at -114, ending at 114
>>> z_spec = ([-70,100], 86) # voxels of size 2 in z, starting at -70, ending at 100
>>> x30 = xslice(30, y_spec, z_spec)
>>> x30([0,0])
array([ 30., -114., -70.])
>>> x30([114,85])
array([ 30., 114., 100.])
>>> x30
AffineTransform(
function_domain=CoordinateSystem(coord_names=('i_y', 'i_z'), name='slice', coord_dtype=float64),
function_range=CoordinateSystem(coord_names=('x+LR', 'y+PA', 'z+SI'), name='', coord_dtype=float64),
affine=array([[ 0., 0., 30.],
[ 2., 0., -114.],
[ 0., 2., -70.],
[ 0., 0., 1.]])
)
>>> bounding_box(x30, (y_spec[1], z_spec[1]))
([30.0, 30.0], [-114.0, 114.0], [-70.0, 100.0])
"""
zlim = z_spec[0]
ylim = y_spec[0]
shape = (z_spec[1], y_spec[1])
origin = [x,ylim[0],zlim[0]]
colvectors = [[0,(ylim[1]-ylim[0])/(shape[1] - 1.),0],
[0,0,(zlim[1]-zlim[0])/(shape[0] - 1.)]]
T = from_matrix_vector(np.vstack(colvectors).T, origin)
affine_domain = CoordinateSystem(['i_y', 'i_z'], 'slice')
affine_range = CoordinateSystem(lps_output_coordnames, output_space)
return AffineTransform(affine_domain,
affine_range,
T)
def zslice(z, x_spec, y_spec, output_space=''):
""" Return a slice through a 3d box with z fixed.
Parameters
----------
z : float
The value at which z is fixed.
x_spec : sequence
A sequence with 2 values of form ((float, float), int). The
(float, float) components are the min and max x values; the int
is the number of points.
y_spec : sequence
As for `x_spec` but for y
output_space : str, optional
Origin of the range CoordinateSystem.
Returns
-------
affine_transform : AffineTransform
An affine transform that describes a plane in LPS coordinates with z
fixed.
Examples
--------
>>> x_spec = ([-92,92], 93) # voxels of size 2 in x, starting at -92, ending at 92
>>> y_spec = ([-114,114], 115) # voxels of size 2 in y, starting at -114, ending at 114
>>> z40 = zslice(40, x_spec, y_spec)
>>> z40
AffineTransform(
function_domain=CoordinateSystem(coord_names=('i_x', 'i_y'), name='slice', coord_dtype=float64),
function_range=CoordinateSystem(coord_names=('x+LR', 'y+PA', 'z+SI'), name='', coord_dtype=float64),
affine=array([[ 2., 0., -92.],
[ 0., 2., -114.],
[ 0., 0., 40.],
[ 0., 0., 1.]])
)
>>> z40([0,0])
array([ -92., -114., 40.])
>>> z40([92,114])
array([ 92., 114., 40.])
>>> bounding_box(z40, (x_spec[1], y_spec[1]))
((-92.0, 92.0), (-114.0, 114.0), (40.0, 40.0))
"""
(xmin, xmax), xno = x_spec
x_tick = (xmax-xmin) / (xno - 1.0)
(ymin, ymax), yno = y_spec
y_tick = (ymax-ymin) / (yno - 1.0)
origin = [xmin, ymin, z]
colvectors = np.asarray([[x_tick, 0],
[0, y_tick],
[0, 0]])
T = from_matrix_vector(colvectors, origin)
affine_domain = CoordinateSystem(['i_x', 'i_y'], 'slice')
affine_range = CoordinateSystem(lps_output_coordnames, output_space)
return AffineTransform(affine_domain,
affine_range,
T)
def from_params(innames, outnames, params):
"""
Create an `Affine` instance from sequences of innames and outnames.
Parameters
----------
innames : ``tuple`` of ``string``
The names of the axes of the input coordinate systems
outnames : ``tuple`` of ``string``
The names of the axes of the output coordinate systems
params : `Affine`, `ndarray` or `(ndarray, ndarray)`
An affine mapping between the input and output coordinate
systems. This can be represented either by a single
ndarray (which is interpreted as the representation of the
mapping in homogeneous coordinates) or an (A,b) tuple.
Returns
-------
aff : `Affine` object instance
Notes
-----
:Precondition: ``len(shape) == len(names)``
:Raises ValueError: ``if len(shape) != len(names)``
"""
if type(params) == type(()):
A, b = params
params = affines.from_matrix_vector(A, b)
ndim = (len(innames) + 1, len(outnames) + 1)
if params.shape != ndim[::-1]:
raise ValueError('shape and number of axis names do not agree')
dtype = params.dtype
input_coords = CoordinateSystem(innames, "input")
output_coords = CoordinateSystem(outnames, 'output')
return Affine(params, input_coords, output_coords)
def test_from_matrix_vector():
mat, vec, xform = build_xform()
newxform = affines.from_matrix_vector(mat, vec)
assert_equal, newxform, xform
def yslice(y, x_spec, z_spec, output_space=''):
""" Return a slice through a 3d box with y fixed.
Parameters
----------
y : float
The value at which y is fixed.
xspec : ([float,float], int)
Tuple representing the x-limits of the bounding
box and the number of points.
zspec : ([float,float], int)
Tuple representing the z-limits of the bounding
box and the number of points.
output_space : str, optional
Origin of the range CoordinateSystem.
Returns
-------
affine_transform : AffineTransform
An affine transform that describes an plane in
LPS coordinates with y fixed.
Examples
--------
>>> x_spec = ([-92,92], 93) # voxels of size 2 in x, starting at -92, ending at 92
>>> z_spec = ([-70,100], 86) # voxels of size 2 in z, starting at -70, ending at 100
>>>
>>> y70 = yslice(70, x_spec, z_spec)
>>> y70
AffineTransform(
function_domain=CoordinateSystem(coord_names=('i_x', 'i_z'), name='slice', coord_dtype=float64),
function_range=CoordinateSystem(coord_names=('x+LR', 'y+PA', 'z+SI'), name='', coord_dtype=float64),
affine=array([[ 2., 0., -92.],
[ 0., 0., 70.],
[ 0., 2., -70.],
[ 0., 0., 1.]])
)
>>> y70([0,0])
array([-92., 70., -70.])
>>> y70([92,85])
array([ 92., 70., 100.])
>>>
>>> bounding_box(y70, (x_spec[1], z_spec[1]))
([-92.0, 92.0], [70.0, 70.0], [-70.0, 100.0])
"""
xlim = x_spec[0]
zlim = z_spec[0]
shape = (z_spec[1], x_spec[1])
origin = [xlim[0],y,zlim[0]]
colvectors = [[(xlim[1]-xlim[0])/(shape[1] - 1.),0,0],
[0,0,(zlim[1]-zlim[0])/(shape[0] - 1.)]]
T = from_matrix_vector(np.vstack(colvectors).T, origin)
affine_domain = CoordinateSystem(['i_x', 'i_z'], 'slice')
affine_range = CoordinateSystem(lps_output_coordnames, output_space)
return AffineTransform(affine_domain,
affine_range,
T)
