5.1. Geometry¶
Handles geometry of the inversion task. This includes definition of reconstruction grid, creating artificial geometry and computation of geometry (sensitivity/contribution) matrices. Currently only algorithms using single line of sight approximation are implemented.
5.1.1. Geometry matrix¶
Module with numeric generators of geometry matrix.
-
tomotok.core.geometry.generators.calcam_sparse_line_3d(pupil, dirs, grid, step=0.001, rmin=None, elong=1.0, steps=None) Computes geometry matrix from calcam input using sparse_line_3d algorithm.
Assumes that pupil and dirs coordinates are (x, y, z) = (horizontal, horizontal, vertical)
Parameters: pupil : np.ndarray
(x, y, z) coordinates of pupil position
dirs : np.ndarray
(#rows, #columns, 3) line of sight direction vector coordinates
grid : tomotok.core.geometry.RegularGrid
reconstruction grid
step : float, optional
Integration step in meters.
rmin : float, optional
cut lines of sight if they intersect cylinder with radius of rmin, by default 0.3
elong : float, optional
multiplier for direction vectors elongation
Returns: sparse.csr_matrix
-
tomotok.core.geometry.generators.sparse_line(starts, ends, grid, step=0.001, rmin=-1) Computes geometry matrix using simple numerical integration algorithm.
Uses lines of sight start and end points in 3D Cartesian coordinates as input.
Parameters: starts, ends : ndarray
Contains lines of sight start/end points, with shape (…, 3)
grid : RegularGrid
Reconstruction grid
step : float, optional
Integration step, by default 1e-3
rmin : int, optional
Stops the lines of sight if they intersect cylinder with radius of rmin, by default -1
Returns: sparse.csr_matrix
-
tomotok.core.geometry.generators.sparse_line_3d(rchord, vchord, grid, ychord=None, step=0.001, rmin=None) Computes geometry matrix using simple numerical integration algorithm.
Assumes toroidally symmetric reconstruction nodes. Optimized version working with sparse matrices.
Parameters: rchord : array-like
radial coordinates of chord start and end points
vchord : array-like
vertical coordinates of chord start and end points
grid : RegularGrid
ychord : array_like, optional
if specified, 3D Cartesian coordinates are assumed and rchord represents coordinates of x axis
step : float, optional
Integration step in meters.
rmin : float, optional
Stop iteration if r is lower. Useful when chords may go through central column.
Returns: sparse.csr_matrix
5.1.2. Reconstruction grids¶
-
class
tomotok.core.geometry.RegularGrid(nr: int, nz: int, rlims: typing.Tuple[float, float], zlims: typing.Tuple[float, float]) → None Rectangular grid of regularly spaced rectangles of same size
Describes rectangular reconstruction grid consisting of regularly spaced toroidally symmetric nodes that have rectangular projection to reconstruction plane.
Attributes
nr (int) number of nodes along r (radial) axis nz (int) number of nodes along z (vertical) axis nodes_num (int) total number of nodes rmin, rmax (float) limits of r axis zmin, zmax (float) limits of z axis rlims, zlims (Tuple[float, float]) grid limits along respective axis dr, dz (float) dimension of node in r or z axis r_border, z_border (numpy.ndarray) arrays containing r resp. z coordinates of node borders r_center, z_center (numpy.ndarray) arrays containing r resp. z coordinates of node centers Methods
-
centre Returns the mean of rmin, rmax and zmin, zmax
-
corners(mask: numpy.ndarray = None) → numpy.ndarray Creates an array with r, z coordinates of node corners.
Corners are in clockwise order starting with top left corner.
Parameters: mask : numpy.ndarray
2D bool matrix for selecting nodes, shape (#z, #r)
Returns: numpy.ndarray
corner coordinates for each node in reconstruction plane, shape (#z, #r, 4, 2)
-
extent Grid extent in format for use in matplotlib
Returns: tuple of floats
rmin, rmax, zmin, zmax
-
is_inside(r: numpy.ndarray, z: numpy.ndarray) → numpy.ndarray Selects nodes with centers inside given polygon.
Parameters: r, z : numpy.ndarray
Coordinate vectors of polygon
Returns: numpy.ndarray
Mask matrix for pixgrid with True values for nodes inside polygon
-
is_inside_any(r: numpy.ndarray, z: numpy.ndarray) → numpy.ndarray Selects nodes with at least one corner inside given polygon.
Parameters: r, z : numpy.ndarray
Coordinate vectors of polygon
Returns: numpy.ndarray
Mask matrix for pixgrid with True values for nodes inside polygon
-
nodevol Volumes of individual nodes
Returns: numpy.ndarray
matrix with volume values for each node with shape (nz, nr)
-
5.1.3. Lines of sight¶
Routines for generation of line of sight start and end points.
Creates the lines of sights in x axis direction and then rotates them about the other horizontal axis, then about vertical axis.
-
tomotok.core.geometry.los.generate_directions(num=(10, 1), fov=(45, 0), axis=(1, 0, 0), elong=1.0) Creates direction vectors for lines of sight using camera like convention.
The first line of sight is top left, then the numbering follows a row, the last one is bottom right.
Parameters: num : int or (int,int), optional
number of generated chords (vertical, horizontal)
fov : float, or tuple of two float, optional
vertical or (vertical, horizontal) field of view in degrees
axis : tuple of three floats, optional
direction of symmetry axis
elong : float, optional
vector length multiplier
Returns: dirs : numpy.ndarray
contains direction vectors cartesian coordinates, shape (#los, 3)
-
tomotok.core.geometry.los.generate_los(pinhole=(0, 0, 0), num=(10, 1), fov=(45, 0), axis=(1, 0, 0), elong=1.0) Creates line of sight endpoints with uniform distribution.
Parameters: num : int or (int,int), optional
number of generated chords (vertical, horizontal)
pinhole : tuple of three floats, optional
r and z coordinates of pinhole
fov : float, or tuple of two float, optional
vertical and horizontal field of view in degrees
axis : tuple of three floats, optional
direction of chordal axis
elong : float, optional
chord length multiplier
Returns: start : numpy.ndarray
array with line of sight start points coordinates, shape (#los, 3)
end : numpy.ndarray
array with line of sight end points coordinates, shape (#los, 3)
-
tomotok.core.geometry.los.rot_h(points, angle) Rotates given points in horizontal direction, that is about vertical axis z.
Parameters: points : numpy.ndarray
3D coordinates of points to be rotated with shape (#points, 3)
angle : float
angle of rotation in radians
Returns: numpy.ndarray
array of rotated points
-
tomotok.core.geometry.los.rot_v(points, angle) Rotates given points in vertical direction, that is about horizontal y axis perpendicular to r/x.
Should be done before horizontal rotation.
Parameters: points : numpy.ndarray
3D coordinates of points to be rotated with shape (#points, 3)
angle : float
angle of rotation in radians
Returns: numpy.ndarray
array of rotated points