# -*- coding: utf-8 -*-
# Copyright 2016 by Forschungszentrum Juelich GmbH
# Author: J. Caron
#
"""Provide simple shapes.
This module is a collection of some methods that return a 3-dimensional
matrix that represents the field volume and consists of boolean values.
This matrix is used in the functions of the :mod:`~.magcreator` module to create
:class:`~pyramid.fielddata.VectorData` objects which store the field information.
"""
import logging
import numpy as np
__all__ = ['slab', 'disc', 'ellipse', 'ellipsoid', 'sphere', 'filament', 'pixel']
_log = logging.getLogger(__name__)
def slab(dim, center, width):
"""Create the shape of a slab.
Parameters
----------
dim : tuple (N=3)
The dimensions of the grid `(z, y, x)`.
center : tuple (N=3)
The center of the slab in pixel coordinates `(z, y, x)`.
width : tuple (N=3)
The width of the slab in pixel coordinates `(z, y, x)`.
Returns
-------
shape : :class:`~numpy.ndarray` (N=3)
The shape as a 3D-array.
"""
_log.debug('Calling slab')
assert np.shape(dim) == (3,), 'Parameter dim has to be a tuple of length 3!'
assert np.shape(center) == (3,), 'Parameter center has to be a tuple of length 3!'
assert np.shape(width) == (3,), 'Parameter width has to be a tuple of length 3!'
zz, yy, xx = np.indices(dim) + 0.5
xx_shape = np.where(abs(xx - center[2]) <= width[2] / 2, True, False)
yy_shape = np.where(abs(yy - center[1]) <= width[1] / 2, True, False)
zz_shape = np.where(abs(zz - center[0]) <= width[0] / 2, True, False)
return np.logical_and(np.logical_and(xx_shape, yy_shape), zz_shape)
def disc(dim, center, radius, height, axis='z'):
"""Create the shape of a cylindrical disc in x-, y-, or z-direction.
Parameters
----------
dim : tuple (N=3)
The dimensions of the grid `(z, y, x)`.
center : tuple (N=3)
The center of the disc in pixel coordinates `(z, y, x)`.
radius : float
The radius of the disc in pixel coordinates.
height : float
The height of the disc in pixel coordinates.
axis : {'z', 'y', 'x'}, optional
The orientation of the disc axis. The default is 'z'.
Returns
-------
shape : :class:`~numpy.ndarray` (N=3)
The shape as a 3D-array.
"""
_log.debug('Calling disc')
assert np.shape(dim) == (3,), 'Parameter dim has to be a a tuple of length 3!'
assert np.shape(center) == (3,), 'Parameter center has to be a a tuple of length 3!'
assert radius > 0 and np.shape(radius) == (), 'Radius has to be a positive scalar value!'
assert height > 0 and np.shape(height) == (), 'Height has to be a positive scalar value!'
assert axis in {'z', 'y', 'x'}, 'Axis has to be x, y or z (as a string)!'
zz, yy, xx = np.indices(dim) + 0.5
xx -= center[2]
yy -= center[1]
zz -= center[0]
if axis == 'z':
uu, vv, ww = xx, yy, zz
elif axis == 'y':
uu, vv, ww = zz, xx, yy
elif axis == 'x':
uu, vv, ww = yy, zz, xx
else:
raise ValueError('{} is not a valid argument (use x, y or z)'.format(axis))
return np.logical_and(np.where(np.hypot(uu, vv) <= radius, True, False),
np.where(abs(ww) <= height / 2, True, False))
def ellipse(dim, center, width, height, axis='z'):
"""Create the shape of an elliptical cylinder in x-, y-, or z-direction.
Parameters
----------
dim : tuple (N=3)
The dimensions of the grid `(z, y, x)`.
center : tuple (N=3)
The center of the ellipse in pixel coordinates `(z, y, x)`.
width : tuple (N=2)
Length of the two axes of the ellipse.
height : float
The height of the ellipse in pixel coordinates.
axis : {'z', 'y', 'x'}, optional
The orientation of the ellipse axis. The default is 'z'.
Returns
-------
shape : :class:`~numpy.ndarray` (N=3)
The shape as a 3D-array.
"""
_log.debug('Calling ellipse')
assert np.shape(dim) == (3,), 'Parameter dim has to be a a tuple of length 3!'
assert np.shape(center) == (3,), 'Parameter center has to be a a tuple of length 3!'
assert np.shape(width) == (2,), 'Parameter width has to be a a tuple of length 2!'
assert height > 0 and np.shape(height) == (), 'Height has to be a positive scalar value!'
assert axis in {'z', 'y', 'x'}, 'Axis has to be x, y or z (as a string)!'
zz, yy, xx = np.indices(dim) + 0.5
xx -= center[2]
yy -= center[1]
zz -= center[0]
if axis == 'z':
uu, vv, ww = xx, yy, zz
elif axis == 'y':
uu, vv, ww = xx, zz, yy
elif axis == 'x':
uu, vv, ww = yy, zz, xx
else:
raise ValueError('{} is not a valid argument (use x, y or z)'.format(axis))
distance = np.hypot(uu / (width[1] / 2), vv / (width[0] / 2))
return np.logical_and(np.where(distance <= 1, True, False),
np.where(abs(ww) <= height / 2, True, False))
def ellipsoid(dim, center, width):
"""Create the shape of an ellipsoid.
Parameters
----------
dim : tuple (N=3)
The dimensions of the grid `(z, y, x)`.
center : tuple (N=3)
The center of the ellipsoid in pixel coordinates `(z, y, x)`.
width : tuple (N=3)
The width of the ellipsoid `(z, y, x)`.
Returns
-------
shape : :class:`~numpy.ndarray` (N=3)
The shape as a 3D-array.
"""
_log.debug('Calling ellipsoid')
assert np.shape(dim) == (3,), 'Parameter dim has to be a a tuple of length 3!'
assert np.shape(center) == (3,), 'Parameter center has to be a a tuple of length 3!'
assert np.shape(width) == (3,), 'Parameter width has to be a a tuple of length 3!'
zz, yy, xx = np.indices(dim) + 0.5
distance = np.sqrt(((xx - center[2]) / (width[2] / 2)) ** 2
+ ((yy - center[1]) / (width[1] / 2)) ** 2
+ ((zz - center[0]) / (width[0] / 2)) ** 2)
return np.where(distance <= 1, True, False)
def sphere(dim, center, radius):
"""Create the shape of a sphere.
Parameters
----------
dim : tuple (N=3)
The dimensions of the grid `(z, y, x)`.
center : tuple (N=3)
The center of the sphere in pixel coordinates `(z, y, x)`.
radius : float
The radius of the sphere in pixel coordinates.
Returns
-------
shape : :class:`~numpy.ndarray` (N=3)
The shape as a 3D-array.
"""
_log.debug('Calling sphere')
assert np.shape(dim) == (3,), 'Parameter dim has to be a a tuple of length 3!'
assert np.shape(center) == (3,), 'Parameter center has to be a a tuple of length 3!'
assert radius > 0 and np.shape(radius) == (), 'Radius has to be a positive scalar value!'
zz, yy, xx = np.indices(dim) + 0.5
distance = np.sqrt((xx - center[2]) ** 2 + (yy - center[1]) ** 2 + (zz - center[0]) ** 2)
return np.where(distance <= radius, True, False)
def filament(dim, pos, axis='y'):
"""Create the shape of a filament.
Parameters
----------
dim : tuple (N=3)
The dimensions of the grid `(z, y, x)`.
pos : tuple (N=2)
The position of the filament in pixel coordinates `(coord1, coord2)`.
`coord1` and `coord2` stand for the two axes, which are perpendicular to `axis`. For
the default case (`axis = y`), it is `(coord1, coord2) = (z, x)`.
axis : {'y', 'x', 'z'}, optional
The orientation of the filament axis. The default is 'y'.
Returns
-------
shape : :class:`~numpy.ndarray` (N=3)
The shape as a 3D-array.
"""
_log.debug('Calling filament')
assert np.shape(dim) == (3,), 'Parameter dim has to be a tuple of length 3!'
assert np.shape(pos) == (2,), 'Parameter pos has to be a tuple of length 2!'
assert axis in {'z', 'y', 'x'}, 'Axis has to be x, y or z (as a string)!'
shape = np.zeros(dim, dtype=bool)
if axis == 'z':
shape[:, pos[0], pos[1]] = True
elif axis == 'y':
shape[pos[0], :, pos[1]] = True
elif axis == 'x':
shape[pos[0], pos[1], :] = True
return shape
def pixel(dim, pixel):
"""Create the shape of a single pixel.
Parameters
----------
dim : tuple (N=3)
The dimensions of the grid `(z, y, x)`.
pixel : tuple (N=3)
The coordinates of the pixel `(z, y, x)`.
Returns
-------
shape : :class:`~numpy.ndarray` (N=3)
The shape as a 3D-array.
"""
_log.debug('Calling pixel')
assert np.shape(dim) == (3,), 'Parameter dim has to be a tuple of length 3!'
assert np.shape(pixel) == (3,), 'Parameter pixel has to be a tuple of length 3!'
shape = np.zeros(dim, dtype=bool)
shape[pixel] = True
return shape