prysm.geometry#

Functions used to generate various geometrical constructs.

prysm.geometry.gaussian(sigma, x, y, center=(0, 0))#

Generate a gaussian mask with a given sigma.

Parameters:

  • sigma (float) – width parameter of the gaussian, expressed in the same units as x and y

  • x (numpy.ndarray) – x spatial coordinates, 2D or 1D

  • y (numpy.ndarray) – y spatial coordinates, 2D or 1D

  • center (tuple of float) – center of the gaussian, (x,y)

Returns:

mask with gaussian shape

Return type:

numpy.ndarray

prysm.geometry.rectangle(width, x, y, height=None, angle=0)#

Generate a rectangular, with the “width” axis aligned to ‘x’.

Parameters:

  • width (float) – diameter of the rectangle, relative to the width of the array. width=1 fills the horizontal extent when angle=0

  • height (float) – diameter of the rectangle, relative to the height of the array. height=1 fills the vertical extent when angle=0. If None, inherited from width to make a square

  • angle (float) – angle

  • x (numpy.ndarray) – x spatial coordinates, 2D

  • y (numpy.ndarray) – y spatial coordinates, 2D

Returns:

array with the rectangle painted at 1 and the background at 0

Return type:

numpy.ndarray

prysm.geometry.rotated_ellipse(width_major, width_minor, x, y, major_axis_angle=0)#

Generate a binary mask for an ellipse, centered at the origin.

Parameters:

  • width_major (float) – width of the ellipse in its major axis

  • width_minor (float) – width of the ellipse in its minor axis

  • major_axis_angle (float) – angle of the major axis w.r.t. the x axis, degrees

  • x (numpy.ndarray) – x spatial coordinates, 2D

  • y (numpy.ndarray) – y spatial coordinates, 2D

Returns:

An ndarray of shape (samples,samples) of value 0 outside the ellipse and value 1 inside the ellipse

Return type:

numpy.ndarray

prysm.geometry.square(x, y)#

Create a square mask.

Parameters:

  • samples (int, optional) – number of samples in the square output array

  • x (numpy.ndarray) – x spatial coordinates, 2D

  • y (numpy.ndarray) – y spatial coordinates, 2D

Returns:

binary ndarray representation of the mask

Return type:

numpy.ndarray

prysm.geometry.truecircle(radius, r)#

Create a “true” circular mask with anti-aliasing.

Parameters:

  • samples (int, optional) – number of samples in the square output array

  • radius (float, optional) – radius of the shape in the square output array. radius=1 will fill the

  • r (numpy.ndarray) – radial coordinate, 2D

Returns:

nonbinary ndarray representation of the mask

Return type:

numpy.ndarray

Notes

Based on a more general algorithm by Jim Fienup

prysm.geometry.circle(radius, r)#

Create a circular mask.

Parameters:

  • radius (float) – radius of the circle, same units as r. The return is 1 inside the radius and 0 outside

  • r (numpy.ndarray) – 2D array of radial coordinates

Returns:

binary ndarray representation of the mask

Return type:

numpy.ndarray

prysm.geometry.regular_polygon(sides, radius, x, y, center=(0, 0), rotation=0)#

Generate a regular polygon mask with the given number of sides.

Parameters:

  • sides (int) – number of sides to the polygon

  • radius (float, optional) – radius of the regular polygon. For R=1, will fill the x and y extent

  • x (numpy.ndarray) – x spatial coordinates, 2D or 1D

  • y (numpy.ndarray) – y spatial coordinates, 2D or 1D

  • center (tuple of float) – center of the gaussian, (x,y)

  • rotation (float) – rotation of the polygon, degrees

Returns:

mask for regular polygon with radius equal to the array radius

Return type:

numpy.ndarray

prysm.geometry.spider(vanes, width, x, y, rotation=0, center=(0, 0), rotation_is_rad=False)#

Generate the mask for a spider.

Parameters:

  • vanes (int) – number of spider vanes

  • width (float) – width of the vanes in array units, i.e. a width=1/128 spider with arydiam=1 and samples=128 will be 1 pixel wide

  • x (numpy.ndarray) – x spatial coordinates, 2D or 1D

  • y (numpy.ndarray) – y spatial coordinates, 2D or 1D

  • rotation (float, optional) – rotational offset of the vanes, clockwise

  • center (tuple of float) – point from which the vanes emanate, (x,y)

  • rotation_is_rad (bool, optional) – if True, the rotation parameter is interpreted to be in radians

Returns:

array, 0 inside the spider and 1 outside

Return type:

numpy.ndarray

prysm.geometry.offset_circle(radius, x, y, center)#

Rasterize an offset circle.

Parameters:

  • radius (float) – radius of the circle, same units as x and y

  • x (numpy.ndarray) – array of x coordinates

  • y (numpy.ndarray) – array of y coordinates

  • center (tuple) – tuple of (x, y) centers

Returns:

ndarray containing the boolean mask

Return type:

numpy.ndarray

prysm.geometry.rectangle_with_corner_fillets(width, height, cradius, x, y, center=(0, 0), rotation=0)#

Shade a rectangle with filleted (circular arc) corners.

Parameters:

  • width (float) – half-width of the rectangle, same units as x and y

  • height (float) – half-height of the rectangle, same units as x and y

  • cradius (float) – radius of the corner fillets

  • x (numpy.ndarray) – x coordinates

  • y (numpy.ndarray) – y coordinates

  • center (tuple of float) – (x,y) center of the rectangle

  • rotation (float) – degrees of rotation about coordinate grid center

Returns:

1 inside “squircle”, 0 outside

Return type:

numpy.ndarray

prysm.geometry.chebygauss_quadrature_xy(rings, radius=1, spokes=-1, center=(0, 0))#

Use Chebyshev-Gauss quadrature to sample a polar coordinate grid.

Parameters:

  • rings (int) – number of rings to use; degree of radial sampling

  • radius (float) – radius of the grid, process units

  • spokes (int, optional) – number of spokes if -1, use rings*2 + 1

  • center (tuple) – (x,y) center point of the grid

Returns:

Chebyshev-Gauss-Lobatto points (x,y)

Return type:

numpy.ndarray