Mask a circular sector in a numpy array

Question

I have a code that slices a numpy array into a circle. I wish to recover only the values included in a certain range of angles from the circle and mask the array. For example: mask the original array with the (x,y) positions comprised between 0 and 45 degrees of the circle.

Is there a pythonic way for doing so?

Here's my (simplified) original code:

import numpy as np
matrix = np.zeros((500,500))
x = 240
y = 280
radius = 10
mask=np.ogrid[x-radius:x+radius+1,y-radius:y+radius+1]
matrix[mask]

Thanks in advance

Edit: I omitted that radius can vary.

Answer 1

I would do this by converting from cartesian to polar coordinates and constructing boolean masks for the circle and for the range of angles you want:

import numpy as np

def sector_mask(shape,centre,radius,angle_range):
    """
    Return a boolean mask for a circular sector. The start/stop angles in  
    `angle_range` should be given in clockwise order.
    """

    x,y = np.ogrid[:shape[0],:shape[1]]
    cx,cy = centre
    tmin,tmax = np.deg2rad(angle_range)

    # ensure stop angle > start angle
    if tmax < tmin:
            tmax += 2*np.pi

    # convert cartesian --> polar coordinates
    r2 = (x-cx)*(x-cx) + (y-cy)*(y-cy)
    theta = np.arctan2(x-cx,y-cy) - tmin

    # wrap angles between 0 and 2*pi
    theta %= (2*np.pi)

    # circular mask
    circmask = r2 <= radius*radius

    # angular mask
    anglemask = theta <= (tmax-tmin)

    return circmask*anglemask

For example:

from matplotlib import pyplot as pp
from scipy.misc import lena

matrix = lena()
mask = sector_mask(matrix.shape,(200,100),300,(0,50))
matrix[~mask] = 0
pp.imshow(matrix)
pp.show()