Generates a very accurate antialiased disk, without super sampling a very large bitmap. Works correctly only for even values of N.

antialiased_disk_mask.py

import numpy
import scipy.integrate as integrate

def get_disk_mask(N):
    def F(x):
        return (1 - x ** 2) ** .5

    # Build a quarter
    M = N // 2
    quarter = numpy.zeros((M, M))
    for i in range(M):
        max_slice_len = F((i + 0) / M)
        min_slice_len = F((i + 1) / M)

        j_max = int(numpy.floor(M * max_slice_len))
        j_min = int(numpy.floor(M * min_slice_len))

        if i <= j_max:
            column_area, err = integrate.quad(F, i / M, (i + 1) / M)

            delta = column_area - j_min / M ** 2
            fraction = delta * M ** 2
        
            if j_max == j_min:
                quarter[i,:j_min], quarter[i,j_min]  = 1, fraction
                quarter[:j_min, i], quarter[j_min,i]  = 1, fraction
            else:
                if fraction < 1:
                   quarter[i,:j_min], quarter[i,j_min]  = 1, fraction
                   quarter[:j_min,i], quarter[j_min,i]  = 1, fraction
                else:
                    quarter[i,:j_max], quarter[i,j_max]  = 1, fraction - 1
                    quarter[:j_max,i], quarter[j_max,i]  = 1, fraction - 1

    # Assemble the quarters
    ret = numpy.zeros((N, N))
    ret[M:,M:] = quarter
    ret[:M,M:] = numpy.flip(quarter, axis = 0)
    ret[M:,:M] = numpy.flip(quarter, axis = 1)
    ret[:M,:M] = numpy.flip(quarter, axis = (0, 1))
    
    # Job done
    return ret