Compute the number of unique lines in a grid

uniquelines.py

#!/usr/bin/python

#
# Compute the number of unique lines in a grid
# @author Daniel Pulido <dpmcmlxxvi@gmail.com>
# @copyright Copyright (c) 2015 Daniel Pulido <dpmcmlxxvi@gmail.com>
# @file uniquelines.py
# @license MIT License (http://opensource.org/licenses/MIT)
#

import math

def uniquelines(nrows, ncols):
    """
    :param nrows: Number of rows
    :param ncols: Number of columns
    """

    def gridscan():
        for row in range(nrows):
            for col in range(ncols):
                yield col, row

    lines = set()
    for point1 in gridscan():
        for point2 in gridscan():
            if point1 == point2: continue
            dc = point1[0]-point2[0]
            dr = point2[1]-point1[1]
            R = math.sqrt(dc*dc + dr*dr)
            theta = math.atan2(dc, dr)
            rho = (point2[1] * point1[0] - point1[1] * point2[0]) / R
            line = (rho,theta)
            if line not in lines:
                lines.add(line)

    # Account for ambiguous 180 rotation
    numLines = len(lines)/2

    return numLines

def main():

    # Define grid sizes to compute
    for M in range(1, 10):
        for N in range(M, 10):
            count = uniquelines(M,N)
            print "M = ", M, "   N = ", N, "   Count = ", count

if __name__ == "__main__":
    main()