The Python Game Book

calculates the tiles connected by a line in a 2D-array:

see also: https://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm

def get_line(start, end):
    """Bresenham's Line Algorithm
       Produces a list of tuples from start and end
       source: http://www.roguebasin.com/index.php?title=Bresenham%27s_Line_Algorithm#Python
       see also: https://en.wikipedia.org/wiki/Bresenham%27s_line_algorithm

       #>>> points1 = get_line((0, 0), (3, 4))
       # >>> points2 = get_line((3, 4), (0, 0))
       #>>> assert(set(points1) == set(points2))
       #>>> print points1
       #[(0, 0), (1, 1), (1, 2), (2, 3), (3, 4)]
       #>>> print points2
       #[(3, 4), (2, 3), (1, 2), (1, 1), (0, 0)]
    """
    # Setup initial conditions
    x1, y1 = start
    x2, y2 = end
    dx = x2 - x1
    dy = y2 - y1

    # Determine how steep the line is
    is_steep = abs(dy) > abs(dx)

    # Rotate line
    if is_steep:
        x1, y1 = y1, x1
        x2, y2 = y2, x2

    # Swap start and end points if necessary and store swap state
    swapped = False
    if x1 > x2:
        x1, x2 = x2, x1
        y1, y2 = y2, y1
        swapped = True

    # Recalculate differentials
    dx = x2 - x1
    dy = y2 - y1

    # Calculate error
    error = int(dx / 2.0)
    ystep = 1 if y1 < y2 else -1

    # Iterate over bounding box generating points between start and end
    y = y1
    points = []
    for x in range(x1, x2 + 1):
        coord = (y, x) if is_steep else (x, y)
        points.append(coord)
        error -= abs(dy)
        if error < 0:
            y += ystep
            error += dx

    # Reverse the list if the coordinates were swapped
    if swapped:
        points.reverse()
    return points