matrix_thing.py

def eastward(level, position):
    return (2**(level - 1)) * (int(position) % 2)

def southward(level, position):
    if int(position) < 2:
        return 0
    else:
        return 2**(level - 1)

def absolute_position(quadkey, x=0, y=0):
    level = len(quadkey)
    if level == 0:
        return (x,y)
    else:
        next_x = x + eastward(level, quadkey[0])
        next_y = y + southward(level, quadkey[0])
        return absolute_position(quadkey[1:], next_x, next_y)
    
class TestAbsolutePosition(unittest.TestCase):

    def test_absolute_position_top(self):
        x_0, y_0 = absolute_position('00')
        x_1, y_1 = absolute_position('01')
        x_2, y_2 = absolute_position('02')
        x_3, y_3 = absolute_position('03')
        self.assertEqual(0, x_0)
        self.assertEqual(0, y_0)
        self.assertEqual(1, x_1)
        self.assertEqual(0, y_1)
        self.assertEqual(0, x_2)
        self.assertEqual(1, y_2)
        self.assertEqual(1, x_3)
        self.assertEqual(1, y_3)

    def test_absolute_position_children(self):
        x_0, y_0 = absolute_position('003')
        x_1, y_1 = absolute_position('013')
        x_2, y_2 = absolute_position('022')
        x_3, y_3 = absolute_position('030')
        self.assertEqual(1, x_0)
        self.assertEqual(1, y_0)
        self.assertEqual(3, x_1)
        self.assertEqual(1, y_1)
        self.assertEqual(0, x_2)
        self.assertEqual(3, y_2)
        self.assertEqual(2, x_3)
        self.assertEqual(2, y_3)