Hanna moves in a lattice

hanna_moves.py

# Hanna moves in a lattice where every point can be represented by a pair of integers.
# She moves from point A to point B and then takes a turn 90 degrees rightand starts 
# moving till she reaches the first point on the lattice. Find what's the 
# point she would reach?
#      A' . |
#      .    |
#      .    |  .   .  .  A
#      .    |            .
# -------------------------
#           |
#           |
#           |
#
# When you rotate clockwise a point A 90 degrees from origin,
#   you get A' => f(x,y) = (-y, x)
#
#
#           |         A   
#           |       .
#           |     B
#           |   .
#           | . 
# ----------O-------------
#           |
#           |
#           |
#
# Based on a point A from origin, you can find point B by:
#   By/Ay = Bx/Ax => By = Bx * Ay/Ax
#
#           |
#   A       |
#     .     |
#       .   |
#         . |
# ----------B--------------
#        .  |
#    .      |
# C         |
#
# To make things easier, we can move the points to get point B on origin.
# After Hanna rotate 90 degrees to the right on point B, 
#   she will find eventually point C.
# Let say that D is a point in a rect that is on B-C.
# Hanna will stop on a point on the lattice when the point (x,y) is integer
# So, from B we need to iterate Dx until we find a Dy integer
#
def rotate_90_clockwise(A):
  return (-A[1], A[0])

def find_B_y(A, x):
  return x * A[1]/A[0] if A[0] else A[1]

def find_next(A, B):
  # make B the origin
  Ao = (A[0] - B[0], A[1] - B[1])
  Bo = (0,0)
  # rotate Ao 90 clockwise
  C = rotate_90_clockwise(Ao)
  if C[0] == 0:
    # C is on y axis
    x = 0
    # Dy is one unit from origin
    y = C[1]/abs(C[1])
  else:
    found = False
    # from origin
    x = 0
    while not found:
      # inc x one unit
      x += C[0]/abs(C[0])
      y = find_B_y(C, x)
      # check if y is integer
      found = y == round(y)
  # move back from origin
  x, y = (x + B[0], y + B[1])
  return x, y

A = (-2, 3)
B = (3, 2)
D = find_next(A, B)
print(D)

B = (-4, 2)
A = (-2, 2)
D = find_next(A, B)
print(D)

B = (1, 20)
A = (1, 5)
D = find_next(A, B)
print(D)