feat: implement 2D and 3D taxicab (Manhattan) metrics

csa/geometry.py

@@ -169,3 +169,50 @@ def euclidMetric3d (g1, g2 = None):
     """
     g2 = g1 if g2 == None else g2
     return lambda i, j: euclidDistance3d (g1 (i), g2 (j))
+
+
+def taxicabDistance2d(p1, p2):
+    """Returns the taxicab (Manhattan) distance in 2D between two points
+    :param p1: The first point
+    :type p1: tuple (x, y)
+    :param p2: The second point
+    :type p2: tuple (x, y)
+    :return: The taxicab distance
+    :rtype: float
+    """
+    return abs(p1[0] - p2[0]) + abs(p1[1] - p2[1])
+
+def taxicabMetric2d(g1, g2=None):
+    """Returns a taxicab metric for 2D points
+    :param g1: The first group of points
+    :type g1: callable
+    :param g2: The second group of points. If None, the first group of points is used
+    :type g2: callable
+    :return: A 2D taxicab metric function
+    :rtype: function
+    """
+    g2 = g1 if g2 is None else g2
+    return lambda i, j: taxicabDistance2d(g1(i), g2(j))
+
+def taxicabDistance3d(p1, p2):
+    """Returns the taxicab (Manhattan) distance in 3D between two points
+    :param p1: The first point
+    :type p1: numpy.array((3))
+    :param p2: The second point
+    :type p2: numpy.array((3))
+    :return: The taxicab distance
+    :rtype: float
+    """
+    return abs(p1[0] - p2[0]) + abs(p1[1] - p2[1]) + abs(p1[2] - p2[2])
+
+def taxicabMetric3d(g1, g2=None):
+    """Returns a taxicab metric for 3D points
+    :param g1: The first group of points
+    :type g1: callable
+    :param g2: The second group of points. If None, the first group of points is used
+    :type g2: callable
+    :return: A 3D taxicab metric function
+    :rtype: function
+    """
+    g2 = g1 if g2 is None else g2
+    return lambda i, j: taxicabDistance3d(g1(i), g2(j))