Commenting on https://twitter.com/AlbertoGzG/status/937262615457345539

ikePoleMathTest.py

import unittest

def ikePoleVector(root, mid, end):
    result = []
    for i in range(len(root)):
        v1 = end[i] - root[i]
        midV1 = v1 * 0.5
        v2 = end[i] - midV1
        v3 = mid[i] - v2
        vf = mid[i] + v3
        result.append(vf)
    return result


def normalizedPoleVector(root, mid, end):
    indices = range(len(root))
    a = [mid[i] - root[i] for i in indices]
    c = [end[i] - root[i] for i in indices]
    dotAC = sum([a[i] * c[i] for i in indices])
    dotCC = sum([c[i] * c[i] for i in indices])
    ratio = dotAC / dotCC

    result = []
    for i in indices:
        ref = c[i] * ratio
        v2 = root[i] + ref
        v3 = mid[i] - v2
        vf = mid[i] + v3
        result.append(vf)
    return result

class PoleVectorCase(unittest.TestCase):
    def test_ike_regular_sides(self):
        self.assertEqual(ikePoleVector([0.0, 0.0], [1.0, -1.0], [2.0, 0.0]), [1.0, -2.0])

    def test_ike_irregular_sides(self):
        self.assertEqual(ikePoleVector([0.0, 0.0], [0.1, -1.0], [2.0, 0.0]), [0.1, -2.0])  # fails

    def test_norm_regular_sides(self):
        self.assertEqual(normalizedPoleVector([0.0, 0.0], [1.0, -1.0], [2.0, 0.0]), [1.0, -2.0])

    def test_norm_irregular_sides(self):
        self.assertEqual(normalizedPoleVector([0.0, 0.0], [0.1, -1.0], [2.0, 0.0]), [0.1, -2.0])

if __name__ == "__main__":
    unittest.main(exit=False)