import numpy


def centroid(points: numpy.ndarray) -> numpy.ndarray:
    return points.mean(axis=0)


def kabsch_algorithm(actual_points: numpy.ndarray, expected_points: numpy.ndarray) -> numpy.ndarray:
    # TODO Заменить безликие C, V, S, W на что-то более внятное
    C = numpy.dot(numpy.transpose(actual_points), expected_points)
    V, S, W = numpy.linalg.svd(C)

    if (numpy.linalg.det(V) * numpy.linalg.det(W)) < 0.0:
        S[-1] = -S[-1]
        V[:, -1] = -V[:, -1]

    return numpy.dot(V, W)