import numpy as np
from math import cos, sin
from typing import List, Union, Tuple


def create_rx(unit_axis: np.ndarray) -> np.ndarray:
    (a, b, c) = unit_axis.tolist()
    d = (b ** 2 + c ** 2) ** 0.5
    return np.array(
        [[1, 0, 0, 0], [0, c / d, -b / d, 0], [0, b / d, c / d, 0], [0, 0, 0, 1]]
    )


def create_ry(unit_axis: np.ndarray) -> np.ndarray:
    (a, b, c) = unit_axis.tolist()
    d = (b ** 2 + c ** 2) ** 0.5
    return np.array([[d, 0, -a, 0], [0, 1, 0, 0], [a, 0, d, 0], [0, 0, 0, 1]])


def create_rz(angel: float) -> np.ndarray:
    return np.array(
        [
            [cos(angel), -sin(angel), 0, 0],
            [sin(angel), cos(angel), 0, 0],
            [0, 0, 1, 0],
            [0, 0, 0, 1],
        ]
    )


def create_t(axis: np.ndarray) -> np.ndarray:
    (x1, y1, z1) = axis.tolist()
    return np.array([[1, 0, 0, -x1], [0, 1, 0, -y1], [0, 0, 1, -z1], [0, 0, 0, 1]])


def rotation_matrix(
    angel: float, axis_start: np.ndarray, axis_end: np.ndarray
) -> np.ndarray:
    # 依据《计算机图形学》第4版 9.28公式
    axis = axis_end - axis_start
    unit_axis = axis / np.linalg.norm(axis)
    rz = create_rz(angel)
    rx = create_rx(unit_axis)
    ry = create_ry(unit_axis)
    t = create_t(axis_start)
    t_i = np.linalg.inv(t)
    rx_i = np.linalg.inv(rx)
    ry_i = np.linalg.inv(ry)
    r_transform = t_i @ rx_i @ ry_i @ rz @ ry @ rx @ t
    return r_transform


def rotation(
    angel: float, axis_start: np.ndarray, axis_end: np.ndarray, points: np.ndarray
) -> np.ndarray:
    _rotation = Rotation(angel, axis_start.tolist(), axis_end.tolist())
    return np.array(_rotation.rotate(points.tolist()))


class Rotation:
    def __init__(self, angel: float, axis_start: List[float], axis_end: List[float]):
        self._r_transform = rotation_matrix(
            angel, np.array(axis_start), np.array(axis_end)
        )

    def rotate(self, points: List[Union[List[float], Tuple[float]]])->List:
        np_points = np.array(points)
        r_transform = self._r_transform
        expand_point = np.concatenate(
            (np_points, np.ones((np_points.shape[0], 1))), axis=1
        )
        transformed_points = r_transform @ expand_point.T
        return transformed_points[:-1, :].T.tolist()