"""Different Reflectance function definition.

Author: Travis Driver
"""
import numpy as np

from typing import Tuple


def lunar_lambert_reflectance(
    R_CB: np.ndarray, r_BC_C: np.ndarray, l_B: np.ndarray, s_C: np.ndarray, n_B: np.ndarray
) -> Tuple[float, float, float, float]:
    s_B = (R_CB.T @ s_C.reshape((3, -1))).flatten()
    r_B = (-R_CB.T @ r_BC_C.reshape((3, -1))).flatten()
    e_B = r_B - l_B
    e_B /= np.linalg.norm(e_B)
    cs = np.sum(s_B * n_B)
    ce = np.sum(e_B * n_B)
    phi = np.arccos(np.sum(s_B * e_B))
    L = np.exp(-np.rad2deg(phi) / 60.0)
    reflect = (1 - L) * cs + L * 2.0 * cs / (cs + ce)

    return reflect, np.arccos(cs), np.arccos(ce), phi


def schroder2013_reflectance(
    R_CB: np.ndarray, r_BC_C: np.ndarray, l_B: np.ndarray, s_C: np.ndarray, n_B: np.ndarray
) -> Tuple[float, float, float, float]:
    s_B = (R_CB.T @ s_C.reshape((3, -1))).flatten()
    r_B = (-R_CB.T @ r_BC_C.reshape((3, -1))).flatten()
    e_B = r_B - l_B
    e_B /= np.linalg.norm(e_B)
    cs = np.sum(s_B * n_B)
    ce = np.sum(e_B * n_B)
    phi = np.arccos(np.sum(s_B * e_B))

    cp0, cp1 = 0.830, -7.22e-3 * 180 / np.pi
    L = cp0 + cp1 * phi

    c0, c1, c2, c3, c4 = (
        0.301,
        -5.17e-3 * 180.0 / np.pi,
        5.51e-5 * (180.0 / np.pi) ** 2,
        -3.13e-7 * (180.0 / np.pi) ** 3,
        0.699e-9 * (180.0 / np.pi) ** 4,
    )
    aeq = c0 + c1 * phi + c2 * phi ** 2 + c3 * phi ** 3 + c4 * phi ** 4

    reflect = aeq / 0.301 * ((1 - L) * cs + L * 2.0 * cs / (cs + ce))

    return reflect, np.arccos(cs), np.arccos(ce), phi