import numpy as np
from sympy import *
import math

unit = lambda v: v/np.linalg.norm(v)

def problem_1():
    p = np.array([1, 4, 8])
    e = np.array([0, 0, 0])
    s = np.array([2, 2, 10])

    i = p - e
    print("incoming", i)
    print("|I| =", np.linalg.norm(i))
    n = s - p
    print("normal", n)

    n_norm = unit(n)
    print("normal_norm", n_norm)
    cos_theta_i = np.dot(-i, n) / (np.linalg.norm(i) * np.linalg.norm(n))
    print("part a = cos^{-1} of ", cos_theta_i)
    print(np.arccos(cos_theta_i))

    proj = n_norm * np.linalg.norm(i) * cos_theta_i
    print("proj", proj)

    p_ = p + proj
    print("proj point", p_)

    v2 = p_ - e
    print("v2", v2)

    sin_theta_i = np.sin(np.arccos(cos_theta_i))
    print("sin theta_i =", sin_theta_i)

    print("approx answer for part d", np.arcsin(1.0 / 1.5 * sin_theta_i))

def problem_4():
    print("part 4a.")

def problem_8():
    def P(left, right, bottom, top, near, far):
        return np.array([
            [2.0 * near / (right - left), 0, (right + left) / (right - left), 0],
            [0, 2.0 * near / (top - bottom), (top + bottom) / (top - bottom), 0],
            [0, 0, -(far + near) / (far - near), -(2.0 * far * near) / (far - near)],
            [0, 0, -1, 0],
        ])

    near = 0.5
    far = 20

    def compute_view(vfov, hfov):
        left = -math.tan(hfov) * near
        right = math.tan(hfov) * near
        bottom = -math.tan(vfov) * near
        top = math.tan(vfov) * near
        return left, right, bottom, top


    print("part 8a")
    vfov = hfov = math.radians(60)
    left, right, bottom, top = compute_view(vfov, hfov)
    print(P(left, right, bottom, top, near, far))
    print()

print("\nPROBLEM 4 -------------------------"); problem_4()
print("\nPROBLEM 8 -------------------------"); problem_8()
print("\nPROBLEM 1 -------------------------"); problem_1()