136 lines
3.4 KiB
Python
136 lines
3.4 KiB
Python
import numpy as np
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from sympy import *
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import math
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unit = lambda v: v/np.linalg.norm(v)
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def problem_1():
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p = np.array([1, 4, 8])
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e = np.array([0, 0, 0])
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s = np.array([2, 2, 10])
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i = p - e
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print("incoming", i)
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print("|I| =", np.linalg.norm(i))
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n = s - p
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print("normal", n)
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n_norm = unit(n)
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print("normal_norm", n_norm)
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cos_theta_i = np.dot(-i, n) / (np.linalg.norm(i) * np.linalg.norm(n))
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print("part a = cos^{-1} of ", cos_theta_i)
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print(np.arccos(cos_theta_i))
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proj = n_norm * np.linalg.norm(i) * cos_theta_i
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print("proj", proj)
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p_ = p + proj
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print("proj point", p_)
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v2 = p_ - e
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print("v2", v2)
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sin_theta_i = np.sin(np.arccos(cos_theta_i))
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print("sin theta_i =", sin_theta_i)
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theta_t = np.arcsin(1.0 / 1.5 * sin_theta_i)
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print("approx answer for part d", theta_t)
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uin = unit(n_norm)
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print("unit inv normal", uin)
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uperp = unit(v2)
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print("uperp", uperp)
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answer_1e = uin + math.tan(theta_t) * uperp - p
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print("1e answer", unit(answer_1e))
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def problem_4():
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print("part 4a.")
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up = np.array([0, 1, 0])
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viewing_dir = np.array([1, -1, -1])
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n = unit(viewing_dir)
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print(f"{n = }")
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u = unit(np.cross(up, n))
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print(f"{u = }")
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v = np.cross(n, u)
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print(f"{v = }")
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print(math.sqrt(1 / 6.0))
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print(math.sqrt(2 / 3.0))
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def build_translation_matrix(vec):
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return np.array([
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[1, 0, 0, vec[0]],
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[0, 1, 0, vec[1]],
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[0, 0, 1, vec[2]],
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[0, 0, 0, 1],
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])
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def problem_5():
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b1 = build_translation_matrix(np.array([0, 0, 5]))
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theta = math.radians(-90)
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sin_theta = round( math.sin(theta), 5)
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cos_theta = round(math.cos(theta), 5)
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b2 = np.array([
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[cos_theta, 0, sin_theta, 0],
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[0, 1, 0, 0],
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[-sin_theta, 0, cos_theta, 0],
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[0, 0, 0, 1],
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])
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b3 = build_translation_matrix(np.array([0, 0, -5]))
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print("b1", b1)
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print("b2", b2)
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print("b3", b3)
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M = b3 @ b2 @ b1
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print("M", M)
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ex1 = np.array([1, 1, -4, 1])
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print("ex1", ex1, M @ ex1)
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up = np.array([0, 1, 0])
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n = np.array([1, 0, 0])
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u = unit(np.cross(up, n))
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v = np.cross(n, u)
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print(f"{up = }, {n = }, {u = }, {v = }")
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eye = np.array([5, 0, -5])
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dx = -(np.dot(eye, u))
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dy = -(np.dot(eye, v))
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dz = -(np.dot(eye, n))
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print(f"{dx = }, {dy = }, {dz = }")
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def problem_8():
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def P(left, right, bottom, top, near, far):
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return np.array([
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[2.0 * near / (right - left), 0, (right + left) / (right - left), 0],
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[0, 2.0 * near / (top - bottom), (top + bottom) / (top - bottom), 0],
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[0, 0, -(far + near) / (far - near), -(2.0 * far * near) / (far - near)],
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[0, 0, -1, 0],
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])
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near = 0.5
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far = 20
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def compute_view(vfov, hfov):
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left = -math.tan(hfov) * near
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right = math.tan(hfov) * near
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bottom = -math.tan(vfov) * near
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top = math.tan(vfov) * near
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return left, right, bottom, top
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print("part 8a")
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vfov = hfov = math.radians(60)
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left, right, bottom, top = compute_view(vfov, hfov)
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print(P(left, right, bottom, top, near, far))
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print()
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print("\nPROBLEM 4 -------------------------"); problem_4()
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print("\nPROBLEM 8 -------------------------"); problem_8()
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print("\nPROBLEM 1 -------------------------"); problem_1()
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print("\nPROBLEM 5 -------------------------"); problem_5()
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