51 lines
1.3 KiB
Python
51 lines
1.3 KiB
Python
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import numpy as np
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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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print("approx answer for part d", np.arcsin(1.0 / 1.5 * sin_theta_i))
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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, far = left, right = bottom, top = -1, 1
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print("part 8a", P(left, right, bottom, top, near, far))
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print()
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problem_8()
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problem_1()
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