72 lines
2.3 KiB
Python
72 lines
2.3 KiB
Python
import math as math
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import numpy as np
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def lookAt(eyeX, eyeY, eyeZ, cX, cY, cZ, upX, upY, upZ):
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F = np.matrix([eyeX - cX, eyeY -cY, eyeZ - cZ])
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UP = np.matrix([upX, upY, upZ])
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f = F / math.sqrt(np.sum(np.square(F)))
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UP = UP / math.sqrt(np.sum(np.square(UP)))
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s = np.cross(f, UP)
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u = np.cross((s / math.sqrt(np.sum(np.square(s)))), f)
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mat = np.matrix([
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[s[0, 0], s[0, 1], s[0, 2], 0],
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[u[0, 0], u[0, 1], u[0, 2], 0],
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[-f[0, 0], -f[0, 1], -f[0, 2], 0],
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[0, 0, 0, 1]
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])
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return np.transpose(mat)
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def orthogonalMatrix(r, l, t, b, f, n):
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mat = np.matrix([
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[2 / (r - l), 0, 0, -(r + l) / (r - l)],
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[0, 2 / (t - b), 0, -(t + b) / (t - b)],
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[0, 0, -2 / (f - n), -(f + n) / (f - n)],
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[0, 0, 0, 1]
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])
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return np.transpose(mat)
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def perspectiveMatrix(fovy, aspect, znear, zfar):
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fovy_rads = fovy * math.pi / 180
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f = math.cos(fovy_rads / 2.0) / math.sin(fovy_rads / 2.0)
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a = (zfar + znear) / (znear - zfar)
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b = (2 * zfar * znear) / (znear - zfar)
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mat = np.matrix([[f / aspect, 0, 0, 0],
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[0, f, 0, 0],
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[0, 0, a, b],
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[0, 0, -1, 0]], np.float32)
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return np.transpose(mat)
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def translate(x, y, z):
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mat = np.matrix([[1, 0, 0, x],
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[0, 1, 0, y],
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[0, 0, 1, z],
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[0, 0, 0, 1]], np.float32)
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return np.transpose(mat)
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def rotate(x, y, z, d4=False):
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if not d4:
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mat = np.matrix([[1, 0, 0], [0, math.cos(x), -math.sin(x)], [0, math.sin(x), math.cos(x)]], np.float32)
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mat = mat * np.matrix([[math.cos(y), 0, -math.sin(y)], [0, 1, 0], [math.sin(y), 0, math.cos(y)]], np.float32)
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mat = mat * np.matrix([[math.cos(z), -math.sin(z), 0], [math.sin(z), math.cos(z), 0], [0, 0, 1]], np.float32)
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else:
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mat = np.matrix(
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[[1, 0, 0, 0], [0, math.cos(x), -math.sin(x), 0], [0, math.sin(x), math.cos(x), 0], [0, 0, 0, 1]],
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np.float32)
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mat = mat * np.matrix(
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[[math.cos(y), 0, -math.sin(y), 0], [0, 1, 0, 0], [math.sin(y), 0, math.cos(y), 0], [0, 0, 0, 1]],
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np.float32)
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mat = mat * np.matrix(
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[[math.cos(z), -math.sin(z), 0, 0], [math.sin(z), math.cos(z), 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]],
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np.float32)
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return np.transpose(mat)
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