kopia lustrzana https://github.com/jaseg/gerbolyze
61 wiersze
1.7 KiB
Python
61 wiersze
1.7 KiB
Python
#!/usr/bin/env python3
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from math import *
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def calc(mat):
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[xx, yx], [xy, yy] = mat
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a = xx**2 + xy**2
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b = xx*yx + xy*yy
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c = yy**2 + yx**2
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print(f'{a=:.2f} {c=:.2f} {b=:.2f}')
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tan_2_alpha = 2*b/(a-c)
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print(f'atan2={atan2(2*b, a-c)/pi:.2f}*pi')
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#tan_alpha = tan_2_alpha / (1 + sqrt(1 + tan_2_alpha**2)) # FIXME: bounds?
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cos_2_alpha = 1/sqrt(1 + tan_2_alpha**2)
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sin_2_alpha = tan_2_alpha / sqrt(1 + tan_2_alpha**2)
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print(f'tan(2a)={tan_2_alpha:.2f} cos(2a)={cos_2_alpha:.2f} sin(2a)={sin_2_alpha:.2f}')
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cos_alpha = sqrt((1 + cos_2_alpha)/2)
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sin_alpha = sqrt((1 - cos_2_alpha)/2)
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print(f'cos(a)={cos_alpha:.2f} sin(a)={sin_alpha:.2f}')
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for sgn_cos, sgn_sin in [(-1, -1), (-1, 1), (1, -1), (1, 1)]:
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p = xx * sgn_cos * cos_alpha + yx * sgn_sin * sin_alpha
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q = xy * sgn_cos * cos_alpha + yy * sgn_sin * sin_alpha
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dist = hypot(p, q)
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yield dist
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def gen(sx, sy, m, theta):
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xx = sx * cos(theta)
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xy = sx * sin(theta)
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yy = sy * (cos(theta) + m * sin(theta))
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yx = sy * (m * cos(theta) - sin(theta))
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mat = [xx, yx], [xy, yy]
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return mat
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for sx, sy in [
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(1, 0.9),
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(1, 1.0),
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(1, 1.1),
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(0.9, 1),
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(1.0, 1),
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(1.1, 1)]:
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for m in [0, 0.1, 1, 10]:
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for theta in [0, pi/8, pi/4, pi/3, pi/2, pi, 3*pi/4]:
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print(f'{sx=:.1f} {sy=:.1f} {m=:.1f} theta={theta/pi:.2f}*pi |', end=' ')
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mat = gen(sx, sy, m, theta)
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try:
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dists = list(calc(mat))
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str_dists = ' '.join(f'{x:.2f}' for x in dists)
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print(f'[{str_dists}] | min={min(dists):.2f} max={max(dists):.2f}')
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except:
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print('E')
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break
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break
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break
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