1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
|
#!/usr/bin/env python3
from math import *
def calc(mat):
[xx, yx], [xy, yy] = mat
a = xx**2 + xy**2
b = xx*yx + xy*yy
c = yy**2 + yx**2
print(f'{a=:.2f} {c=:.2f} {b=:.2f}')
tan_2_alpha = 2*b/(a-c)
print(f'atan2={atan2(2*b, a-c)/pi:.2f}*pi')
#tan_alpha = tan_2_alpha / (1 + sqrt(1 + tan_2_alpha**2)) # FIXME: bounds?
cos_2_alpha = 1/sqrt(1 + tan_2_alpha**2)
sin_2_alpha = tan_2_alpha / sqrt(1 + tan_2_alpha**2)
print(f'tan(2a)={tan_2_alpha:.2f} cos(2a)={cos_2_alpha:.2f} sin(2a)={sin_2_alpha:.2f}')
cos_alpha = sqrt((1 + cos_2_alpha)/2)
sin_alpha = sqrt((1 - cos_2_alpha)/2)
print(f'cos(a)={cos_alpha:.2f} sin(a)={sin_alpha:.2f}')
for sgn_cos, sgn_sin in [(-1, -1), (-1, 1), (1, -1), (1, 1)]:
p = xx * sgn_cos * cos_alpha + yx * sgn_sin * sin_alpha
q = xy * sgn_cos * cos_alpha + yy * sgn_sin * sin_alpha
dist = hypot(p, q)
yield dist
def gen(sx, sy, m, theta):
xx = sx * cos(theta)
xy = sx * sin(theta)
yy = sy * (cos(theta) + m * sin(theta))
yx = sy * (m * cos(theta) - sin(theta))
mat = [xx, yx], [xy, yy]
return mat
for sx, sy in [
(1, 0.9),
(1, 1.0),
(1, 1.1),
(0.9, 1),
(1.0, 1),
(1.1, 1)]:
for m in [0, 0.1, 1, 10]:
for theta in [0, pi/8, pi/4, pi/3, pi/2, pi, 3*pi/4]:
print(f'{sx=:.1f} {sy=:.1f} {m=:.1f} theta={theta/pi:.2f}*pi |', end=' ')
mat = gen(sx, sy, m, theta)
try:
dists = list(calc(mat))
str_dists = ' '.join(f'{x:.2f}' for x in dists)
print(f'[{str_dists}] | min={min(dists):.2f} max={max(dists):.2f}')
except:
print('E')
break
break
break
|
