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comparison OrthancStone/Resources/Computations/ComputeShearOnSlice.py @ 1512:244ad1e4e76a

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reorganization of folders
author Sebastien Jodogne <s.jodogne@gmail.com>
date Tue, 07 Jul 2020 16:21:02 +0200
parents Resources/Computations/ComputeShearOnSlice.py@46cb2eedc2e0
children 8c5f9864545f
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1511:9dfeee74c1e6 1512:244ad1e4e76a
1 #!/usr/bin/python
2
3 from sympy import *
4 import pprint
5
6 init_printing(use_unicode=True)
7
8
9 # Setup "T * S * M_shear" (Equation A.16)
10
11 ex, ey, ew = symbols('ex ey ew')
12 sx, sy = symbols('sx, sy')
13 ti, tj = symbols('ti tj')
14
15 T = Matrix([[ 1, 0, 0, ti ],
16 [ 0, 1, 0, tj ],
17 [ 0, 0, 1, 0 ],
18 [ 0, 0, 0, 1 ]])
19
20 # Equation (A.15), if "sx == sy == f"
21 S = Matrix([[ sx, 0, 0, 0 ],
22 [ 0, sy, 0, 0 ],
23 [ 0, 0, 1, 0 ],
24 [ 0, 0, 0, 1 ]])
25
26 # MM_shear, in Equation (A.14)
27 M = Matrix([[ 1, 0, ex, 0 ],
28 [ 0, 1, ey, 0 ],
29 [ 0, 0, 1, 0 ],
30 [ 0, 0, ew, 1 ]])
31
32
33 x, y, z, w = symbols('x y z w')
34 p = Matrix([ x, y, z, w ])
35
36 print("\nT =" % T)
37 pprint.pprint(T);
38
39 print("\nS =" % T)
40 pprint.pprint(S);
41
42 print("\nM'_shear =" % T)
43 pprint.pprint(M);
44
45 print("\nGeneral form of a Lacroute's shear matrix (Equation A.16): T * S * M'_shear =")
46 pprint.pprint(T * S * M);
47
48 print("\nHence, alternative parametrization:")
49 a11, a13, a14, a22, a23, a24, a43 = symbols('a11 a13 a14 a22 a23 a24 a43')
50
51 A = Matrix([[ a11, 0, a13, a14 ],
52 [ 0, a22, a23, a24 ],
53 [ 0, 0, 1, 0 ],
54 [ 0, 0, a43, 1 ]])
55 pprint.pprint(A);
56
57 v = A * p
58 v = v.subs(w, 1)
59
60 print("\nAction of Lacroute's shear matrix A on plane z (taking w=1):\n%s\n" % v)
61
62 print('Output x\' = %s\n' % (v[0]/v[3]))
63 print('Output y\' = %s\n' % (v[1]/v[3]))
64 print('Output z\' = %s\n' % (v[2]/v[3]))