Mercurial > hg > orthanc-stone
comparison OrthancStone/Resources/Computations/ComputeShearOnSlice.py @ 1512:244ad1e4e76a
reorganization of folders
author | Sebastien Jodogne <s.jodogne@gmail.com> |
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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 |
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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])) |