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annotate OrthancStone/Resources/Computations/ComputeShearOnSlice.py @ 1589:8c5f9864545f

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adding missing headers
author Sebastien Jodogne <s.jodogne@gmail.com>
date Thu, 22 Oct 2020 16:59:23 +0200
parents 244ad1e4e76a
children 8563ea5d8ae4
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46cb2eedc2e0 ShearWarpProjectiveTransform
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1 #!/usr/bin/python
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2
1589
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3 # Stone of Orthanc
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4 # Copyright (C) 2012-2016 Sebastien Jodogne, Medical Physics
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5 # Department, University Hospital of Liege, Belgium
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6 # Copyright (C) 2017-2020 Osimis S.A., Belgium
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7 #
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8 # This program is free software: you can redistribute it and/or
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9 # modify it under the terms of the GNU Affero General Public License
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10 # as published by the Free Software Foundation, either version 3 of
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11 # the License, or (at your option) any later version.
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12 #
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13 # This program is distributed in the hope that it will be useful, but
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14 # WITHOUT ANY WARRANTY; without even the implied warranty of
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15 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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16 # Affero General Public License for more details.
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17 #
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18 # You should have received a copy of the GNU Affero General Public License
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19 # along with this program. If not, see <http://www.gnu.org/licenses/>.
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46cb2eedc2e0 ShearWarpProjectiveTransform
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22 from sympy import *
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23 import pprint
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24
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25 init_printing(use_unicode=True)
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28 # Setup "T * S * M_shear" (Equation A.16)
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29
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30 ex, ey, ew = symbols('ex ey ew')
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31 sx, sy = symbols('sx, sy')
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32 ti, tj = symbols('ti tj')
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33
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34 T = Matrix([[ 1, 0, 0, ti ],
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35 [ 0, 1, 0, tj ],
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36 [ 0, 0, 1, 0 ],
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37 [ 0, 0, 0, 1 ]])
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38
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39 # Equation (A.15), if "sx == sy == f"
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40 S = Matrix([[ sx, 0, 0, 0 ],
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41 [ 0, sy, 0, 0 ],
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42 [ 0, 0, 1, 0 ],
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43 [ 0, 0, 0, 1 ]])
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44
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45 # MM_shear, in Equation (A.14)
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46 M = Matrix([[ 1, 0, ex, 0 ],
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47 [ 0, 1, ey, 0 ],
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48 [ 0, 0, 1, 0 ],
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49 [ 0, 0, ew, 1 ]])
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50
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51
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52 x, y, z, w = symbols('x y z w')
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53 p = Matrix([ x, y, z, w ])
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54
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55 print("\nT =" % T)
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56 pprint.pprint(T);
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57
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58 print("\nS =" % T)
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59 pprint.pprint(S);
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60
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61 print("\nM'_shear =" % T)
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62 pprint.pprint(M);
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64 print("\nGeneral form of a Lacroute's shear matrix (Equation A.16): T * S * M'_shear =")
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65 pprint.pprint(T * S * M);
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67 print("\nHence, alternative parametrization:")
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68 a11, a13, a14, a22, a23, a24, a43 = symbols('a11 a13 a14 a22 a23 a24 a43')
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69
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70 A = Matrix([[ a11, 0, a13, a14 ],
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71 [ 0, a22, a23, a24 ],
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72 [ 0, 0, 1, 0 ],
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73 [ 0, 0, a43, 1 ]])
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74 pprint.pprint(A);
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75
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76 v = A * p
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77 v = v.subs(w, 1)
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78
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79 print("\nAction of Lacroute's shear matrix A on plane z (taking w=1):\n%s\n" % v)
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80
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81 print('Output x\' = %s\n' % (v[0]/v[3]))
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82 print('Output y\' = %s\n' % (v[1]/v[3]))
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83 print('Output z\' = %s\n' % (v[2]/v[3]))