Mercurial > hg > orthanc-stone

annotate Resources/Computations/ComputeShearOnSlice.py @ 191:46cb2eedc2e0 wasm

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ShearWarpProjectiveTransform
author Sebastien Jodogne <s.jodogne@gmail.com>
date Fri, 16 Mar 2018 15:01:52 +0100
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46cb2eedc2e0 ShearWarpProjectiveTransform
Sebastien Jodogne <s.jodogne@gmail.com>
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1 #!/usr/bin/python
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2
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3 from sympy import *
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4 import pprint
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5
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6 init_printing(use_unicode=True)
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7
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8
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9 # Setup "T * S * M_shear" (Equation A.16)
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10
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11 ex, ey, ew = symbols('ex ey ew')
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12 sx, sy = symbols('sx, sy')
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13 ti, tj = symbols('ti tj')
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14
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15 T = Matrix([[ 1, 0, 0, ti ],
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16 [ 0, 1, 0, tj ],
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17 [ 0, 0, 1, 0 ],
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18 [ 0, 0, 0, 1 ]])
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19
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20 # Equation (A.15), if "sx == sy == f"
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21 S = Matrix([[ sx, 0, 0, 0 ],
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22 [ 0, sy, 0, 0 ],
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23 [ 0, 0, 1, 0 ],
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24 [ 0, 0, 0, 1 ]])
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25
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26 # MM_shear, in Equation (A.14)
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27 M = Matrix([[ 1, 0, ex, 0 ],
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28 [ 0, 1, ey, 0 ],
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29 [ 0, 0, 1, 0 ],
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30 [ 0, 0, ew, 1 ]])
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31
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32
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33 x, y, z, w = symbols('x y z w')
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34 p = Matrix([ x, y, z, w ])
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35
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36 print("\nT =" % T)
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37 pprint.pprint(T);
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38
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39 print("\nS =" % T)
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40 pprint.pprint(S);
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41
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42 print("\nM'_shear =" % T)
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43 pprint.pprint(M);
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44
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45 print("\nGeneral form of a Lacroute's shear matrix (Equation A.16): T * S * M'_shear =")
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46 pprint.pprint(T * S * M);
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47
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48 print("\nHence, alternative parametrization:")
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49 a11, a13, a14, a22, a23, a24, a43 = symbols('a11 a13 a14 a22 a23 a24 a43')
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50
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51 A = Matrix([[ a11, 0, a13, a14 ],
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52 [ 0, a22, a23, a24 ],
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53 [ 0, 0, 1, 0 ],
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54 [ 0, 0, a43, 1 ]])
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55 pprint.pprint(A);
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56
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57 v = A * p
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58 v = v.subs(w, 1)
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59
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60 print("\nAction of Lacroute's shear matrix A on plane z (taking w=1):\n%s\n" % v)
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61
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62 print('Output x\' = %s\n' % (v[0]/v[3]))
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63 print('Output y\' = %s\n' % (v[1]/v[3]))
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64 print('Output z\' = %s\n' % (v[2]/v[3]))