Mercurial > hg > orthanc-stone
view Resources/Computations/ComputeShearOnSlice.py @ 1113:3924ddbbadda
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author | Alain Mazy <alain@mazy.be> |
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date | Mon, 04 Nov 2019 12:47:13 +0100 |
parents | 46cb2eedc2e0 |
children |
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#!/usr/bin/python from sympy import * import pprint init_printing(use_unicode=True) # Setup "T * S * M_shear" (Equation A.16) ex, ey, ew = symbols('ex ey ew') sx, sy = symbols('sx, sy') ti, tj = symbols('ti tj') T = Matrix([[ 1, 0, 0, ti ], [ 0, 1, 0, tj ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ]]) # Equation (A.15), if "sx == sy == f" S = Matrix([[ sx, 0, 0, 0 ], [ 0, sy, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ]]) # MM_shear, in Equation (A.14) M = Matrix([[ 1, 0, ex, 0 ], [ 0, 1, ey, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, ew, 1 ]]) x, y, z, w = symbols('x y z w') p = Matrix([ x, y, z, w ]) print("\nT =" % T) pprint.pprint(T); print("\nS =" % T) pprint.pprint(S); print("\nM'_shear =" % T) pprint.pprint(M); print("\nGeneral form of a Lacroute's shear matrix (Equation A.16): T * S * M'_shear =") pprint.pprint(T * S * M); print("\nHence, alternative parametrization:") a11, a13, a14, a22, a23, a24, a43 = symbols('a11 a13 a14 a22 a23 a24 a43') A = Matrix([[ a11, 0, a13, a14 ], [ 0, a22, a23, a24 ], [ 0, 0, 1, 0 ], [ 0, 0, a43, 1 ]]) pprint.pprint(A); v = A * p v = v.subs(w, 1) print("\nAction of Lacroute's shear matrix A on plane z (taking w=1):\n%s\n" % v) print('Output x\' = %s\n' % (v[0]/v[3])) print('Output y\' = %s\n' % (v[1]/v[3])) print('Output z\' = %s\n' % (v[2]/v[3]))