Sympy Solver Example

solve2d.py

"""
Example recovering the C_x and C_y equations from OpenCV's rotation matrix

http://docs.opencv.org/2.4/modules/imgproc/doc/geometric_transformations.html?highlight=getrotationmatrix2d#getrotationmatrix2d
"""

from sympy.solvers import solve
from sympy import Symbol, Eq, simplify

Alpha = Symbol('α')
Beta = Symbol('β')
C_x = Symbol('center.x')
C_y = Symbol('center.y')
T_x = Symbol('T_x')
T_y = Symbol('T_y')

F0 = Eq(T_x, (1 - Alpha) * C_x - Beta * C_y)
F1 = Eq(T_y, Beta * C_x + (1 - Alpha) * C_y)

system = solve([F0, F1], [C_x, C_y])

#  - Solve
F_C_x = simplify(system[C_x])
F_C_y = simplify(system[C_y])


print('%s = %s' % (C_x, F_C_x))
print('%s = %s' % (C_y, F_C_y))

"""
center.x = (-T_x*(α - 1) + T_y*β)/(β**2 + (α - 1)**2)
center.y = -(T_x*β + T_y*(α - 1))/(β**2 + (α - 1)**2)
"""