A procedure for computing the symmetric difference of regions defined by polygonal curves

Given any two regions A, B   in the plane, defined by polygonal (simple, closed and oriented) curves, associated with their respective boundaries, we describe a procedure to compute the symmetric difference A⊕BA⊕B. The output is also presented in the form of polygonal curves, where in particular the curves describing the union A∪BA∪B, the intersection A∩BA∩B, the difference A∖BA∖B, and the complement of the difference B∖AB∖A, are also obtained. This is related with the two equivalent formulas to compute the symmetric difference, namely A⊕B=(A∪B)∖(A∩B)=(A∖B)∪(B∖A)A⊕B=(A∪B)∖(A∩B)=(A∖B)∪(B∖A).