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

作者：Gaspar Miguel Belbut^*; Martins Ferreira Nelson

来源：Journal of Symbolic Computation, 2014, 61-62: 53-65.

DOI：10.1016/jjsc.2013.10.008

• Symmetric difference
• Operation
• Regions in the plane
• Oriented closed simple curves
• Graph with symmetry
• Intersection
• Union
• Set difference

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 circle plus B. The output is also presented in the form of polygonal curves, where in particular the curves describing the union A boolean OR B, the intersection A boolean AND B, the difference A\B, and the complement of the difference B\A, are also obtained. This is related with the two equivalent formulas to compute the symmetric difference, namely A circle plus B = (A boolean OR B)\(A boolean AND B) = (A\B) boolean OR (B\A).

• 出版日期2014-3