Boolean operations of 2-manifolds through vertex neighborhood classification
ACM Transactions on Graphics (TOG)
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
An Algorithm for Geometric Set Operations Using Cellular Subdivision Techniques
IEEE Computer Graphics and Applications
Polygon properties calculated from the vertex neighborhoods
SCG '87 Proceedings of the third annual symposium on Computational geometry
Generating Topological Structures for Surface Models
IEEE Computer Graphics and Applications
Conflict-Free Coloring of Points and Simple Regions in the Plane
Discrete & Computational Geometry
A new algorithm for computing Boolean operations on polygons
Computers & Geosciences
Technical section: A new algorithm for Boolean operations on general polygons
Computers and Graphics
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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@?B. The output is also presented in the form of polygonal curves, where in particular the curves describing the union A@?B, the intersection A@?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@?B=(A@?B)@?(A@?B)=(A@?B)@?(B@?A).