An algebra of polygons through the notion of negative shapes
CVGIP: Image Understanding
A generic solution to polygon clipping
Communications of the ACM
Efficient clipping of arbitrary polygons
ACM Transactions on Graphics (TOG)
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
An algorithm for polygon clipping, and for determining polygon intersections and unions
Computers & Geosciences
A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums
Computers and Operations Research
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A heuristic for nesting problems of irregular shapes
Computer-Aided Design
A new algorithm for computing Boolean operations on polygons
Computers & Geosciences
Expert Systems with Applications: An International Journal
An improved method for calculating the no-fit polygon
Computers and Operations Research
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Cutting and packing problems are found in numerous industries such as garment, wood and shipbuilding. The collision free region concept is presented, as it represents all the translations possible for an item to be inserted into a container with already placed items. The often adopted nofit polygon concept and its analogous concept inner fit polygon are used to determine the collision free region. Boolean operations involving nofit polygons and inner fit polygons are used to determine the collision free region. New robust non-regularized Boolean operations algorithm is proposed to determine the collision free region. The algorithm is capable of dealing with degenerated boundaries. This capability is important because degenerated boundaries often represent local optimal placements. A parallelized version of the algorithm is also proposed and tests are performed in order to determine the execution times of both the serial and parallel versions of the algorithm.