An algebra of polygons through the notion of negative shapes
CVGIP: Image Understanding
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
An algorithm to compute the Minkowski sum outer-face of two simple polygons
Proceedings of the twelfth annual symposium on Computational geometry
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
The irregular cutting-stock problem mdash; a new procedure for deriving the no-fit polygon
Computers and Operations Research
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
Optimization in computer-aided pattern packing (marking, envelopes)
Optimization in computer-aided pattern packing (marking, envelopes)
A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem
INFORMS Journal on Computing
Mathematical model and efficient algorithms for object packing problem
Computational Geometry: Theory and Applications
A beam search implementation for the irregular shape packing problem
Journal of Heuristics
Irregular Packing Using the Line and Arc No-Fit Polygon
Operations Research
Irregular stock cutting system based on AutoCAD
Advances in Engineering Software
Collision free region determination by modified polygonal Boolean operations
Computer-Aided Design
Algorithms for nesting with defects
Discrete Applied Mathematics
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The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing problems. Although the concept was first described in 1966, it was not until the early 90s that the general trend of research moved away from direct trigonometry to favour the nofit polygon. Since then, the ability to calculate the nofit polygon has practically become a pre-requisite for researching irregular packing problems. However, realization of this concept in the form of a robust algorithm is a highly challenging task with few instructive approaches published. In this paper, a procedure using the mathematical concept of Minkowski sums for the calculation of the nofit polygon is presented. The described procedure is more robust than other approaches using Minkowski sum knowledge and includes details of the removal of internal edges to find holes, slits and lock and key positions. The procedure is tested on benchmark data sets and gives examples of complicated cases. Scope and purpose: Cutting and packing problems involving irregular shapes feature in a wide variety of manufacturing processes. Automated solution techniques that can generate packing arrangements more efficiently than current technology that employs user intervention, must be able to handle the complex geometry that arises from these problems. The nofit polygon has been demonstrated to be an effective tool in providing efficient handling of the geometric characteristics of these problems. The paper presents a new algorithmic procedure for deriving this tool.