Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
An algebra of polygons through the notion of negative shapes
CVGIP: Image Understanding
The irregular cutting-stock problem mdash; a new procedure for deriving the no-fit polygon
Computers and Operations Research
Computational Geometry in C
Optimization in computer-aided pattern packing (marking, envelopes)
Optimization in computer-aided pattern packing (marking, envelopes)
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The no-fit polygon (NFP) is the set of feasible locations that one polygon may take with respect to another polygon, such that the polygons do not overlap. Feasible locations are required for most of the solutions to two-dimensional packing problems, and also for other problems such as robot motion planning.Efficient methods to calculate the NFP of two convex polygons, or one convex and one non-convex polygon have been developed by other researchers. However, when both polygons are non-convex, the current methods of calculation are inefficient or difficult to implement. This paper presents an extension of Ghosh's (CVGIP: Image Understanding 54(1991)119) NFP algorithm, and uses manipulation of sorted lists of polygon edges to find the NFP efficiently.