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We present a fast algorithm to solve nesting problems based on asemi-discrete representation of both the 2D non-convex pieces and the strip.The pieces and the strip are represented by a set of equidistant vertical linesegments. The discretization algorithm uses a sweep-line method and appliesminimal extensions to the line segments of a piece to ensure thatnon-overlapping placement of the segments, representing two pieces, cannotcause overlap of the original pieces. We implemented a bottom-left-fill greedyplacement procedure, using an optimised ordering of the segments overlap tests.The C++ implementation of our algorithm uses appropriate data structures thatallow fast execution. It executes the bottom-left-fill algorithm for typicalESICUP data sets in a few milliseconds, even when rotation of the pieces isconsidered, and thus provides a suitable `building block' for integration inmetaheuristics. Moreover, we show that the algorithm scales well when thenumber of pieces increases.

A fast and scalable bottom-left-fill algorithm to solve nesting problems using a semi-discrete representation