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`!Nesting algorithms`! are used to make the `F33f`_`[most efficient use`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Nesting_(process)]`_`f of material or space. This could for instance be done by evaluating many different possible combinations via `F33f`_`[recursion`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Recursion_(computer_science)]`_`f.

1. Linear (1-dimensional): The simplest of the `F33f`_`[algorithms`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Algorithms]`_`f illustrated here. For an existing set there is only one position where a new cut can be placed – at the end of the last cut. Validation of a combination involves a simple Stock - Yield - `F33f`_`[Kerf`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Kerf]`_`f = Scrap calculation.

2. Plate (2-dimensional): These algorithms are significantly more complex. For an existing set, there may be as many as eight positions where a new cut may be introduced next to each existing cut, and if the new cut is not perfectly square then different rotations may need to be checked. Validation of a potential combination involves checking for intersections between `F33f`_`[two-dimensional`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Two-dimensional]`_`f objects.`:cite-ref-a-1-0[`F5bf`_`[1`#cite-note-a-1]`_`f]

3. Packing (3-dimensional): These algorithms are the most complex illustrated here due to the larger number of possible combinations. Validation of a potential combination involves checking for intersections between `F33f`_`[three-dimensional`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Three-dimensional_space]`_`f objects.

`:cite-ref-a-1-1[`F5bf`_`[1`#cite-note-a-1]`_`f]

>>References

`:cite-note-a-1`!1.`! `F0af`_`[↑`#cite-ref-a-1-0]`_`f `:citerefherrmanndelalio`aHerrmann, Jeffrey; Delalio, David. "Algorithms for Sheet Metal Nesting" (PDF). IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION. Retrieved 29 August 2015.

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