Paper by Martin L. Demaine

Zachary Abel, Hugo Akitaya, Man-Kwun Chiu, Erik D. Demaine, Martin L. Demaine, Adam Hesterberg, Matias Korman, Jayson Lynch, André van Renssen, and Marcel Roeloffzen, “Snipperclips: Cutting Tools into Desired Polygons using Themselves”, Computational Geometry: Theory and Applications, volume 98, October 2021, pages 101784.

We study Snipperclips, a computer puzzle game whose objective is to create a target shape with two tools. The tools start as constant-complexity shapes, and each tool can snip (i.e., subtract its current shape from) the other tool. We study the computational problem of, given a target shape represented by a polygonal domain of n vertices, is it possible to create it as one of the tools' shape via a sequence of snip operations? If so, how many snip operations are required? We consider several variants of the problem (such as allowing the tools to be disconnected and/or using an undo operation) and bound the number of operations needed for each of the variants.

This paper is also available from ScienceDirect and as arXiv:2105.08305.

The paper is 24 pages.

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