Snipperclips: Cutting tools into desired polygons using themselves

Zachary Abel; Hugo Akitaya; Man Kwun Chiu; Erik D. Demaine; Martin L. Demaine; Adam Hesterberg; Matias Korman; Jayson Lynch; André van Renssen; Marcel Roeloffzen

doi:10.1016/j.comgeo.2021.101784

Snipperclips: Cutting tools into desired polygons using themselves

Zachary Abel, Hugo Akitaya, Man Kwun Chiu, Erik D. Demaine, Martin L. Demaine, Adam Hesterberg, Matias Korman, Jayson Lynch, André van Renssen (Corresponding author), Marcel Roeloffzen

Applied Geometric Algorithms

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Abstract

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.

Original language	English
Article number	101784
Number of pages	15
Journal	Computational Geometry
Volume	98
DOIs	https://doi.org/10.1016/j.comgeo.2021.101784
Publication status	Published - Oct 2021

Keywords

Cutting tool
Puzzle game
Shape matching

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10.1016/j.comgeo.2021.101784

published versionFinal published version, 1.02 MBLicence: TAVERNE

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title = "Snipperclips: Cutting tools into desired polygons using themselves",

abstract = "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.",

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T2 - Cutting tools into desired polygons using themselves

AU - Abel, Zachary

AU - Akitaya, Hugo

AU - Chiu, Man Kwun

AU - Demaine, Erik D.

AU - Demaine, Martin L.

AU - Hesterberg, Adam

AU - Korman, Matias

AU - Lynch, Jayson

AU - van Renssen, André

AU - Roeloffzen, Marcel

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AB - 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.

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Snipperclips: Cutting tools into desired polygons using themselves

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Keywords

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