Recent Results in Computational Origami
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Computational origami is a recent branch of computer science studying efficient ... Most results in computational origami fit into at least one of three ...
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Recent Results in Computational OrigamiPage 1Recent Results in Computational OrigamiErik D. DemaineMartin L. DemaineAbstractComputational origami is a recent branch of computer science studying efficientalgorithms for solving paperfolding problems. This field essentially began with RobertLangs work on algorithmic origami design 25] starting around 1993. Since then thefield of computational origami has grown significantly. The purpose of this paper isto survey the work in the field with a focus on recent results and to present severalopen problems that remain. The survey cannot hope to be complete but we attemptto cover most areas of interest.1 OverviewMost results in computational origami fit into at least one of three categories: universalityresults efficient decision algorithms and computational intractability results.A universality result shows that subject to a certain model of folding everything ispossible. For example any treeshaped origami base (Section 2.1) any polygonal silhouette(Section 2.3) and any polyhedral surface (Section 2.3) can be folded out of a largeenoughpiece of paper. Universality results often come with efficient algorithms for finding thefoldings; pure existence results are rare.When universality results are impossible (some objects cannot be folded) the nextbestresult is an efficient decision algorithm to determine whether a given object is foldable.Here efficient normally means polynomial time. For example there is a polynomialtime algorithm to decide whether a map (grid of creases marked mountain and valley) canbe folded by a sequence of simple folds (Section 3.4).Not all paperfolding problems have efficient algorithms and this can be proved by acomputational intractability result. For example it is NPhard to tell whether a given creasepattern folds into any flat origami (Section 3.2) even when folds are restricted to simplefolds (Section 3.4). These results mean that there are no polynomialtime algorithms forthese problems unless some o ...
Source: theory.csail.mit.edu
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