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http://dx.doi.org/10.12941/jksiam.2011.15.4.307

PAPER TEMPLATES FOR TRIANGULATED SURFACES  

Min, Cho-Hong (Mathematics Department, Ewha Womans University)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.15, no.4, 2011 , pp. 307-318 More about this Journal
Abstract
We introduce an algorithm that automatically generates paper templates of a triangulated surface. The surface can be built by cutting, folding, and pasting the paper templates. The algorithm is branched to two strategies : one is to select the longest neghboring edge among many choices, and the other is to select the largest neighboring triangle. Three surfaces, whose triangulation sizes widely range, are successfully built by the algorithm. The two strategies are empirically evaluated in building the surfaces with respect to paper consumption, a measure of cost efficiency, and boundary length, a measure of speed efficiency. Strategy 1 performs in most cases better than the other one with respect to boundary length, but sometimes wins and sometimes loese with respect to paper consumption.
Keywords
paper templates; simplex; computational geometry; triangulation;
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