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This paper explains how to transform a triangular mesh into a full-quad mesh. It uses the well known algorithm of Edmunds that finds optimal perfect matching.

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This page is a summary of: Blossom‐Quad: A non‐uniform quadrilateral mesh generator using a minimum‐cost perfect‐matching algorithm, International Journal for Numerical Methods in Engineering, February 2012, Wiley,
DOI: 10.1002/nme.3279.
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