Canonical Ordering for Triangulations on the Cylinder, with Applications to Periodic Straight-Line Drawings

@inproceedings{Aleardi2012CanonicalOF,
  title={Canonical Ordering for Triangulations on the Cylinder, with Applications to Periodic Straight-Line Drawings},
  author={Luca Castelli Aleardi and Olivier Devillers and {\'E}ric Fusy},
  booktitle={International Symposium Graph Drawing and Network Visualization},
  year={2012}
}
We extend the notion of canonical orderings to cylindric triangulations. This allows us to extend the incremental straight-line drawing algorithm of de Fraysseix, Pach and Pollack to this setting. Our algorithm yields in linear time a crossing-free straight-line drawing of a cylindric triangulation G with n vertices on a regular grid ℤ/wℤ×[0..h], with w≤2n and h≤n(2d+1), where d is the (graph-) distance between the two boundaries. As a by-product, we can also obtain in linear time a crossing… 

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