Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees

@article{Tierny2009LoopSF,
  title={Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees},
  author={Julien Tierny and Attila Gyulassy and Eddie Simon and Valerio Pascucci},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  year={2009},
  volume={15},
  pages={1177-1184}
}
This paper introduces an efficient algorithm for computing the Reeb graph of a scalar function f defined on a volumetric mesh M in Ropf3. We introduce a procedure called "loop surgery" that transforms M into a mesh M' by a sequence of cuts and guarantees the Reeb graph of f(M') to be loop free. Therefore, loop surgery reduces Reeb graph computation to the simpler problem of computing a contour tree, for which well-known algorithms exist that are theoretically efficient (O(n log n)) and fast in… 

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