Loops in Reeb Graphs of 2-Manifolds

Conference · Tue Feb 11 00:00:00 EST 2003

DOI:https://doi.org/10.1145/777792.777844· OSTI ID:15004529

Cole-McLaughlin, K; Edelsbrunner, H; Harer, J; Natarajan, V; Pascucci, V

Given a Morse function f over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight upper and lower bounds on the number of loops in the Reeb graph that depend on the genus, the number of boundary components, and whether or not the 2-manifold is orientable. We also give an algorithm that constructs the Reeb graph in time O(n log n), where n is the number of edges in the triangulation used to represent the 2-manifold and the Morse function.

• Research Organization: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 15004529
• Report Number(s): UCRL-JC-151933; TRN: US201015%%683
• Resource Relation: Conference: Association for Computing Machinery Symposium on Computational Geometry, San Diego, CA, Jun 08 - Jun 10, 2003
• Country of Publication: United States
• Language: English

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