Algorithms and Computation

Volume 5369 of the series Lecture Notes in Computer Science pp 556-567

Efficient Output-Sensitive Construction of Reeb Graphs

  • Harish DoraiswamyAffiliated withDepartment of Computer Science and Automation
  • , Vijay NatarajanAffiliated withDepartment of Computer Science and AutomationSupercomputer Education and Research Centre, Indian Institute of Science

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The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. This paper describes a near-optimal two-step algorithm that constructs the Reeb graph of a Morse function defined over manifolds in any dimension. The algorithm first identifies the critical points of the input manifold, and then connects these critical points in the second step to obtain the Reeb graph. A simplification mechanism based on topological persistence aids in the removal of noise and unimportant features. A radial layout scheme results in a feature-directed drawing of the Reeb graph. Experimental results demonstrate the efficiency of the Reeb graph construction in practice and its applications.