Gasp: A Gradient-Aware Shortest Path Algorithm For Boundary-Confined Visualization Of 2-Manifold Reeb Graphs

Reeb graphs are an important tool for abstracting and representing the topological structure of a function defined on a manifold. We have identified three properties for faithfully representing Reeb graphs in a visualization. Namely, they should be constrained to the boundary, compact, and aligned with the function gradient. Existing algorithms for drawing Reeb graphs are agnostic to or violate these properties. In this paper, we introduce an algorithm to generate Reeb graph visualizations, called textit{GASP}, that is cognizant of these properties, thereby producing visualizations that are more representative of the underlying data. To demonstrate the improvements, the resulting Reeb graphs are evaluated both qualitatively and quantitatively against the geometric barycenter algorithm, using its implementation available in the Topology ToolKit (TTK), a widely adopted tool for calculating and visualizing Reeb graphs.

Sefat Rahman, Tushar M. Athawale, and Paul Rosen. Gasp: A Gradient-Aware Shortest Path Algorithm For Boundary-Confined Visualization Of 2-Manifold Reeb Graphs. Topological Data Analysis and Visualization (TopoInVis), 2025.

@article{rahman2025reeb,
  title = {GASP: A Gradient-Aware Shortest Path Algorithm for Boundary-Confined
    Visualization of 2-Manifold Reeb Graphs},
  author = {Rahman, Sefat and Athawale, Tushar M. and Rosen, Paul},
  journal = {Topological Data Analysis and Visualization (TopoInVis)},
  year = {2025},
  abstract = {Reeb graphs are an important tool for abstracting and representing the
    topological structure of a function defined on a manifold. We have identified three
    properties for faithfully representing Reeb graphs in a visualization. Namely, they
    should be constrained to the boundary, compact, and aligned with the function gradient.
    Existing algorithms for drawing Reeb graphs are agnostic to or violate these properties.
    In this paper, we introduce an algorithm to generate Reeb graph visualizations, called
    textit{GASP}, that is cognizant of these properties, thereby producing visualizations
    that are more representative of the underlying data. To demonstrate the improvements,
    the resulting Reeb graphs are evaluated both qualitatively and quantitatively against
    the geometric barycenter algorithm, using its implementation available in the Topology
    ToolKit (TTK), a widely adopted tool for calculating and visualizing Reeb graphs.}
}