VIS '97 Proceedings of the 8th conference on Visualization '97
Geometry and topology for mesh generation
Geometry and topology for mesh generation
Loops in Reeb Graphs of 2-Manifolds
Discrete & Computational Geometry
Topology-Controlled Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Efficient Output-Sensitive Construction of Reeb Graphs
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
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The Reeb graph of a scalar function represents the evolution of the topology of its level sets. In this video, we describe a near-optimal output-sensitive algorithm for computing the Reeb graph of scalar functions defined over manifolds. Key to the simplicity and efficiency of the algorithm is an alternate definition of the Reeb graph that considers equivalence classes of level sets instead of individual level sets. The algorithm works in two steps. The first step locates all critical points of the function in the domain. Arcs in the Reeb graph are computed in the second step using a simple search procedure that works on a small subset of the domain that corresponds to a pair of critical points. The algorithm is also able to handle non-manifold domains.