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Exact Computation of Trait-induced Merge Trees for Bivariate Fields
Petar Hristov, Ingrid Hotz, Talha Bin Masood
Trait-induced merge trees (TIMTs) provide a robust topology-based method for selecting and browsing feature level sets in multivariate data by analyzing the distance field induced…
Singular Arrange and Traverse Algorithm for Computing Reeb Spaces of Bivariate PL Maps
Petar Hristov, Ingrid Hotz, Talha Bin Masood
We present an exact and efficient algorithm for computing the Reeb space of a bivariate PL map. The Reeb space is a topological structure that generalizes the Reeb graph to the set…
Robust Geometric Predicates for Bivariate Computational Topology
Petar Hristov, Ingrid Hotz, Talha Bin Masood
We present theory and practice for robust implementations of bivariate Jacobi set and Reeb space algorithms. Robustness is a fundamental topic in computational geometry that deals…