Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Measuring and computing natural generators for homology groups
Computational Geometry: Theory and Applications
Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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In this paper, we provide the theoretical foundation and an effective algorithm for localizing topological attributes such as tunnels and voids. Unlike previous work that fo- cused on 2-manifolds with restricted geometry, our theory is general and localizes arbitrary-dimensional attributes in arbitrary spaces. We implement our algorithm and present experiments to validate our approach in practice.