Representing geometric structures in d dimensions: topology and order
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Fast algorithms for sorting and searching strings
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
The tidy set: a minimal simplicial set for computing homology of clique complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Efficient data structure for representing and simplifying simplicial complexes in high dimensions
Proceedings of the twenty-seventh annual symposium on Computational geometry
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Graph induced complex on point data
Proceedings of the twenty-ninth annual symposium on Computational geometry
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This paper introduces a new data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the complex. This data structure allows to efficiently implement a large range of basic operations on simplicial complexes. We provide theoretical complexity analysis as well as detailed experimental results. We more specifically study Rips and witness complexes.