Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Lectures on Discrete Geometry
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Alpha-shapes and flow shapes are homotopy equivalent
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Proceedings of the twenty-fifth annual symposium on Computational geometry
Manifold homotopy via the flow complex
SGP '09 Proceedings of the Symposium on Geometry Processing
A parallel algorithm for computing the flow complex
Proceedings of the twenty-ninth annual symposium on Computational geometry
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The flow complex is a geometric structure, similar to the Delaunay tessellation, to organize a set of (weighted) points in R^k. Flow shapes are topological spaces corresponding to substructures of the flow complex. The flow complex and flow shapes have found applications in surface reconstruction, shape matching, and molecular modeling. In this article we give an algorithm for computing the flow complex of weighted points in any dimension. The algorithm reflects the recursive structure of the flow complex. On the basis of the algorithm we establish a topological similarity between flow shapes and the nerve of a corresponding ball set, namely homotopy equivalence.