TY - JOUR

T1 - Recursive geometry of the flow complex and topology of the flow complex filtration

AU - Buchin, K.

AU - Dey, T.K.

AU - Giesen, J.

AU - John, M.

PY - 2008

Y1 - 2008

N2 - The flow complex is a geometric structure, similar to the Delaunay tessellation, to organize a set of (weighted) points in . 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.

AB - The flow complex is a geometric structure, similar to the Delaunay tessellation, to organize a set of (weighted) points in . 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.

U2 - 10.1016/j.comgeo.2007.05.005

DO - 10.1016/j.comgeo.2007.05.005

M3 - Article

SN - 0925-7721

VL - 40

SP - 115

EP - 137

JO - Computational Geometry

JF - Computational Geometry

IS - 2

ER -