Capítulo de Libro
A Graph-with-Loop Structure for a Topological Representation of 3D Objects
Autor/es | González Díaz, Rocío
Jiménez Rodríguez, María José Medrano Garfia, Belén Real Jurado, Pedro |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I |
Fecha de publicación | 2007 |
Fecha de depósito | 2015-11-12 |
Publicado en |
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Resumen | Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). ... Given a cell complex K whose geometric realization |K| is embedded in R 3 and a continuous function h: |K|→R (called the height function), we construct a graph G h (K) which is an extension of the Reeb graph R h (|K|). More concretely, the graph G h (K) without loops is a subdivision of R h (|K|). The most important difference between the graphs G h (K) and R h (|K|) is that G h (K) preserves not only the number of connected components but also the number of “tunnels” (the homology generators of dimension 1) of K. The latter is not true in general for R h (|K|). Moreover, we construct a map ψ: G h (K)→K identifying representative cycles of the tunnels in K with the ones in G h (K) in the way that if e is a loop in G h (K), then ψ(e) is a cycle in K such that all the points in |ψ(e)| belong to the same level set in |K|. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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A graph with Loop structure.pdf | 547.4Kb | [PDF] | Ver/ | |