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Characterization and Detection of Loops in n-Dimensional Discrete Toric Spaces

Abstract : Since a toric space is not simply connected, it is possible to find in such spaces some loops which are not homotopic to a point: we call them toric loops. Some applications, such as the study of the relationship between the geometrical characteristics of a material and its physical properties, rely on three-dimensional discrete toric spaces and require detecting objects having a toric loop. In this work, we study objects embedded in discrete toric spaces, and propose a new definition of loops and equivalence of loops. Moreover, we introduce a characteristic of loops that we call wrapping vector: relying on this notion, we propose a linear time algorithm which detects whether an object has a toric loop or not.
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Submitted on : Monday, September 12, 2011 - 2:14:47 PM
Last modification on : Tuesday, June 30, 2020 - 9:09:54 AM
Long-term archiving on: : Tuesday, December 13, 2011 - 2:25:48 AM

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  • HAL Id : hal-00622425, version 1

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John Chaussard, Gilles Bertrand, Michel Couprie. Characterization and Detection of Loops in n-Dimensional Discrete Toric Spaces. Journal of Mathematical Imaging and Vision, Springer Verlag, 2010, 36 (2), pp.111-124. ⟨hal-00622425⟩

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