Journal of Mathematical Imaging and Vision

, Volume 36, Issue 2, pp 111–124 | Cite as

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

  • John Chaussard
  • Gilles Bertrand
  • Michel Couprie


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.

Fluid flow Fluid flow simulation Grains Porous material Torus Loop Toric loop Wrapped subset Homotopy Toric space Wrapping vector Fundamental group 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • John Chaussard
    • 1
  • Gilles Bertrand
    • 1
  • Michel Couprie
    • 1
  1. 1.Université Paris EstNoisy le Grand CedexFrance

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