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Fractality of refined triangular grids and space-filling curves

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Abstract

In this paper we explain the fractal geometry of refined and derefined triangular and tetrahedral meshes by means of the application of iterated function systems (IFS). These meshes feature a remarkable amplifying invariance under changes of scale. The applications of IFS families are shown equivalent to the use of adaptive strategies that combine the refinement procedure with the derefinement procedure. In addition, space-filling curves (SFC) are used to assign a binary code for any 2D triangular refined mesh. SFC are also shown as useful for the problem of automatic domain decomposition.

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Acknowledgements

This work has been partially supported by Project UNI-2003/16 of the University of Las Palmas de Gran Canaria and by Project PI2003/35 of the Gobierno de Canarias.

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Authors and Affiliations

  1. Department of Mathematics, University of Las Palmas de Gran Canaria, 35017, Las Palmas de Gran Canaria, Spain

    A. Plaza

  2. Department of Cartography and Graphic Engineering, ULPGC, Spain

    J. P. Suárez

  3. Department of Civil Engineering, ULPGC, Spain

    M. A. Padrón

Authors
  1. A. Plaza
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  2. J. P. Suárez
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  3. M. A. Padrón
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Correspondence to A. Plaza.

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Plaza, A., Suárez, J.P. & Padrón, M.A. Fractality of refined triangular grids and space-filling curves. Engineering with Computers 20, 323–332 (2005). https://doi.org/10.1007/s00366-004-0301-7

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  • DOI: https://doi.org/10.1007/s00366-004-0301-7

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