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Combinatorial Generation of Planar Sets

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Abstract

We introduce a multi-dimensional generalization of the Euclidean algorithm and show how it is related to digital geometry and particularly to the generation and recognition of digital planes. We show how to associate with the steps of the algorithm geometrical extensions of substitutions, i.e., rules that replace faces by unions of faces, to build finite sets called patterns. We examine several of their combinatorial, geometrical and topological properties. This work is a first step toward the incremental computation of patterns that locally fit a digital surface for the accurate approximation of tangent planes.

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Acknowledgements

This work has been funded by PARADIS ANR-18-CE23-0007-01 research grant.

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Authors and Affiliations

  1. UMR5205, INSA Lyon, CNRS, UCBL, LIRIS, Univ Lyon, 69622, Villeurbanne, France

    Tristan Roussillon

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  1. Tristan Roussillon
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Tristan Roussillon wrote the whole paper and prepared all figures.

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Correspondence to Tristan Roussillon.

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Roussillon, T. Combinatorial Generation of Planar Sets. J Math Imaging Vis 65, 702–717 (2023). https://doi.org/10.1007/s10851-023-01152-z

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