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A generalized combinatorial marching hypercube algorithm

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Abstract

We present a Generalized Combinatorial Marching Hypercubes algorithm to compute a cell complex approximation of a manifold of any dimension and co-dimension, that is, a manifold of dimension \(n-k\) embedded into an n-dimensional space. The algorithm uses combinatorial and topological methods to avoid the use of expensive lookup tables and hence is efficient in higher dimensions. We illustrate the effectiveness of our algorithm in higher dimensions and compare its performance with a similar algorithm based on a simplicial decomposition of the domain.

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Data Availability

The data which supports the findings of this study was generated using the code available at https://github.com/gknakassima/GCMH. The images were generated using this data and the visualization software available at https://github.com/GSBicalho/TrueNgineJS.

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Acknowledgements

The authors would like to thank Gabriel Scalet Bicalho for providing the software used to project and visualize the manifolds in this paper. The source code for the visualization software can be downloaded at https://github.com/GSBicalho/TrueNgineJS. This work was supported by the São Paulo Research Foundation (FAPESP) Grants 2013/07375-0 and 2019/07316-0, Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grant No. 307483/2017-7). The work of G.N. was supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001. The work of L.M.B. was supported by the São Paulo Research Foundation (FAPESP) Grant 2017/25631-4. The work of M.G. was partially supported by the National Science Foundation under awards DMS-1839294 and HDR TRIPODS award CCF-1934924, DARPA contract HR0011-16-2-0033, National Institutes of Health award R01 GM126555, and Air Force Office of Scientific Research under award numbers FA9550-23-1-0011 and AWD00010853-MOD002, by FAPESP Grant 2019/06249-7 and CNPq Grant 309073/2019-7.

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Authors and Affiliations

  1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Antonio Castelo, Guilherme Nakassima, Lucas Moutinho Bueno & Marcio Gameiro

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, USA

    Marcio Gameiro

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  1. Antonio Castelo
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  2. Guilherme Nakassima
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  3. Lucas Moutinho Bueno
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  4. Marcio Gameiro
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Correspondence to Guilherme Nakassima.

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Communicated by Carlos Hoppen.

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Castelo, A., Nakassima, G., Bueno, L.M. et al. A generalized combinatorial marching hypercube algorithm. Comp. Appl. Math. 43, 127 (2024). https://doi.org/10.1007/s40314-024-02627-4

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