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A Mathematica Package for Visualizing Objects Inmersed in \(\mathbb {R}^{4}\)

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Computational Science and Its Applications – ICCSA 2019 (ICCSA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11624))

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Abstract

Visualizing objects in a space of a certain dimension is quite useful to facilitate the understanding of the mathematical concepts linked to such objects, through the geometric interpretation of them. This paper describes a new Mathematica package, 4DSketches, for visualizing objects immersed in \(\mathbb {R}^{4}\) (points, lines, arrows, curves, surfaces, solids and complex surfaces) using 3D models as an extension of the 2D models, already established, for visualizing objects immersed in \(\mathbb {R}^{3}\). To simulate the change of views in \(\mathbb {R}^{4}\) rotational matrices are used. In addition, our outputs are consistent with Mathematica’s notation. To show the performance of the package, several illustrative and interesting examples are described.

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Acknowledgements

The authors would like to thank to the authorities of the Universidad Nacional de Piura for the acquisition of the Mathematica 11.0 license and the reviewers for their valuable comments and suggestions.

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Authors and Affiliations

  1. Universidad Nacional de Piura, Urb. Miraflores s/n, Castilla, Piura, Peru

    Ricardo Velezmoro & Robert Ipanaqué

  2. Universidad Privada Antenor Orrego, Av. Los Tallanes Zona Los Ejidos s/n, Piura, Peru

    Josel A. Mechato

Authors
  1. Ricardo Velezmoro
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  2. Robert Ipanaqué
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  3. Josel A. Mechato
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Corresponding author

Correspondence to Robert Ipanaqué .

Editor information

Editors and Affiliations

  1. Covenant University, Ota, Nigeria

    Sanjay Misra

  2. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  3. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir Korkhov

  6. Polytechnic University of Bari, Bari, Italy

    Carmelo Torre

  7. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  8. Monash University, Clayton, VIC, Australia

    David Taniar

  9. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  10. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

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Velezmoro, R., Ipanaqué, R., Mechato, J.A. (2019). A Mathematica Package for Visualizing Objects Inmersed in \(\mathbb {R}^{4}\). In: Misra, S., et al. Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science(), vol 11624. Springer, Cham. https://doi.org/10.1007/978-3-030-24311-1_35

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  • DOI: https://doi.org/10.1007/978-3-030-24311-1_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24310-4

  • Online ISBN: 978-3-030-24311-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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