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Non-parametric Realtime Rendering of Subspace Objects in Arbitrary Geometric Algebras

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Advances in Computer Graphics (CGI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11542))

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Abstract

This paper introduces a novel visualization method for elements of arbitrary Geometric Algebras. The algorithm removes the need for a parametric representation, requires no precomputation, and produces high quality images in realtime. It visualizes the outer product null space (OPNS) of 2-dimensional manifolds directly and uses an isosurface approach to display 1- and 0-dimensional manifolds. A multi-platform browser based implementation is publicly available.

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Acknowledgments

The author would like to thank Vincent Nozick for posing the challenge that ultimately led to the implementation presented here, Stephane Breuils for such an exquisite stress test with his QCGA and Leo Dorst for his extensive review of the manuscript. Further thanks go to Charles Gunn and Hugo Hadfield for proofreading.

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Authors and Affiliations

  1. Matrix Factory, Hingene, Bornem, Belgium

    Steven De Keninck

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  1. Steven De Keninck
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Correspondence to Steven De Keninck .

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Editors and Affiliations

  1. University of Calgary, Calgary, AB, Canada

    Marina Gavrilova

  2. Bournemouth University, Poole, UK

    Jian Chang

  3. University of Geneva, MIRALab, Carouge, Switzerland

    Nadia Magnenat Thalmann

  4. International Christian University, Tokyo, Japan

    Eckhard Hitzer

  5. Waseda University, Tokyo, Japan

    Hiroshi Ishikawa

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De Keninck, S. (2019). Non-parametric Realtime Rendering of Subspace Objects in Arbitrary Geometric Algebras. In: Gavrilova, M., Chang, J., Thalmann, N., Hitzer, E., Ishikawa, H. (eds) Advances in Computer Graphics. CGI 2019. Lecture Notes in Computer Science(), vol 11542. Springer, Cham. https://doi.org/10.1007/978-3-030-22514-8_54

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  • DOI: https://doi.org/10.1007/978-3-030-22514-8_54

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22513-1

  • Online ISBN: 978-3-030-22514-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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