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

  • Steven De KeninckEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11542)


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.


Geometric algebra Implicit visualization OPNS 



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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Matrix FactoryBornemBelgium

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