Non-parametric Realtime Rendering of Subspace Objects in Arbitrary Geometric Algebras
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.
KeywordsGeometric 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.
- 3.Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science: An Object-Oriented Approach To Geometry. Morgan Kaufmann, Burlington (2007)Google Scholar
- 4.Dorst, L., Fontijne, D., Mann, S.: GAViewer. http://www.geometricalgebra.net
- 5.Perwass, C.: CLUCalc/CLUViz. http://www.clucalc.info
- 6.De Keninck, S.: Ganja.js. Geometric Algebra - Not Just Algebra (2017). https://github.com/enkimute/ganja.js
- 8.Inigo Quilez - iq/rgba: Rendering worlds with two triangles. NVSCENE (2008). http://www.iquilezles.org/www/material/nvscene2008/rwwtt.pdf
- 12.Hadfield, H., Lasenby, J.: Direct linear interpolation of geometric objects in conformal geometric algebra. To be publishedGoogle Scholar