Top

Published in:

2019 | OriginalPaper | Chapter

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

Author : Steven De Keninck

Published in: Advances in Computer Graphics

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Cubic Curves and Cubic Surfaces from Contact Points in Conformal Geometric Algebra

next chapter Automatic Normal Orientation in Point Clouds of Building Interiors

Gunn, C.: Geometric algebras for Euclidean geometry. Adv. Appl. Clifford Algebra 27(1), 185–208 (2017). https://arxiv.org/abs/1411.650MathSciNetCrossRef

Hestenes, D.: New Foundations for Classical Mechanics, 2nd edn. D. Reidel, Dordrecht/Boston (1999)MATH

Dorst, L., Fontijne, D., Mann, S.: Geometric Algebra for Computer Science: An Object-Oriented Approach To Geometry. Morgan Kaufmann, Burlington (2007)

Dorst, L., Fontijne, D., Mann, S.: GAViewer. http://www.geometricalgebra.net

Perwass, C.: CLUCalc/CLUViz. http://www.clucalc.info

De Keninck, S.: Ganja.js. Geometric Algebra - Not Just Algebra (2017). https://github.com/enkimute/ganja.js

Hart, J.C.: sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces (1994). https://doi.org/10.1007/s003710050084CrossRef

Inigo Quilez - iq/rgba: Rendering worlds with two triangles. NVSCENE (2008). http://www.iquilezles.org/www/material/nvscene2008/rwwtt.pdf

Breuils, S., Nozick, V., Sugimoto, A., Hitzer, E.: Quadric conformal geometric algebra of \(\mathbb{R}_{4,4}\). Adv. Appl. Cliord Algebras 28, 35 (2018). https://doi.org/10.1007/s00006-018-0851-1MathSciNetCrossRefMATH

10.

Juan, D., Goldman, R., Mann, S.: Modeling 3D Geometry in the clifford algebra \(\mathbb{R}_{4,4}\) Adv. Appl. Appl. Clifford Algebras 27(4), 3039–3062 (2017)MathSciNetCrossRef

11.

Zamora-Esquivel, J.: \(G_{6,3}\) geometric algebra; description and implementation. Adv. Appl. Clifford Algebras 24(2), 493–514 (2014)MathSciNetCrossRef

12.

Hadfield, H., Lasenby, J.: Direct linear interpolation of geometric objects in conformal geometric algebra. To be published

Title: Non-parametric Realtime Rendering of Subspace Objects in Arbitrary Geometric Algebras
Author: Steven De Keninck
Publisher: Springer International Publishing
Book: Advances in Computer Graphics
Print ISBN: 978-3-030-22513-1

Electronic ISBN: 978-3-030-22514-8

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-22514-8_54

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner