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Raytracing Point Clouds Using Geometric Algebra

Deul, Crispin ; Burger, Michael ; Hildenbrand, Dietmar ; Koch, Andreas (2022):
Raytracing Point Clouds Using Geometric Algebra. (Publisher's Version)
In: GraVisMa 2009 Proceedings, pp. 32-39,
Darmstadt, University of West Bohemia, Plzen, International Workshop on Computer Graphics, Computer Vision and Mathematics, Plzen, Czech Republic, 01.-04.09.2009, ISBN 978-80-86943-90-9,
DOI: 10.26083/tuprints-00021261,
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Item Type: Conference or Workshop Item
Origin: Secondary publication service
Status: Publisher's Version
Title: Raytracing Point Clouds Using Geometric Algebra
Language: English

Geometric Algebra (GA) supports the geometrically intuitive development of an algorithm with its build-in geometric primitives such as points, lines, spheres or planes. But on the negative side GA has a huge computational footprint. In this paper we study how GA can compete with traditional methods from Linear Algebra (LA) in the field of raytracing. We examine the raytracing algorithm for both GA and LA on the basis of primitive operations. Furthermore we introduce a novel framework for rendering point clouds based on spheres and planes as surface elements. We use this model to benchmark implementations of both algebras. Our results show that depending on the microprocessor architecture like CPUs, FPGAs or GPUs Geometric Algebra and Linear Algebra can raytrace with comparable speed.

Book Title: GraVisMa 2009 Proceedings
Place of Publication: Darmstadt
Publisher: University of West Bohemia, Plzen
Uncontrolled Keywords: Forschungsgruppe Geometric Algebra Computing (GACO), Geometric algebra (GA), General Purpose Computation on Graphics Processing Unit (GPGPU), Point clouds, Field-programmable gate array (FPGA)
Classification DDC: 000 Allgemeines, Informatik, Informationswissenschaft > 004 Informatik
500 Naturwissenschaften und Mathematik > 510 Mathematik
Divisions: 20 Department of Computer Science > Embedded Systems and Applications
20 Department of Computer Science > Interactive Graphics Systems
20 Department of Computer Science > Scientific Computing
Event Title: International Workshop on Computer Graphics, Computer Vision and Mathematics
Event Location: Plzen, Czech Republic
Event Dates: 01.-04.09.2009
Date Deposited: 03 May 2022 11:52
Last Modified: 07 Nov 2022 10:22
DOI: 10.26083/tuprints-00021261
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-212616
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/21261
PPN: 49550405X
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