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Raytracing Point Clouds Using Geometric Algebra

Deul, Crispin and Burger, Michael and Hildenbrand, Dietmar and Koch, Andreas :
Raytracing Point Clouds Using Geometric Algebra.
In: International Workshop on Computer Graphics, Computer Vision and Mathematics. University of West Bohemia, Plzen
[Conference or Workshop Item] , (2009)

Abstract

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.

Item Type: Conference or Workshop Item
Erschienen: 2009
Creators: Deul, Crispin and Burger, Michael and Hildenbrand, Dietmar and Koch, Andreas
Title: Raytracing Point Clouds Using Geometric Algebra
Language: English
Abstract:

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.

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)
Divisions: Department of Computer Science
Department of Computer Science > Scientific Computing
Department of Computer Science > Simulation of multibody systems and deformable bodies
Zentrale Einrichtungen
Event Title: International Workshop on Computer Graphics, Computer Vision and Mathematics
Date Deposited: 26 Mar 2015 14:07
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