Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Raytracing point clouds using geometric algebra
 Skala, Vaclav (Ed.); Hildenbrand, Dietmar (Ed.) ; European Association for Computer Graphics EUROGRAPHICS: GraVisMa 2009, International Workshop on Computer Graphics, Computer Vision and Mathematics. Workshop proceedings : Held at the University of West Bohemia in Plzen, Czech Republic on September 2  4, 2009 / in cooperation with EUROGRAPHICS Pilsen: University of West Bohemia, 2009 ISBN: 9788086943909 pp.3239 
 International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) <1, 2009, Plzen> 

 English 
 Conference Paper 
 Fraunhofer IGD () 
 geometric algebra; General Purpose Computation on Graphics Processing Unit (GPGPU); point cloud; Field Programmable Gate Array (FPGA); Forschungsgruppe Geometric Algebra Computing (GACO) 
Abstract
Geometric Algebra (GA) supports the geometrically intuitive development of an algorithm with its buildin 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.