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Raytracing point clouds using geometric algebra

: Deul, Crispin; Burger, Michael; Hildenbrand, Dietmar; Koch, Andreas

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: 978-80-86943-90-9
International Workshop on Computer Graphics, Computer Vision and Mathematics (GraVisMa) <1, 2009, Plzen>
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)

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.