Title: | Duality and Intersection Computation in Projective Space with GPU support |
Authors: | Skala, Václav |
Citation: | Latest Trends on Applied Mathematics, Simulation, Modelling : 4th International Conference on Applied Mathematics, Simulation, Modelling (ASM'10), p. 66-71. |
Issue Date: | 2010 |
Publisher: | WSEAS |
Document type: | konferenční příspěvek conferenceObject |
URI: | http://hdl.handle.net/11025/11797 |
ISBN: | 978-960-474-210-3 |
ISSN: | 1792-4332 |
Keywords: | aplikovaná matematika;výpočet průsečíků;grafické procesory;počítačová grafika |
Keywords in different language: | applied mathematics;intersection computation;graphic processing units;computer graphics |
Abstract: | There are many geometric algorithms based on computation of intersection of lines, planes etc. Sometimes, very complex mathematical notations are used to express simple mathematical solutions, even if their formulation in the projective space offers much more simple solution. This paper presents solution of selected problems using principle of duality and projective space representation. It will be shown that alternative formulation in the projective space offers quite surprisingly simple solutions that lead to more robust and faster algorithms which are convenient for use within parallel architectures as GPU (Graphical Processor Units- NVIDIA) or Larrabee (Intel), which can speed up solutions of numerical problems in magnitude of 10-100. It is shown that a solution of a system of linear equations is equivalent to generalized cross product, which leads with the duality principle to new algorithms. This is presented on a new formulation of a line in 3D given as intersection of two planes which is robust and fast, based on duality of Plücker coordinates.The presented approach for intersection computation is well suited especially for applications where robustness is required, e.g. large GIS/CAD/CAM systems etc. |
Rights: | Original paper is published under copyright license: © 2012 WSEAS |
Appears in Collections: | Konferenční příspěvky / Conference Papers (KIV) |
Files in This Item:
File | Description | Size | Format | |
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Skala_2010_Corfu-NAUN-Duality.pdf | Plný text | 759,78 kB | Adobe PDF | View/Open |
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