Title: Computation in Projective Space
Authors: Skala, Václav
Citation: Mathematical Methods, System Theory and Control: Proceedings of the 11th WSEAS International Conference on Mathematicla Methods, Computational Techniques & Intelligent Systems (MAMECTIS´09), p. 152-157.
Issue Date: 2009
Publisher: WSEAS
Document type: preprint
URI: http://hdl.handle.net/11025/11344
ISBN: 978-960-474-094-9
Keywords: počítačová grafika;homogenní souřadnice;Plückerovy souřadnice;projektivní geometrie;princip duality
Keywords in different language: computer graphics;homogeneous coordinates;Plücker coordinates;projective geometry;principle of duality
Abstract: This paper presents solutions of some selected problems that can be easily solved by the projective space representation. If the principle of duality is used, quite surprising solutions can be found and new useful theorems can be generated as well. There are many algorithms based on computation of intersection of lines, planes, barycentric coordinates etc. Those algorithms are based on representation in the Euclidean space. Sometimes, very complex mathematical notations are used to express simple mathematical solutions. It will be shown that it is not necessary to solve linear system of equations to find the intersection of two lines in the case of E2 or the intersection of three planes in the case of E3. Plücker coordinates and principle of duality are used to derive an equation of a parametric line in E3 as an intersection of two planes. This new formulation avoids division operations and increases the robustness of computation.
Rights: Original article published under copyright license: © 2009 WSEAS
Appears in Collections:Preprinty / Preprints (KIV)

Files in This Item:
File Description SizeFormat 
Skala_2009_Projective-Tenerife.pdfPlný text495,84 kBAdobe PDFView/Open

Please use this identifier to cite or link to this item: http://hdl.handle.net/11025/11344

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.