Fractions, Projective Representation, Duality, Linear Algebra and Geometry

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F16%3A43952030" target="_blank" >RIV/49777513:23520/16:43952030 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Fractions, Projective Representation, Duality, Linear Algebra and Geometry

Popis výsledku v původním jazyce

This contribution describes relationship between fractions, projective representation, duality, linear algebra and geometry. Many problems lead to a system of linear equations. This paper presents equivalence of the Cross-product operation and solution of a system of linear equations Ax=0 or Ax=b using projective space representation and homogeneous coordinates. It leads to conclusion that division operation is not required for a solution of a system of linear equations, if the projective representation and homogeneous coordinates are used. An efficient solution on CPU and GPU based architectures is presented with an application to barycentric coordinates computation as well.

Název v anglickém jazyce

Fractions, Projective Representation, Duality, Linear Algebra and Geometry

Popis výsledku anglicky

This contribution describes relationship between fractions, projective representation, duality, linear algebra and geometry. Many problems lead to a system of linear equations. This paper presents equivalence of the Cross-product operation and solution of a system of linear equations Ax=0 or Ax=b using projective space representation and homogeneous coordinates. It leads to conclusion that division operation is not required for a solution of a system of linear equations, if the projective representation and homogeneous coordinates are used. An efficient solution on CPU and GPU based architectures is presented with an application to barycentric coordinates computation as well.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/LH12181" target="_blank" >LH12181: Vývoj algoritmů počítačové grafiky a pro CAD/CAM systémy Development of Algorithms for Computer Graphics and CAD/CAM systems</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů