Projective Geometric Algebra - Barycentric and Plücker Coordinates Computation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43976554" target="_blank" >RIV/49777513:23520/22:43976554 - 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

Projective Geometric Algebra - Barycentric and Plücker Coordinates Computation

Popis výsledku v původním jazyce

This paper presents the computation of the barycentric coordinates and Plücker coordinates using the projective extension of the Euclidean space and geometric algebra. Using the projective extension, it also presents a relationship between linear systems of equations Ax=b and Ax=0 using the projective extension. An application of the principle of duality enables solving dual problems efficiently. The given approach uses vector notation leading to efficient implementation on GPU or efficient use of SSE instructions. As the presented approach is based on projective notation, the division operation is postponed and the proposed method leads to higher computational robustness

Název v anglickém jazyce

Projective Geometric Algebra - Barycentric and Plücker Coordinates Computation

Popis výsledku anglicky

This paper presents the computation of the barycentric coordinates and Plücker coordinates using the projective extension of the Euclidean space and geometric algebra. Using the projective extension, it also presents a relationship between linear systems of equations Ax=b and Ax=0 using the projective extension. An application of the principle of duality enables solving dual problems efficiently. The given approach uses vector notation leading to efficient implementation on GPU or efficient use of SSE instructions. As the presented approach is based on projective notation, the division operation is postponed and the proposed method leads to higher computational robustness

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

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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