Обложка Interpolation in Conformal Geometric Algebra
Название книги:

Interpolation in Conformal Geometric Algebra

Toward Unified Interpolation of Euclidean Motions in the Conformal Model of Geometric Algebra

LAP LAMBERT Academic Publishing (2011-03-06 )

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ISBN-13:

978-3-8433-8091-1

ISBN-10:
3843380910
EAN:
9783843380911
Язык Книги:
Английский
Краткое описание:
This thesis shows how the conformal model in geometric algebra is able to describe Euclidean geometry. Since transformations in this model are structure preserving, this algebra is able to treat motions in a unified way. In our search for a general interpolation method of transformations, we focus on determining their logarithms. First we look at how Taylor series can be evaluated for transformations in this algebra. A drawback is that in general infinite series has to be evaluated to achieve exact results. Therefore we also present our generalized Chasles theorem, that classically only takes care of rotations and translations, to decompose motions such that they can be interpolated having a closed form expression. The proposed method successfully describes logarithms of certain compositions of basic transformations, but is not able to yield the general logarithm of a conformal transformation. In our search for such a general logarithm, we have investigated many potentially useful properties and representations, summarized in the appendices.
Издательский Дом:
LAP LAMBERT Academic Publishing
Веб-сайт:
https://www.lap-publishing.com/
By (author) :
Arvid Halma
Количество страниц:
152
Опубликовано:
2011-03-06
Акции:
В наличии
Категория:
Геометрия
Цена:
59.00 €
Ключевые слова:
Mathematics, geometry, interpolation, Geometric Algebra, Clifford Algebra, Conformal Model, Euclidean Motions, Chasles Theorem, Interpolationsangriff

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