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Examination of new geometric algebras including a visualization and integration in a geometric algebra compiler

Steinmetz, Christian (2013):
Examination of new geometric algebras including a visualization and integration in a geometric algebra compiler.
TU Darmstadt, [Master Thesis]

Abstract

Geometric algebra is a powerful mathematical framework which enables one to formulate and compute geometric intuitive algorithms, especially on massively-parallel hardware. A geometric algebra compiler facilitates the integration of geometric algebra algorithms in source code. This work makes a geometric algebra compiler capable of supporting arbitrary geometric algebras. It also integrates a visualization tool in this geometric algebra compiler. The visualization tool will be able to visualize elements of arbitrary geometric algebras with a minimum of preceding knowledge on the concrete geometric algebra. This results in a less researcher effort. Furthermore, some new geometric algebras will be investigated by using the developed visualization tool.

Item Type: Master Thesis
Erschienen: 2013
Creators: Steinmetz, Christian
Title: Examination of new geometric algebras including a visualization and integration in a geometric algebra compiler
Language: English
Abstract:

Geometric algebra is a powerful mathematical framework which enables one to formulate and compute geometric intuitive algorithms, especially on massively-parallel hardware. A geometric algebra compiler facilitates the integration of geometric algebra algorithms in source code. This work makes a geometric algebra compiler capable of supporting arbitrary geometric algebras. It also integrates a visualization tool in this geometric algebra compiler. The visualization tool will be able to visualize elements of arbitrary geometric algebras with a minimum of preceding knowledge on the concrete geometric algebra. This results in a less researcher effort. Furthermore, some new geometric algebras will be investigated by using the developed visualization tool.

Divisions: 20 Department of Computer Science
Date Deposited: 30 Mar 2017 06:48
Alternative Abstract:
Alternative abstract Language

Die Geometrische Algebra ist ein mächtiges mathematisches Framework, das es einem ermöglicht, geometrisch intuitive Algorithmen zu formulieren und zu berechnen, vor allem auf massiv-paralleler Hardware. Ein Geometrische Algebra Compiler vereinfacht die Integration von Geometrische Algebra Algorithmen in Quelltext. Diese Arbeit befähigt einen Geometrische Algebra Compiler beliebige Geometrische Algebren zu unterstützen. Sie integriert auch ein Visualisierungswerkzeug in diesen Geometrische Algebra Compiler. Das Visualisierungswerkzeug wird fähig sein, Elemente von beliebigen Geometrischen Algebras mit einem Minimum an vorhergehendem Wissen von einer konkreten Geometrischen Algebra zu visualisieren. Dies führt zu einem geringeren Aufwand für den Forscher. Des Weiteren werden einige neue geometrische Algebras unter zu Hilfenahme des entwickelten Visualisierungswerkzeugs untersucht.

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