Title: Interpolation in Conformal Geometric Algebra: Toward Unified Interpolation of Euclidean Motions in the Conformal Model of Geometric Algebra
Publisher: LAP LAMBERT Academic Publishing
Publication Date: 2011
Language: English
ISBN 10: 3843380910
ISBN 13: 9783843380911
Binding: Soft cover
Condition: New
Weight: 354 grams

About this title

Synopsis

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.

About the Author

Arvid Halma holds the position of Innovator at the Computer Vision and Statistics department of the Netherlands Organization for Applied Scientific Research, TNO. He obtained a MSc degree with honor in Artificial Intelligence from the University of Amsterdam.

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