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Rigid Body Dynamics and Conformal Geometric Algebra Read chapter Read first chapter

2011 | OriginalPaper | Chapter

10. On Geometric Theorem Proving with Null Geometric Algebra

Authors : Hongbo Li, Yuanhao Cao

Published in: Guide to Geometric Algebra in Practice

Publisher: Springer London

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Abstract

The bottleneck in symbolic geometric computation is middle expression swell. Another embarrassing problem is geometric explanation of algebraic results, which is often impossible because the results are not invariant under coordinate transformations. In classical invariant-theoretical methods, the two difficulties are more or less alleviated but stay, while new difficulties arise.
In this chapter, we introduce a new framework for symbolic geometric computing based on conformal geometric algebra: the algebra for describing geometric configuration is null Grassmann–Cayley algebra, the algebra for advanced invariant manipulation is null bracket algebra, and the algebra underlying both algebras is null geometric algebra. When used in geometric computing, the new approach not only brings about amazing simplifications in algebraic manipulation, but can be used to extend and generalize existing theorems by removing some geometric constraints from the hypotheses.

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previous chapter Color Object Recognition Based on a Clifford Fourier Transform
next chapter On the Use of Conformal Geometric Algebra in Geometric Constraint Solving
Footnotes
1
Editorial note: This characterization of CGA is more restrictive than elsewhere in this book, where (10.19) is employed.
 
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Metadata
Title
On Geometric Theorem Proving with Null Geometric Algebra
Authors
Hongbo Li
Yuanhao Cao
Copyright Year
2011
Publisher
Springer London
Book
Guide to Geometric Algebra in Practice

Print ISBN: 978-0-85729-810-2

Electronic ISBN: 978-0-85729-811-9

Copyright Year: 2011

DOI
https://doi.org/10.1007/978-0-85729-811-9_10

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