Geometric Algebra with Applications in Engineering

✍ Scribed by Christian Perwass (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2009
• Tongue: English
• Leaves: 386
• Series: Geometry and Computing 4
• Edition: 1
• Category: Library

✦ Synopsis

The application of geometric algebra to the engineering sciences is a young, active subject of research. The promise of this field is that the mathematical structure of geometric algebra together with its descriptive power will result in intuitive and more robust algorithms.

This book examines all aspects essential for a successful application of geometric algebra: the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data. Formally, the book consists of two parts: theoretical foundations and applications. The first part includes chapters on random variables in geometric algebra, linear estimation methods that incorporate the uncertainty of algebraic elements, and the representation of geometry in Euclidean, projective, conformal and conic space. The second part is dedicated to applications of geometric algebra, which include uncertain geometry and transformations, a generalized camera model, and pose estimation.

Graduate students, scientists, researchers and practitioners will benefit from this book. The examples given in the text are mostly recent research results, so practitioners can see how to apply geometric algebra to real tasks, while researchers note starting points for future investigations. Students will profit from the detailed introduction to geometric algebra, while the text is supported by the author's visualization software, CLUCalc, freely available online, and a website that includes downloadable exercises, slides and tutorials.

✦ Table of Contents

Front Matter....Pages i-xiv
Introduction....Pages 1-23
Learning Geometric Algebra with CLUCalc....Pages 25-48
Algebra....Pages 51-117
Geometries....Pages 119-195
Numerics....Pages 197-251
Uncertain Geometric Entities and Operators....Pages 255-276
The Inversion Camera Model....Pages 277-297
Monocular Pose Estimation....Pages 299-324
Versor Functions....Pages 325-349
Random-Variable Space....Pages 351-368
Back Matter....Pages 369-385

✦ Subjects

Computer Imaging, Vision, Pattern Recognition and Graphics; Geometry; Computational Intelligence; Algebraic Geometry; Visualization; Computer-Aided Engineering (CAD, CAE) and Design