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Geometry and Computing #4: Geometric Algebra with Applications in Engineering

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Geometry and Computing #4: Geometric Algebra with Applications in Engineering Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book examines all aspects essential for a successful application of geometric algebra to engineering--the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data.

Table of Contents

Introduction.- Learning Geometric Algebra with CLUCalc.- Algebra.- Geometries.- Numerics.- Uncertain Geometric Entities and Operators.- The Inversion Camera Model.- Monocular Pose Estimation.- Versor Functions.- Random Variable Space.

Product Details

ISBN:
9783540890676
Author:
Perwass, Christian
Publisher:
Springer
Subject:
Computer Vision
Subject:
CAD-CAM - General
Subject:
Geometry - Algebraic
Subject:
Algebra
Subject:
Applied mathematics
Subject:
CLUCalc
Subject:
Computer graphics
Subject:
geometric algebra
Subject:
geometric computing
Subject:
Geometry
Subject:
Inversion camera model
Subject:
Machine vision.
Subject:
Pose estimation
Subject:
Pythagorean-hodographs
Subject:
Robotics
Subject:
Uncertain geometry
Subject:
Versor functions
Subject:
Visualization
Subject:
Computer Imaging, Vision, Pattern Recognition and Graphics
Subject:
Computational intelligence
Subject:
Algebraic Geometry
Subject:
Computer-Aided Engineering (CAD, CAE) and Design
Subject:
Computers-Reference - General
Copyright:
Edition Description:
Book
Series:
Geometry and Computing
Series Volume:
4
Publication Date:
20081216
Binding:
HARDCOVER
Language:
English
Pages:
400
Dimensions:
235 x 155 mm

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Geometry and Computing #4: Geometric Algebra with Applications in Engineering New Hardcover
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Product details 400 pages Springer - English 9783540890676 Reviews:
"Synopsis" by , This book examines all aspects essential for a successful application of geometric algebra to engineering--the theoretical foundations, the representation of geometric constraints, and the numerical estimation from uncertain data.
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