Invariant Algebras and Geometric Reasoning

Invariant Algebras and Geometric Reasoning

by Hongbo Li
     
 

ISBN-10: 9812708081

ISBN-13: 9789812708083

Pub. Date: 03/04/2008

Publisher: World Scientific Publishing Company, Incorporated

The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics — among them, Grassmann–Cayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries.This book contains the author and…  See more details below

Overview

The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics — among them, Grassmann–Cayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries.This book contains the author and his collaborators' most recent, original development of Grassmann–Cayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras — Cayley bracket algebra, conformal geometric algebra, and null bracket algebra — for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide.

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Product Details

ISBN-13:
9789812708083
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
03/04/2008
Pages:
532
Product dimensions:
6.60(w) x 9.80(h) x 1.30(d)

Related Subjects

Table of Contents

1 Introduction 1

2 Projective Space, Bracket Algebra and Grassmann-Cayley Algebra 25

3 Projective Incidence Geometry with Cayley Bracket Algebra 89

4 Projective Conic Geometry with Bracket Algebra and Quadratic Grassmann-Cayley Algebra 151

5 Inner-product Bracket Algebra and Clifford Algebra 219

6 Geometric Algebra 273

7 Euclidean Geometry and Conformal Grassmann-Cayley Algebra 339

8 Conformal Clifford Algebra and Classical Geometries 411

Appendix A Cayley Expansion Theory for 2D and 3D Projective Geometries 469

Bibliography 495

Index 505

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