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# ðŸ“™ Invariant Algebras And Geometric Reasoning by Hongbo Li â€” download pdf

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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's most recent, original development of Grassmann-Cayley algebra and geometric algebra and their applications in automated reasoning of classical geometries. It includes 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. Read more... Projective Space, Bracket Algebra and Grassmann-Cayley Algebra; Projective Incidence Geometry with Cayley Bracket Algebra; Projective Conic Geometry and Binary Grassmann-Cayley Algebra; Clifford Algebra and Geometric Algebra; Conformal Geometric Algebra for Classical Geometries; Null Bracket Algebra and Euclidean Geometry

## About book:

## About file:

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- Author:
**Hongbo Li** - Year:
**2008** - Publisher:
**World Scientific Publishing Company** - Language:
**English** - ISBN:
**9812708081,9789812708083,9789812770110**

- File size:
**8 957 280** - Format:
**pdf**

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Geometry is a powerful tool to solve a great number of problems in robotics and computer vision. Impressive results have been obtained in these fields in the last decade. It is a new challenge to solve problems of the actual world which require the abilit...

This book covers the design, construction, and implementation of algebraic-geometric codes from Hermitian curves. Matlab simulations of algebraic-geometric codes and Reed-Solomon codes compare their bit error rate using different modulation schemes over a...

This book presents a collection of articles on the general framework of mechanizing deduction in the logics of practical reasoning. Topics treated are novel approaches in the field of constructive algebraic methods (theory and algorithms) to handle geomet...

Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In th...

The central subject of the book - the theory of shift-invariant algebras - is an outgrowth of the established theory of generalized analytic functions. Associated subalgebras of almost periodic functions of real variables and of bounded analytic functions...

Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, a...

Within the last decade, Geometric Algebra (GA) has emerged as a powerful alternative to classical matrix algebra as a comprehensive conceptual language and computational system for computer science. This book will serve as a standard introduction and refe...

Algebraic projective geometry, with its multilinear relations and its embedding into Grassmann-Cayley algebra, has become the basic representation of multiple view geometry, resulting in deep insights into the algebraic structure of geometric relations, a...

Shift-invariant algebras are uniform algebras of continuous functions de?ned on compactconnectedgroups,thatareinvariantundershiftsbygroupelements. They areoutgrowths of generalized analytic functions, introduced almost ?fty yearsago by Arens and Singer, a...