Geometric Algebra With Applications In Engineering

The application of geometric algebra to the engineering sciences is a youngactive subject of research. The promise of this field is that the mathematicalstructu... » 

The application of geometric algebra to the engineering sciences is a youngactive subject of research. The promise of this field is that the mathematicalstructure of geometric algebra together with its descriptive power will resultin intuitive and more robust algorithms. This book examines all aspectsessential for a successful application of geometric algebra the theoreticalfoundations the representation of geometric constraints and the numericalestimation from uncertain data. Formally the book consists of two partstheoretical foundations and applications. The first part includes chapters onrandom variables in geometric algebra linear estimation methods thatincorporate the uncertainty of algebraic elements and the representation ofgeometry in Euclidean projective conformal and conic space. The second partis dedicated to applications of geometric algebra which include uncertaingeometry and transformations a generalized camera model and pose estimation.Graduate students scientists researchers and practitioners will benefit fromthis book. The examples given in the text are mostly recent research resultsso practitioners can see how to apply geometric algebra to real tasks whileresearchers note starting points for future investigations. Students willprofit from the detailed introduction to geometric algebra while the text issupported by the authors visualization software CLUCalc freely availableonline and a website that includes downloadable exercises slides andtutorials. TOCIntroduction. 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. «