Li H. Invariant Algebras and Geometric Reasoning

World Scientific Publ., 2008. — 533 p. — ISBN 9812708081.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,…Projective Space, Bracket Algebra and Grassmann Cayley Algebra;
Projective Incidence Geometry with Cayley Bracket Algebra;
Projective Conic Geometry with Bracket Algebra and Quadratic Grassmann Cayley Algebra;
Inner-product Bracket Algebra and Clifford Algebra;
Geometric Algebra;
Euclidean Geometry and Conformal Grassmann Cayley Algebra;
Conformal Clifford Algebra and Classical Geometries.