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. Key Features • Contains unique, up-to-date symbolic algebraic development of Grassmann–Cayley algebra and geometric algebra for immediate applications to discrete and computational geometry, computer vision, graphics and robotics • Captures the intrinsic beauty of geometric languages and conducted computing through highly efficient geometric computing algorithms and abundant examples from practice • Suitable for researchers in discrete and computational geometry, computer algebra and symbolic computation, practitioners of invariant methods, as well as graduate students with a moderate algebraic background

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