Foundations of Geometry

In Part One of this comprehensive and frequently cited treatment, the authors develop Euclidean and Bolyai-Lobachevskian geometry on the basis of an axiom system due, in principle, to the work of David Hilbert. Part Two develops projective geometry in much the same way. An Introduction provides background on topological space, analytic geometry, and other relevant topics, and rigorous proofs appear throughout the text.

This proceedings book helps bring insights from this array of technical sub-topics together, as advanced robot algorithms draw on the combined expertise of many fields—including control theory, computational geometry and topology, geometrical and physical modeling, reasoning under uncertainty, probabilistic algorithms, game theory, and theoretical computer science. Intelligent robots and autonomous systems depend on algorithms that efficiently realize functionalities ranging from perception to decision making, from motion planning to control.