This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra, triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and Steiner trees. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm.
Geometric constraint solving, C.M. Hoffmann; computational geometry, B.
Chazelle; the Exact Computation Paradigm, C. Yap; mesh generation and optimal
triangulation, M. Bern and D. Eppstein; machine proofs of geometry theorems,
S.-C. Chou and M. Rathi; randomized geometric algorithms, K.L. Clarkson;
Voronoi diagrams and Delauney triangulations, S. Fortune; the state of art on
Steiner ratio problems, D.-Z. Du and F. Hwang; on the development of
quantitative geometry from Pythagoras to Grassmann, W.-Y. Hsiang;
computational geometry and topological network design, J.M. Smith and P.
Winter; polar forms and triangular B-spline surfaces, H.P Seidel.
