edited by Ding-Zhu Du (Univ. Minnesota & Inst. of Applied Maths) & Frank Hwang (AT&T Bell Labs.)

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.

• On the Development of Quantitative Geometry from Phythagoras to Grassmann (W-Y Hsiang)
• Computational Geometry: A Retrospective (B Chazelle)
• Mesh Generation and Optimal Triangulation (M Bern & D Eppstein)
• Machine Proofs of Geometry Theorems (S-C Chou & M Rathi)
• Randomized Geometric Algorithms (K L Clarkson)
• The State of Art on Steiner Ratio Problems (D-Z Du & F Hwang)
• Voronoi Diagrams and Delaunay Triangulations (S Fortune)
• Geometric Constraint Solving in R² and R³ (C M Hoffmann & P J Vermeer)
• Polar Forms and Triangular B-Spline Surfaces (H-P Seidel)
• Computational Geometry and Topological Network Design (J M Smith & P Winter)
• The Exact Computation Paradigm (C Yap & T Dubé)