edited by Ding-Zhu Du (University of Minnesota) & Frank Hwang (AT&T Bell Laboratories)

This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a 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. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.

• 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)
• Voronoi Diagrams and Delauney Triangulations (S Fortune)
• The State of Art on Steiner Ratio Problems (D-Z Du & F Hwang)
• On the Development of Quantitative Geometry from Pythagoras to Grassmann (W-Y Hsiang)
• Computational Geometry and Topological Network Design (J M Smith & P Winter)
• Polar Forms and Triangular B-Spline Surfaces (H-P Seidel)