Computational Geometry is study of algorithms for geometric problems. Historically, Computational Geometry has meant several different, but related, disciplines. The classical book Perceptrons, by Minsky and Pappert (1969), was about neural networks but was subtitled "An introduction to computational geometry". Another classical book was Computational Geometry for Design and Manufacture, by Faux and Pratt (1979); it was about what is now called computer-aided design and geometric modeling.
Nowadays, Computational Geometry is a well-established sub-discipline of computer science and deals mainly with discrete geometry, with emphasis on algorithms that are optimal in the worst case. The classical reference for this brand of Computational Geometry is the book Computational Geometry: An Introduction by Preparata and Shamos (1985). Since the mid 1990s an effort has been under way to attack practical geometric problems with an increasing emphasis on algorithms that can be implemented in practice, so as to get closer to industrial applications.
Boissonat and Teillard have collected in this book the foundations of a computational geometry that no longer deals exclusively with linear objects but also with curved objects that arise in applications. The book is composed of eight chapters written by teams of experts in each theme, and is the result of an European Union project named ECG .
The book can serve as an advanced graduate course on computational geometry and as a reference for researchers interested in geometric algorithms for curved objects.
Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.