Algorithmic Geometry

Advanced textbook in computational geometry; algorithmic approach.

The goals of this book are twofold: first to present a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions to problems that are simple to state but which nevertheless are applicable in practical situations. The prerequisites for using the book are few, which will make it ideal for teaching advanced courses in computational geometry.The design and analysis of geometric algorithms have seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goals of this book are twofold: first to provide a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions that are amenable to rigorous analysis and are efficient in practical situations. When possible, the algorithms are presented in their most general d-dimensional setting. Specific developments are given for the 2- or 3-dimensional cases when this results in significant improvements. The presentation is confined to Euclidean affine geometry, though the authors indicate whenever the treatment can be extended to curves and surfaces. The prerequisites for using the book are few, which will make it ideal for teaching advanced undergraduate or beginning graduate courses in computational geometry.