Algorithmic Geometry [Paperback]

Advanced textbook in computational geometry; algorithmic approach.The design and analysis of geometric algorithms has seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD.The goal of this book is twofold: first to present a coherent and systematic treatment of the foundations; second 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 has seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD.The goal of this book is twofold: first to present a coherent and systematic treatment of the foundations; second 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 has seen remarkable growth in recent years, due to their application in computer vision, graphics, medical imaging, and CAD. Geometric algorithms are built on three pillars: geometric data structures, algorithmic data structuring techniques and results from combinatorial geometry. This comprehensive presents a coherent and systematic treatment of the foundations and gives simple, practical algorithmic solutions to problems. An accessible approach to the subject, Algorithmic Geometry is an ideal guide for instructors or for beginning graduate courses in computational geometry.Preface; Part I. Algorithmic Tools: 1. Notions of complexity; 2. Basic data structures; 3. Deterministic methods used in geometry; 4. Random sampling; 5. Randomized algorithms; 6. Dynamic ralSÃ