Computational Geometry : Algorithms and Applications

The focus of this book is on algorithm and motivation is provided from the application areas-all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. The most recent insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. Computational geometry emerged from the field of algorithms design and anal­ ysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The suc­ cess of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains--computer graphics, geographic in­ formation systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modem algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self-study. In this introduction to computational geometry the the text focuses on algorithms. All solutions and techniques described in the text are from computational geometry and are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Good solutions to algorithmic problems of geometric nature are mostly based on two ingredients.