Computational Geometry - Algorithms and Applications

Computational geometry emerged from the ?eld of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the ?eld 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 information 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 dif?cult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simpli?ed many of the previous approaches. In this textbook we have tried to make these modern 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.

List of contents

Computational Geometry: Introduction.- Line Segment Intersection: Thematic Map Overlay.- Polygon Triangulation: Guarding an Art Gallery.- Linear Programming: Manufacturing with Molds.- Orthogonal Range Searching: Querying a Database.- Point Location: Knowing Where You Are.- Voronoi Diagrams: The Post Office Problem.- Arrangements and Duality: Supersampling in Ray Tracing.- Delaunay Triangulations: Height Interpolation.- More Geometric Data Structures: Windowing.- Convex Hulls: Mixing Things.- Binary Space Partitions: The Painter's Algorithm.- Robot Motion Planning: Getting Where You Want to Be.- Quadtrees: Non-Uniform Mesh Generation.- Visibility Graphs: Finding the Shortest Route.- Simplex Range Searching: Windowing Revisited.- Bibliography.- Index.

Additional text

"An excellent introduction to the field is given here, including a general motivation and usage cases beyond simple graphics rendering or interaction." from the ACM Reviews by William Fahle, University of Texas at Dallas, USA

Report

"An excellent introduction to the field is given here, including a general motivation and usage cases beyond simple graphics rendering or interaction." from the ACM Reviews by William Fahle, University of Texas at Dallas, USA

Product details

• Authors: Otfried Cheong, Mark de Berg, Marc van Kreveld, Mark Overmars, Marc van Kreveld
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 19.10.2010
• EAN: 9783642096815
• ISBN: 978-3-642-09681-5
• No. of pages: 386
• Dimensions: 193 mm x 21 mm x 242 mm
• Weight: 800 g
• Illustrations: XII, 386 p. 370 illus.
• Subjects: Natural sciences, medicine, IT, technology > IT, data processing > IT; Geometrie, B, Geowissenschaften, Algorithmen und Datenstrukturen, Algorithms, Grafikprogrammierung, computer science, geometry, Theory of Computation, Computer Graphics, Mathematical Applications in Computer Science, Earth Sciences, Computers, Algorithms & data structures, Mathematical & statistical software, Mathematical theory of computation, Computer science—Mathematics, Maths for computer scientists, Math Applications in Computer Science, Earth Sciences, general, Algorithm Analysis and Problem Complexity, Graphics programming