Handbook of Discrete and Computational Geometry

3. New Auflage 2017
ISBN: 978-1-4987-1139-5
Verlag: Taylor & Francis Inc

Buch, Englisch, 1950 Seiten, Format (B × H): 183 mm x 257 mm, Gewicht: 3192 g

Reihe: Discrete Mathematics and Its Applications

While much information can be found on discrete and computational geometry, it is scattered among many sources. The Handbook of Discrete and Computational Geometry, Third Edition brings together all of the major results in both these fields into one volume. Thousands of results, theorems, algorithms, and tables definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is readily accessible to the novice, but offers enough depth to appeal to the specialist. Every technical term is defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples.

Autoren/Hrsg.

Goodman, Jacob E.

Toth, Csaba D.

O'Rourke, Joseph

Fachgebiete

• Mathematik | Informatik EDV | Informatik Professionelle Anwendung
• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

Finite point configurations. Packing and covering. Tilings. Helly-type theorems and geometric transversals. Pseudoline arrangements. Oriented matroids.Lattice points and lattice polytopes. Low-distortion embeddings of finite metric spaces. Geometry and topology of polygonal linkages. Geometric graph theory. Euclidean Ramsey theory. Discrete aspects of stochastic geometry. Geometric discrepancy theory and uniform distribution. Polyominoes. Basic properties of convex polytopes. Subdivisions and triangulations of polytopes. Face numbers of polytopes and complexes. Symmetry of polytopes and polyhedra. Polytope skeletons and paths. Polyhedral maps.Topological methods in discrete geometry.Random simplicial complexes. Computational topology of graphs on surfaces. Persistent homology. High-dimensional topological data analysis. Convex hull computations. Voronoi diagrams and Delaunay triangulations. Arrangements.Triangulations and mesh generation. Polygons.Shortest paths and networks. Proximity algorithms. Visibility. Geometric reconstruction problems. Curve and surface reconstruction. Computational convexity. Computational and quantitative real algebraic geometry.Point location. Collision and proximity queries. Range searching. Ray shooting and lines in space. Geometric intersection. Nearest neighbors in high-dimensional spaces.Randomizaton and derandomization. Robust geometric computation. Parallel algorithms in geometry. Epsilon-nets and epsilon-approximations Coresets and sketches. Linear programming. Algorithmic motion planning. Robotics. Computer graphics. Modeling motion. Pattern recognition. Graph drawing.Splines and geometric modeling. Solid modeling. Computation of robust statistics: Depth, median, and related measures. Geographic information systems.Geometric applications of the Grassmann-Cayley algebra. Rigidity of symmetric frameworks. Global rigidity. Crystals, periodic and aperiodic.Applications to structural molecular biology. Geometry and topology of genomics. Software. Two computational geometry libraries: LEDA and CGAL

Über Autor(innen)

Csaba D. Toth is a professor of mathematics at Cal State Northridge, located in the city of Los Angeles, and a visiting professor of computer science at Tufts University in the Boston metro area. He is the author of more than 90 papers in discrete and computational geometry. His main research interests are in hierarchical subdivisions in low-dimensional spaces, topological graph theory, and geometric optimization.

Joseph O'Rourke is professor of Computer Science and of Mathematics at Smith College, and director of the Statistical and Data Science program. His research is in computational geometry, developing algorithms for geometric computations. He has authored or coauthored five books besides this Handbook. His most recent book, "How To Fold It," is written for high-school students.

Jacob E. Goodman is, along with Richard Pollack, a Founding Editor of the journal "Discrete & Computational Geometry." He retired from City College, C.U.N.Y. in 2008. The author of over 60 papers in algebraic geometry, combinatorics, and discrete geometry, he has spent most of his time since his retirement composing music and working on a mystery novel. Goodman received the Lester R. Ford Award from the MAA in 1990, and is a Fellow of the AMS.