On Recent Progress in Computational Synthetic Geometry
Author | : Jürgen Bokowski |
Publisher | : |
Total Pages | : 14 |
Release | : 1994 |
Genre | : |
ISBN | : |
Download On Recent Progress in Computational Synthetic Geometry Book in PDF, ePub and Kindle
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download On Recent Progress In Computational Synthetic Geometry PDF full book. Access full book title On Recent Progress In Computational Synthetic Geometry.
Author | : Jürgen Bokowski |
Publisher | : |
Total Pages | : 14 |
Release | : 1994 |
Genre | : |
ISBN | : |
Author | : Jürgen Bokowski |
Publisher | : Springer |
Total Pages | : 173 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540460136 |
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research.
Author | : Tibor Bisztriczky |
Publisher | : Springer Science & Business Media |
Total Pages | : 515 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401109249 |
The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.
Author | : Jürgen Bokowski |
Publisher | : |
Total Pages | : 180 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662168219 |
Author | : Neil L. White |
Publisher | : Springer Science & Business Media |
Total Pages | : 331 |
Release | : 2013-03-09 |
Genre | : Computers |
ISBN | : 9401584028 |
Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience: Researchers studying mathematics, computers and robotics.
Author | : David Kueker |
Publisher | : Springer Science & Business Media |
Total Pages | : 217 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461240883 |
The field of computational learning theory arose out of the desire to for mally understand the process of learning. As potential applications to artificial intelligence became apparent, the new field grew rapidly. The learning of geo metric objects became a natural area of study. The possibility of using learning techniques to compensate for unsolvability provided an attraction for individ uals with an immediate need to solve such difficult problems. Researchers at the Center for Night Vision were interested in solving the problem of interpreting data produced by a variety of sensors. Current vision techniques, which have a strong geometric component, can be used to extract features. However, these techniques fall short of useful recognition of the sensed objects. One potential solution is to incorporate learning techniques into the geometric manipulation of sensor data. As a first step toward realizing such a solution, the Systems Research Center at the University of Maryland, in conjunction with the Center for Night Vision, hosted a Workshop on Learning and Geometry in January of 1991. Scholars in both fields came together to learn about each others' field and to look for common ground, with the ultimate goal of providing a new model of learning from geometrical examples that would be useful in computer vision. The papers in the volume are a partial record of that meeting.
Author | : Anders Björner |
Publisher | : Cambridge University Press |
Total Pages | : 564 |
Release | : 1999-11-18 |
Genre | : Mathematics |
ISBN | : 052177750X |
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research.
Author | : James C. Robinson |
Publisher | : Cambridge University Press |
Total Pages | : 247 |
Release | : 2016-01-21 |
Genre | : Mathematics |
ISBN | : 1107554977 |
An accessible summary of a wide range of active research topics written by leaders in their field, including exciting new results.
Author | : |
Publisher | : |
Total Pages | : 920 |
Release | : 2001 |
Genre | : Psychology |
ISBN | : |
Author | : Ding-zhu Du |
Publisher | : World Scientific |
Total Pages | : 403 |
Release | : 1992-09-14 |
Genre | : Computers |
ISBN | : 9814505609 |
This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. The topics covered are: a history of Euclidean geometry, Voronoi diagrams, randomized geometric algorithms, computational algebra; triangulations, machine proofs, topological designs, finite-element mesh, computer-aided geometric designs and steiner trees. Each chapter is written by a leading expert in the field and together they provide a clear and authoritative picture of what computational Euclidean geometry is and the direction in which research is going.