Euclidean Shortest Paths in Simple Polygons PDF Download

Author:
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 21

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Author: Fajie Li
Publisher: Springer Science & Business Media
ISBN: 1447122569
Category : Computers
Languages : en
Pages : 377

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Book Description
This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Topics and features: provides theoretical and programming exercises at the end of each chapter; presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms; discusses algorithms for calculating exact or approximate ESPs in the plane; examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves; describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems; includes lists of symbols and abbreviations, in addition to other appendices.

Author: Andrew Goldberg
Publisher: Springer Science & Business Media
ISBN: 3642021573
Category : Computers
Languages : en
Pages : 335

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Book Description
This book constitutes the proceedings of the 5th International Conference on Algorithmic Aspects in Information Management, AAIM 2009, held in San Francisco, CA, USA, in June 2009. The 25 papers presented together with the abstracts of two invited talks were carefully reviewed and selected for inclusion in this book. While the areas of information management and management science are full of algorithmic challenges, the proliferation of data (Internet, biology, finance etc) has called for the design of efficient and scalable algorithms and data structures for their management and processing. This conference is intended for original algorithmic research on immediate applications and/or fundamental problems pertinent to information management and management science, broadly construed. The conference aims at bringing together researchers in Computer Science, Operations Research, Economics, Game Theory, and related disciplines.

Author: J.R. Sack
Publisher: Elsevier
ISBN: 0080529682
Category : Mathematics
Languages : en
Pages : 1087

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Book Description
Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

Author: Gerald Sommer
Publisher: Springer
ISBN: 3540781579
Category : Computers
Languages : en
Pages : 477

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In 1986, B.K.P. Horn published a book entitled Robot Vision, which actually discussed a wider ?eld of subjects, basically addressing the ?eld of computer vision, but introducing “robot vision” as a technical term. Since then, the - teraction between computer vision and research on mobile systems (often called “robots”, e.g., in an industrial context, but also including vehicles, such as cars, wheelchairs, tower cranes, and so forth) established a diverse area of research, today known as robot vision. Robot vision (or, more general, robotics) is a fast-growing discipline, already taught as a dedicated teaching program at university level. The term “robot vision” addresses any autonomous behavior of a technical system supported by visual sensoric information. While robot vision focusses on the vision process, visual robotics is more directed toward control and automatization. In practice, however, both ?elds strongly interact. Robot Vision 2008 was the second international workshop, counting a 2001 workshop with identical name as the ?rst in this series. Both workshops were organized in close cooperation between researchers from New Zealand and Germany, and took place at The University of Auckland, New Zealand. Participants of the 2008 workshop came from Europe, USA, South America, the Middle East, the Far East, Australia, and of course from New Zealand.

Author: Franco P. Preparata
Publisher: Springer Science & Business Media
ISBN: 1461210984
Category : Mathematics
Languages : en
Pages : 413

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From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2

Author: Giuseppe Liotta
Publisher: World Scientific
ISBN: 9789812796608
Category : Mathematics
Languages : en
Pages : 418

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Book Description
This book contains Volume 6 of the Journal of Graph Algorithms and Applications (JGAA) . JGAA is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. Areas of interest include computational biology, computational geometry, computer graphics, computer-aided design, computer and interconnection networks, constraint systems, databases, graph drawing, graph embedding and layout, knowledge representation, multimedia, software engineering, telecommunications networks, user interfaces and visualization, and VLSI circuit design. Graph Algorithms and Applications 3 presents contributions from prominent authors and includes selected papers from the Symposium on Graph Drawing (1999 and 2000). All papers in the book have extensive diagrams and offer a unique treatment of graph algorithms focusing on the important applications. Contents: Triangle-Free Planar Graphs and Segment Intersection Graphs (N de Castro et al.); Traversing Directed Eulerian Mazes (S Bhatt et al.); A Fast Multi-Scale Method for Drawing Large Graphs (D Harel & Y Koren); GRIP: Graph Drawing with Intelligent Placement (P Gajer & S G Kobourov); Graph Drawing in Motion (C Friedrich & P Eades); A 6-Regular Torus Graph Family with Applications to Cellular and Interconnection Networks (M Iridon & D W Matula); and other papers. Readership: Researchers and practitioners in theoretical computer science, computer engineering, and combinatorics and graph theory.

Author: Joseph O'Rourke
Publisher: Oxford University Press, USA
ISBN:
Category : Computers
Languages : en
Pages : 312

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Book Description
Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry.

Author: Christian Chénier
Publisher:
ISBN:
Category : Polygons
Languages : en
Pages : 148

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Book Description
Consider a polygon P and two points $p,\ q\in P.$ Suppose that to move from p to q, we can travel along the edges of P or through the interior of P. Assume that the speed at which we can travel along the edges of P is one unit per second, and the travel speed through the interior of P is 1/s units per seconds ($s>1$). The problem consists of finding the shortest path between p and q. We solve this problem in O(n) time for convex polygons. For simple polygons, we show two algorithms. The first algorithm runs in O(E log n) time using O(E) space (where E is the size of the visibility of P). The second algorithm has two variations which both require O(n E log n) preprocessing (where E is the number of edges in the visibility graph of P). The first variation takes O(n log n) query time and O($n\sp2$ log n) space. The second variation has a query time of O(n log$\sp2$ n) but uses $O(n\sp2)$ space. For the orthogonal case, we give a O(E) time and space algorithm.

Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1351645919
Category : Computers
Languages : en
Pages : 2354

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Book Description
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.