Author: Mark de Berg Publisher: Springer Science & Business Media ISBN: 3662042452 Category : Computers Languages : en Pages : 370
Book Description
This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.
Author: Franco P. Preparata Publisher: Springer Science & Business Media ISBN: 1461210984 Category : Mathematics Languages : en Pages : 413
Book Description
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: Satyan L. Devadoss Publisher: Princeton University Press ISBN: 1400838983 Category : Mathematics Languages : en Pages : 270
Book Description
An essential introduction to discrete and computational geometry Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only)
Author: James M. Van Verth Publisher: CRC Press ISBN: 0123742978 Category : Art Languages : en Pages : 706
Book Description
Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.
Author: Joseph O'Rourke Publisher: Cambridge University Press ISBN: 110726863X Category : Computers Languages : en Pages : 396
Book Description
This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions for this new edition are also available. All code is accessible from the book's Web site (http://cs.smith.edu/~orourke/) or by anonymous ftp.
Author: Michael Joswig Publisher: Springer Science & Business Media ISBN: 1447148177 Category : Mathematics Languages : en Pages : 251
Book Description
Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.
Author: J. Andreas Bærentzen Publisher: Springer Science & Business Media ISBN: 1447140753 Category : Computers Languages : en Pages : 330
Book Description
This book reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. Features: presents an overview of the underlying mathematical theory, covering vector spaces, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations; reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces; examines techniques for computing curvature from polygonal meshes; describes algorithms for mesh smoothing, mesh parametrization, and mesh optimization and simplification; discusses point location databases and convex hulls of point sets; investigates the reconstruction of triangle meshes from point clouds, including methods for registration of point clouds and surface reconstruction; provides additional material at a supplementary website; includes self-study exercises throughout the text.
Author: Ketan Mulmuley Publisher: Prentice Hall ISBN: Category : Computers Languages : en Pages : 472
Book Description
For beginning graduate-level courses in computational geometry. This up-to-date and concise introduction to computational geometry with emphasis on simple randomized methods is designed for quick, easy access to beginners.
Author: Clara Grima Publisher: Springer Science & Business Media ISBN: 9781402002021 Category : Computers Languages : en Pages : 212
Book Description
In the last thirty years Computational Geometry has emerged as a new discipline from the field of design and analysis of algorithms. That dis cipline studies geometric problems from a computational point of view, and it has attracted enormous research interest. But that interest is mostly concerned with Euclidean Geometry (mainly the plane or Eu clidean 3-dimensional space). Of course, there are some important rea sons for this occurrence since the first applieations and the bases of all developments are in the plane or in 3-dimensional space. But, we can find also some exceptions, and so Voronoi diagrams on the sphere, cylin der, the cone, and the torus have been considered previously, and there are manY works on triangulations on the sphere and other surfaces. The exceptions mentioned in the last paragraph have appeared to try to answer some quest ions which arise in the growing list of areas in which the results of Computational Geometry are applicable, since, in practiee, many situations in those areas lead to problems of Com putational Geometry on surfaces (probably the sphere and the cylinder are the most common examples). We can mention here some specific areas in which these situations happen as engineering, computer aided design, manufacturing, geographie information systems, operations re search, roboties, computer graphics, solid modeling, etc.
Author: J.R. Sack Publisher: Elsevier ISBN: 0080529682 Category : Mathematics Languages : en Pages : 1087
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.
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Author: Mark de Berg
Author: Franco P. Preparata
Author: Satyan L. Devadoss
Author: James M. Van Verth
Author: Joseph O'Rourke
Author: Michael Joswig
Author: J. Andreas Bærentzen
Author: Ketan Mulmuley
Author: Clara Grima
Author: J.R. Sack