Geometric Methods and Applications
Geometric Methods and Applications

Author: Jean Gallier

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 584

ISBN-13: 1461301378

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As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

Computational Geometry
Computational Geometry

Author: Franco P. Preparata

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 413

ISBN-13: 1461210984

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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

Computing in Euclidean Geometry
Computing in Euclidean Geometry

Author: Ding-Zhu Du

Publisher: World Scientific

Published: 1995

Total Pages: 520

ISBN-13: 9789810218768

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This book is a collection of surveys and exploratory articles about recent developments in the field of computational Euclidean geometry. Topics covered include the 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. This second edition contains three new surveys covering geometric constraint solving, computational geometry and the exact computation paradigm.

Computational Geometry on Surfaces
Computational Geometry on Surfaces

Author: Clara Grima

Publisher: Springer Science & Business Media

Published: 2001-11-30

Total Pages: 212

ISBN-13: 9781402002021

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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.

Applications of Geometric Algebra in Computer Science and Engineering
Applications of Geometric Algebra in Computer Science and Engineering

Author: Leo Dorst

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 479

ISBN-13: 146120089X

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Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Delaunay Mesh Generation
Delaunay Mesh Generation

Author: Siu-Wing Cheng

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 404

ISBN-13: 1584887311

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Written by authors at the forefront of modern algorithms research, Delaunay Mesh Generation demonstrates the power and versatility of Delaunay meshers in tackling complex geometric domains ranging from polyhedra with internal boundaries to piecewise smooth surfaces. Covering both volume and surface meshes, the authors fully explain how and why thes