The Two Facets of Geometry
Author: Gurajada Suryanarayana Murty
Publisher:
Published: 2010
Total Pages: 112
ISBN-13: 9788190632256
DOWNLOAD EBOOK →Lanterna Rally
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ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics
Author: Luigi Cocchiarella
Publisher: Springer
Published: 2018-07-06
Total Pages: 2334
ISBN-13: 3319955888
DOWNLOAD EBOOK →This book gathers peer-reviewed papers presented at the 18th International Conference on Geometry and Graphics (ICGG), held in Milan, Italy, on August 3-7, 2018. The spectrum of papers ranges from theoretical research to applications, including education, in several fields of science, technology and the arts. The ICGG 2018 mainly focused on the following topics and subtopics: Theoretical Graphics and Geometry (Geometry of Curves and Surfaces, Kinematic and Descriptive Geometry, Computer Aided Geometric Design), Applied Geometry and Graphics (Modeling of Objects, Phenomena and Processes, Applications of Geometry in Engineering, Art and Architecture, Computer Animation and Games, Graphic Simulation in Urban and Territorial Studies), Engineering Computer Graphics (Computer Aided Design and Drafting, Computational Geometry, Geometric and Solid Modeling, Image Synthesis, Pattern Recognition, Digital Image Processing) and Graphics Education (Education Technology Research, Multimedia Educational Software Development, E-learning, Virtual Reality, Educational Systems, Educational Software Development Tools, MOOCs). Given its breadth of coverage, the book introduces engineers, architects and designers interested in computer applications, graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education.
Minkowski Geometry
Author: Anthony C. Thompson
Publisher: Cambridge University Press
Published: 1996-06-28
Total Pages: 380
ISBN-13: 9780521404723
DOWNLOAD EBOOK →The first comprehensive treatment of Minkowski geometry since the 1940's
Computing in Euclidean Geometry
Author: Ding-Zhu Du
Publisher: World Scientific
Published: 1992-09-14
Total Pages: 400
ISBN-13: 9814505609
DOWNLOAD EBOOK →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. Contents:Mesh Generation and Optimal Triangulation (M Bern & D Eppstein)Machine Proofs of Geometry Theorems (S-C Chou & M Rathi)Randomized Geometric Algorithms (K L Clarkson)Voronoi Diagrams and Delauney Triangulations (S Fortune)The State of Art on Steiner Ratio Problems (D-Z Du & F Hwang)On the Development of Quantitative Geometry from Pythagoras to Grassmann (W-Y Hsiang)Computational Geometry and Topological Network Design (J M Smith & P Winter)Polar Forms and Triangular B-Spline Surfaces (H-P Seidel) Readership: Computer scientists and mathematicians. keywords:Computational Geometry;Triangulation;Machine Proof;Randomized Geometric Algorithm;Voronoi Diagram;Delaunay Triangulation;B-Spline;Polar Form;Steiner Tree;Analytic Geometry “D-Z Du and F Hwang have put to rest an optimization problem known as the Steiner ratio conjecture. Their solution closes the book on a problem that had frustrated a generation of geometers, but it also writes the first chapter of a new volume. The key to Du and Hwang's successful attack on the conjecture is a new method that has potential for solving a raft of other optimization problems.” SIAM News, USA “… the eight surveys are well organized. Each survey is preceded by a good introductory section with a rich bibliography. Both beginners and experts will benefit from this book.” Mathematical Reviews “The papers are not just summaries; the authors present new material or fresh points of view … I recommend the book to anyone who works in one of the areas surveyed or who is interested in the interaction of Euclidean geometry and computers.” IEEE Parallel & Distributed Technology
Advances in Discrete Differential Geometry
Author: Alexander I. Bobenko
Publisher: Springer
Published: 2016-08-12
Total Pages: 441
ISBN-13: 3662504472
DOWNLOAD EBOOK →This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
Algorithms in Combinatorial Geometry
Author: Herbert Edelsbrunner
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 423
ISBN-13: 3642615686
DOWNLOAD EBOOK →Computational geometry as an area of research in its own right emerged in the early seventies of this century. Right from the beginning, it was obvious that strong connections of various kinds exist to questions studied in the considerably older field of combinatorial geometry. For example, the combinatorial structure of a geometric problem usually decides which algorithmic method solves the problem most efficiently. Furthermore, the analysis of an algorithm often requires a great deal of combinatorial knowledge. As it turns out, however, the connection between the two research areas commonly referred to as computa tional geometry and combinatorial geometry is not as lop-sided as it appears. Indeed, the interest in computational issues in geometry gives a new and con structive direction to the combinatorial study of geometry. It is the intention of this book to demonstrate that computational and com binatorial investigations in geometry are doomed to profit from each other. To reach this goal, I designed this book to consist of three parts, acorn binatorial part, a computational part, and one that presents applications of the results of the first two parts. The choice of the topics covered in this book was guided by my attempt to describe the most fundamental algorithms in computational geometry that have an interesting combinatorial structure. In this early stage geometric transforms played an important role as they reveal connections between seemingly unrelated problems and thus help to structure the field.
Facets of Algebraic Geometry
Author: Paolo Aluffi
Publisher: Cambridge University Press
Published: 2022-04-07
Total Pages: 417
ISBN-13: 1108792502
DOWNLOAD EBOOK →Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.
Proceedings
Computational Geometry
Author: Mark de Berg
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 370
ISBN-13: 3662042452
DOWNLOAD EBOOK →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.
Algorithmic Geometry
Author: Jean-Daniel Boissonnat
Publisher: Cambridge University Press
Published: 1998-03-05
Total Pages: 548
ISBN-13: 9780521565295
DOWNLOAD EBOOK →The design and analysis of geometric algorithms have seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goals of this book are twofold: first to provide a coherent and systematic treatment of the foundations; secondly to present algorithmic solutions that are amenable to rigorous analysis and are efficient in practical situations. When possible, the algorithms are presented in their most general d-dimensional setting. Specific developments are given for the 2- or 3-dimensional cases when this results in significant improvements. The presentation is confined to Euclidean affine geometry, though the authors indicate whenever the treatment can be extended to curves and surfaces. The prerequisites for using the book are few, which will make it ideal for teaching advanced undergraduate or beginning graduate courses in computational geometry.
