voronoi diagrams and delaunay triangulations

Download Book Voronoi Diagrams And Delaunay Triangulations in PDF format. You can Read Online Voronoi Diagrams And Delaunay Triangulations here in PDF, EPUB, Mobi or Docx formats.

Voronoi Diagrams And Delaunay Triangulations

Author : Franz Aurenhammer
ISBN : 9789814447652
Genre : Computers
File Size : 44. 36 MB
Format : PDF, ePub
Download : 337
Read : 688

Download Now


Voronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets. This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation. Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.

Computing In Euclidean Geometry

Author : Ding-Zhu Du
ISBN : 9810218761
Genre : Mathematics
File Size : 64. 53 MB
Format : PDF, Mobi
Download : 287
Read : 743

Download Now


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.

Triangulations And Applications

Author : Øyvind Hjelle
ISBN : 9783540332619
Genre : Mathematics
File Size : 22. 97 MB
Format : PDF, Docs
Download : 512
Read : 797

Download Now


This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.

Computing In Euclidean Geometry

Author : Dingzhu Du
ISBN : 9810209665
Genre : Mathematics
File Size : 86. 68 MB
Format : PDF, Mobi
Download : 211
Read : 176

Download Now


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.

Delaunay Mesh Generation

Author : Siu-Wing Cheng
ISBN : 9781584887317
Genre : Computers
File Size : 86. 7 MB
Format : PDF, ePub
Download : 822
Read : 919

Download Now


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 these meshing algorithms work. The book is one of the first to integrate a vast amount of cutting-edge material on Delaunay triangulations. It begins with introducing the problem of mesh generation and describing algorithms for constructing Delaunay triangulations. The authors then present algorithms for generating high-quality meshes in polygonal and polyhedral domains. They also illustrate how to use restricted Delaunay triangulations to extend the algorithms to surfaces with ridges and patches and volumes with smooth surfaces. For researchers and graduate students, the book offers a rigorous theoretical analysis of mesh generation methods. It provides the necessary mathematical foundations and core theoretical results upon which researchers can build even better algorithms in the future. For engineers, the book shows how the algorithms work well in practice. It explains how to effectively implement them in the design and programming of mesh generation software.

Spatial Tessellations

Author : Atsuyuki Okabe
ISBN : 9780470317853
Genre : Mathematics
File Size : 82. 63 MB
Format : PDF, Docs
Download : 115
Read : 742

Download Now


Spatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization. With such versatility, the Voronoi diagram and its relative, the Delaunay triangulation, provide valuable tools for the analysis of spatial data. This is a rapidly growing research area and in this fully updated second edition the authors provide an up-to-date and comprehensive unification of all the previous literature on the subject of Voronoi diagrams. Features: * Expands on the highly acclaimed first edition * Provides an up-to-date and comprehensive survey of the existing literature on Voronoi diagrams * Includes a useful compendium of applications * Contains an extensive bibliography A wide range of applications is discussed, enabling this book to serve as an important reference volume on this topic. The text will appeal to students and researchers studying spatial data in a number of areas, in particular, applied probability, computational geometry, and Geographic Information Science (GIS). This book will appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both.

Generalized Voronoi Diagram A Geometry Based Approach To Computational Intelligence

Author : Marina L. Gavrilova
ISBN : 9783540851257
Genre : Mathematics
File Size : 58. 65 MB
Format : PDF, Mobi
Download : 679
Read : 1169

Download Now


The year 2008 is a memorial year for Georgiy Vorono (1868-1908), with a number of events in the scientific community commemorating his tremendous contribution to the area of mathematics, especially number theory, through conferences and scientific gatherings in his honor. A notable event taking place in September 2008 a joint c- ference: the 5th Annual International Symposium on Voronoi Diagrams (ISVD) and the 4th International Conference on Analytic Number Theory and Spatial Tessel- tions held in Kyiv, Georgiy Vorono ’s native land. The main ideas expressed by G. Vorono ’s through his fundamental works have influenced and shaped the key dev- opments in computation geometry, image recognition, artificial intelligence, robotics, computational science, navigation and obstacle avoidance, geographical information systems, molecular modeling, astrology, physics, quantum computing, chemical en- neering, material sciences, terrain modeling, biometrics and other domains. This book is intended to provide the reader with in-depth overview and analysis of the fundamental methods and techniques developed following G. Voronoi ideas, in the context of the vast and increasingly growing area of computational intelligence. It represents the collection of state-of-the art research methods merging the bridges between two areas: geometric computing through Voronoi diagrams and intelligent computation techniques, pushing the limits of current knowledge in the area, impr- ing on previous solutions, merging sciences together, and inventing new ways of approaching difficult applied problems.

Algorithmische Geometrie

Author : Rolf Klein
ISBN : 9783540276197
Genre : Computers
File Size : 57. 68 MB
Format : PDF, Kindle
Download : 579
Read : 1129

Download Now



Visualize This

Author : Nathan Yau
ISBN : 9783527760220
Genre : Statistics / Graphic methods / Data processing
File Size : 86. 56 MB
Format : PDF
Download : 740
Read : 658

Download Now


A guide on how to visualise and tell stories with data, providing practical design tips complemented with step-by-step tutorials.

Geometric Methods And Applications

Author : Jean Gallier
ISBN : 9781461301370
Genre : Mathematics
File Size : 25. 94 MB
Format : PDF, ePub
Download : 501
Read : 212

Download Now


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.

Top Download:

Best Books