Voronoi Diagrams And Delaunay Triangulations

Author : Franz Aurenhammer,Rolf Klein,Der-Tsai Lee
Publisher : World Scientific Publishing Company
Page : 348 pages
File Size : 51,7 Mb
Release : 2013-06-26
Category : Computers
ISBN : 9789814447652

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Voronoi Diagrams and Delaunay Triangulations by Franz Aurenhammer,Rolf Klein,Der-Tsai Lee Pdf

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.

Author : Franz Aurenhammer
Publisher : Unknown
Page : 128 pages
File Size : 53,6 Mb
Release : 2013
Category : Electronic
ISBN : 9814447641

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Voronoi Diagrams and Delaunay Triangulations by Franz Aurenhammer Pdf

Author : Siu-Wing Cheng,Tamal K. Dey,Jonathan Shewchuk
Publisher : CRC Press
Page : 404 pages
File Size : 55,6 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781584887317

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Delaunay Mesh Generation by Siu-Wing Cheng,Tamal K. Dey,Jonathan Shewchuk Pdf

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

Author : Karthikeyan NG
Publisher : Packt Publishing Ltd
Page : 246 pages
File Size : 54,8 Mb
Release : 2018-10-31
Category : Computers
ISBN : 9781788998468

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Machine Learning Projects for Mobile Applications by Karthikeyan NG Pdf

Bring magic to your mobile apps using TensorFlow Lite and Core ML Key FeaturesExplore machine learning using classification, analytics, and detection tasks.Work with image, text and video datasets to delve into real-world tasksBuild apps for Android and iOS using Caffe, Core ML and Tensorflow LiteBook Description Machine learning is a technique that focuses on developing computer programs that can be modified when exposed to new data. We can make use of it for our mobile applications and this book will show you how to do so. The book starts with the basics of machine learning concepts for mobile applications and how to get well equipped for further tasks. You will start by developing an app to classify age and gender using Core ML and Tensorflow Lite. You will explore neural style transfer and get familiar with how deep CNNs work. We will also take a closer look at Google’s ML Kit for the Firebase SDK for mobile applications. You will learn how to detect handwritten text on mobile. You will also learn how to create your own Snapchat filter by making use of facial attributes and OpenCV. You will learn how to train your own food classification model on your mobile; all of this will be done with the help of deep learning techniques. Lastly, you will build an image classifier on your mobile, compare its performance, and analyze the results on both mobile and cloud using TensorFlow Lite with an RCNN. By the end of this book, you will not only have mastered the concepts of machine learning but also learned how to resolve problems faced while building powerful apps on mobiles using TensorFlow Lite, Caffe2, and Core ML. What you will learnDemystify the machine learning landscape on mobileAge and gender detection using TensorFlow Lite and Core MLUse ML Kit for Firebase for in-text detection, face detection, and barcode scanningCreate a digit classifier using adversarial learningBuild a cross-platform application with face filters using OpenCVClassify food using deep CNNs and TensorFlow Lite on iOS Who this book is for Machine Learning Projects for Mobile Applications is for you if you are a data scientist, machine learning expert, deep learning, or AI enthusiast who fancies mastering machine learning and deep learning implementation with practical examples using TensorFlow Lite and CoreML. Basic knowledge of Python programming language would be an added advantage.

Author : Maria Vineeta
Publisher : GRIN Verlag
Page : 33 pages
File Size : 43,9 Mb
Release : 2017-05-10
Category : Computers
ISBN : 9783668444201

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Delaunay Tetrahedralization and its dual Voronoi Diagrams by Maria Vineeta Pdf

Master's Thesis from the year 2014 in the subject Computer Science - Applied, grade: B+, Bournemouth University, course: Msc Computer Animation and Visual Effects, language: English, abstract: The Delaunay tetrahedralization (DT) is one of the most popular and common methods used for solving problems related to meshes. It is either used for generating a mesh or for breaking it up, as Voronoi diagrams, dual of the DT, is a commonly used process for that. The main task of this project is to implement a robust Delaunay Tetrahedralization structure, with a set of points generated from sampling a given 3D Mesh. Points within the volume of the mesh can be obtained by several methods. We present two such methods and discuss the result obtained. These points serve as vertices for the tetrahedrons that are a part of the combinatorial structure DT. 3D Delaunay Tetrahedralization is not as optimal as 2D Delaunay triangulations. Implementing them gives rise to several degeneracies, which are quite difficult to handle. In this project, we have implemented a simple Incremental Insertion Algorithm based on the paper presented by Ledoux (2007), inorder to construct the DT structure. Correctness of the structure is given utmost importance rather than its speed.

Author : Ming-Yang Kao
Publisher : Springer Science & Business Media
Page : 1200 pages
File Size : 44,9 Mb
Release : 2008-08-06
Category : Computers
ISBN : 9780387307701

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Encyclopedia of Algorithms by Ming-Yang Kao Pdf

One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.

Author : Atsuyuki Okabe,Barry Boots,Kokichi Sugihara,Sung Nok Chiu
Publisher : John Wiley & Sons
Page : 696 pages
File Size : 42,5 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317853

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Spatial Tessellations by Atsuyuki Okabe,Barry Boots,Kokichi Sugihara,Sung Nok Chiu Pdf

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.

Author : Ding-Zhu Du,Frank Hwang
Publisher : World Scientific
Page : 520 pages
File Size : 45,9 Mb
Release : 1995
Category : Mathematics
ISBN : 9810218761

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Computing in Euclidean Geometry by Ding-Zhu Du,Frank Hwang Pdf

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.

Author : J. J. Risler
Publisher : Cambridge University Press
Page : 204 pages
File Size : 46,8 Mb
Release : 1992-08-13
Category : Computers
ISBN : 0521436915

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Mathematical Methods for CAD by J. J. Risler Pdf

As computers become the mainstay of most engineering design practices, there has been a growing interest in the theory of computational geometry and computer aided design.

Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 2879 pages
File Size : 48,6 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781351645911

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Handbook of Discrete and Computational Geometry by Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman Pdf

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.

Author : Herbert Edelsbrunner
Publisher : Springer Science & Business Media
Page : 423 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642615689

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Algorithms in Combinatorial Geometry by Herbert Edelsbrunner Pdf

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.

Author : Rolf Klein
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 40,8 Mb
Release : 1989-12-20
Category : Computers
ISBN : 3540520554

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Concrete and Abstract Voronoi Diagrams by Rolf Klein Pdf

The Voronoi diagram of a set of sites is a partition of the plane into regions, one to each site, such that the region of each site contains all points of the plane that are closer to this site than to the other ones. Such partitions are of great importance to computer science and many other fields. The challenge is to compute Voronoi diagrams quickly. The problem is that their structure depends on the notion of distance and the sort of site. In this book the author proposes a unifying approach by introducing abstract Voronoi diagrams. These are based on the concept of bisecting curves, which are required to have some simple properties that are actually possessed by most bisectors of concrete Voronoi diagrams. Abstract Voronoi diagrams can be computed efficiently and there exists a worst-case efficient algorithm of divide-and-conquer type that applies to all abstract Voronoi diagrams satisfying a certain constraint. The author shows that this constraint is fulfilled by the concrete diagrams based on large classes of metrics in the plane.

Author : Dingzhu Du,Frank Hwang
Publisher : World Scientific
Page : 414 pages
File Size : 40,9 Mb
Release : 1992
Category : Mathematics
ISBN : 9810209665

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Computing in Euclidean Geometry by Dingzhu Du,Frank Hwang Pdf

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.

Author : Atsuyuki Okabe,B. N. Boots,Kōkichi Sugihara
Publisher : Chichester, England ; Toronto : J. Wiley
Page : 568 pages
File Size : 52,9 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015029120519

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Spatial Tessellations by Atsuyuki Okabe,B. N. Boots,Kōkichi Sugihara Pdf

"Given a pattern of objects in continuous space, Voronoi diagrams provide a means of naturally partitioning the space into subregions. This is a rapidly expanding topic as these diagrams find application in such areas as spatial data manipulation, modelling spatial structures and spatial processes, pattern analysis and locational optimization. These areas can be found within many different scientific fields, and consequently this increases not only the use of Voronoi diagrams but also the demand for knowledge about them. This is the first book which, dealing exclusively with these diagrams, meets this demand. Material within is synthesized, unified and presented in a structured form. Emphasis of a particular perspective is deliberately avoided in order to provide a comprehensive and balanced treatment of all aspects of Voronoi diagrams. A wide range of applications drawn from over a dozen fields is discussed, enabling this book to serve as an important reference volume on this topic." "This book should appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Author : Øyvind Hjelle,Morten Dæhlen
Publisher : Springer Science & Business Media
Page : 239 pages
File Size : 49,7 Mb
Release : 2006-09-19
Category : Mathematics
ISBN : 9783540332619

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Triangulations and Applications by Øyvind Hjelle,Morten Dæhlen Pdf

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.