CGAL Arrangements and Their Applications

A Step-by-Step Guide

  • Efi Fogel
  • Dan Halperin
  • Ron Wein

Part of the Geometry and Computing book series (GC, volume 7)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Efi Fogel, Dan Halperin, Ron Wein
    Pages 1-18
  3. Efi Fogel, Dan Halperin, Ron Wein
    Pages 19-42
  4. Efi Fogel, Dan Halperin, Ron Wein
    Pages 43-65
  5. Efi Fogel, Dan Halperin, Ron Wein
    Pages 67-81
  6. Efi Fogel, Dan Halperin, Ron Wein
    Pages 83-128
  7. Efi Fogel, Dan Halperin, Ron Wein
    Pages 129-159
  8. Efi Fogel, Dan Halperin, Ron Wein
    Pages 161-173
  9. Efi Fogel, Dan Halperin, Ron Wein
    Pages 175-208
  10. Efi Fogel, Dan Halperin, Ron Wein
    Pages 209-240
  11. Efi Fogel, Dan Halperin, Ron Wein
    Pages 241-261
  12. Efi Fogel, Dan Halperin, Ron Wein
    Pages 263-269
  13. Back Matter
    Pages 271-293

About this book

Introduction

Arrangements of curves constitute fundamental structures that have been intensively studied in computational geometry. Arrangements have numerous applications in a wide range of areas – examples include geographic information systems, robot motion planning, statistics, computer-assisted surgery and molecular biology. Implementing robust algorithms for arrangements is a notoriously difficult task, and the CGAL arrangements package is the first robust, comprehensive, generic and efficient implementation of data structures and algorithms for arrangements of curves.

 

This book is about how to use CGAL two-dimensional arrangements to solve problems. The authors first demonstrate the features of the arrangement package and related packages using small example programs. They then describe applications, i.e., complete standalone programs written on top of CGAL arrangements used to solve meaningful problems – for example, finding the minimum-area triangle defined by a set of points, planning the motion of a polygon translating among polygons in the plane, computing the offset polygon, finding the largest common point sets under approximate congruence, constructing the farthest-point Voronoi diagram, coordinating the motion of two discs moving among obstacles in the plane, and performing Boolean operations on curved polygons.

 

The book contains comprehensive explanations of the solution programs, many illustrations, and detailed notes on further reading, and it is supported by a website that contains downloadable software and exercises. It will be suitable for graduate students and researchers involved in applied research in computational geometry, and for professionals who require worked-out solutions to real-life geometric problems. It is assumed that the reader is familiar with the C++ programming-language and with the basics of the generic-programming paradigm.

Keywords

Boolean set operations Boolean set operations CGAL CGAL Computational geometry Computational geometry Minkowski sums Minkowski sums arrangements of curves arrangements of curves geometric software geometric software robustness robustness

Authors and affiliations

  • Efi Fogel
    • 1
  • Dan Halperin
    • 2
  • Ron Wein
    • 3
  1. 1.School of Computer Science, Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.School of Computer Science, Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  3. 3.School of Computer Science, Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-17283-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-17282-3
  • Online ISBN 978-3-642-17283-0
  • Series Print ISSN 1866-6795
  • Series Online ISSN 1866-6809
  • About this book
Industry Sectors
Automotive
Biotechnology
Electronics
Telecommunications
Aerospace