Geometric Computations with Interval and New Robust Methods :Applications in Computer Graphics, GIS and Computational Geometry

Publication subTitle :Applications in Computer Graphics, GIS and Computational Geometry

Author: Ratschek   H;Rokne   J  

Publisher: Elsevier Science‎

Publication year: 2003

E-ISBN: 9780857099518

P-ISBN(Paperback): 9781898563976

P-ISBN(Hardback):  9781898563976

Subject: O18 geometric topology;O241 数值分析

Language: ENG

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Description

This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free.

  • Familiarises the reader with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations
  • Provides two effective methods for obtaining correct results in interval arithmetic and ESSA

Chapter

Front Cover

pp.:  1 – 4

ABOUT OUR AUTHORS

pp.:  3 – 10

Copyright Page

pp.:  5 – 6

Table of Contents

pp.:  6 – 3

List of Figures

pp.:  10 – 14

List of Tables

pp.:  14 – 15

Preface

pp.:  15 – 20

Chapter 1. Introduction

pp.:  20 – 32

Chapter 2. Interval Analysis

pp.:  32 – 80

Chapter 3. Interval Newton Methods

pp.:  80 – 98

Chapter 4. The Exact Sign of Sum Algorithm (ESSA)

pp.:  98 – 128

Chapter 5. Intersection Tests

pp.:  128 – 204

Chapter 6. The SCCI-Hybrid Method for 2D-Curve Tracing

pp.:  204 – 238

Chapter 7. Interval Versions of Bernstein Polynomials, Bézier Curves and the de Casteljau Algorithm

pp.:  238 – 260

Chapter 8. Robust Computations of Selected Discrete Problems

pp.:  260 – 316

Bibliography

pp.:  316 – 335

Index

pp.:  335 – 338

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