This item is in: Mathematics > Geometry and topology

Geometric computations with interval and new robust methods: Applications in computer graphics, GIS and computational geometry

H Ratschek, Heinrich Heine Universitat, Germany and J Rokne, University of Calgary, Canada

 - 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

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.

ISBN 1 898563 97 7
ISBN-13: 978 1 898563 97 6
December 2003
336 pages  234 x 156mm  paperback  
£50.00 / US$85.00 / €60.00

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About the authors

Helmut Ratschek, Heinrich Heine Universitat, Germany. Jon Rokne, University of Calgary, Canada

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Contents

Introduction

Interval analysis

Interval Newton methods

The exact sign of sum algorithm (ESSA)

Intersection tests

The SCCI-hybrid method for 2D-curve tracing

Interval versions of Bernstein polynomials, Bezier curves and the De Casteljau algorithm

Robust computations of selected discrete problems

Bibliography