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

This undergraduate and postgraduate text will familiarize readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations, and 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. There are also explanations of the applications to global geometric areas such as boxes which are handled with interval arithmetic tools, whereas standard tools can handle only point computations.

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

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