Table of contents

  1. Front Matter
  2. Pages 1-98
  3. Back Matter

About this book

Introduction

One way to advance the science of computational geometry is to make a comprehensive study of fundamental operations that are used in many different algorithms. This monograph attempts such an investigation in the case of two basic predicates: the counterclockwise relation pqr, which states that the circle through points (p, q, r) is traversed counterclockwise when we encounter the points in cyclic order p, q, r, p,...; and the incircle relation pqrs, which states that s lies inside that circle if pqr is true, or outside that circle if pqr is false. The author, Donald Knuth, is one of the greatest computer scientists of our time. A few years ago, he and some of his students were looking at amap that pinpointed the locations of about 100 cities. They asked, "Which ofthese cities are neighbors of each other?" They knew intuitively that some pairs of cities were neighbors and some were not; they wanted to find a formal mathematical characterization that would match their intuition.This monograph is the result.

Keywords

Axiom-Based Algorithm Design Axiomatische Geometrie Axiomen-gestützte Algorithmenentwicklung Convex Hulls Delauny Triangulation Graph Konvexe Hüllen Oriented Matroids Orientierte Matroide Vortex-Free Tournaments algorithms computational geometry computer

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-55611-7
  • Copyright Information Springer-Verlag 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55611-4
  • Online ISBN 978-3-540-47259-9
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349