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.

Bibliographic Information

Book Title: Axioms and Hulls
Editors: Donald E. Knuth
Series Title: Lecture Notes in Computer Science
DOI: https://doi.org/10.1007/3-540-55611-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1992
Softcover ISBN: 978-3-540-55611-4Published: 10 June 1992
eBook ISBN: 978-3-540-47259-9Published: 04 July 2005
Series ISSN: 0302-9743
Series E-ISSN: 1611-3349
Edition Number: 1
Number of Pages: X, 114
Topics: Theory of Computation, Computer Applications, Discrete Mathematics, Computer Graphics, Algorithm Analysis and Problem Complexity, Combinatorics

Publish with us

Policies and ethics

Axioms and Hulls

Overview

Access this book

Other ways to access

Table of contents (1 chapter)

Front Matter

Axioms and Hulls

Back Matter

Keywords

About this book

Bibliographic Information

Publish with us

Search

Navigation