Axioms and Hulls

by Donald Ervin Knuth

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 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.

124 pages, Paperback

First published June 10, 1992

About the author

Donald Ervin Knuth, born January 10th 1938, is a renowned computer scientist and Professor Emeritus of the Art of Computer Programming at Stanford University.

Author of the seminal multi-volume work The Art of Computer Programming ("TAOCP"), Knuth has been called the "father" of the analysis of algorithms, contributing to the development of, and systematizing formal mathematical techniques for, the rigorous analysis of the computational complexity of algorithms, and in the process popularizing asymptotic notation.

In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces.

A prolific writer and scholar, Knuth created the WEB/CWEB computer programming systems designed to encourage and facilitate literate programming, and designed the MMIX instruction set architecture.