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About this book
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.
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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
- algorithm analysis and problem complexity
- combinatorics
Table of contents (1 chapter)
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Front Matter
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Back Matter
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
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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