Axioms and Hulls

Axioms and Hulls

Author: Donald E. Knuth

Publisher: Springer

ISBN: 3540556117

Category: Computers

Page: 114

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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.
Axioms and Hulls
Language: en
Pages: 114
Authors: Donald E. Knuth
Categories: Computers
Type: BOOK - Published: 1992-06-10 - Publisher: Springer

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,
Axioms and Hulls
Language: en
Pages: 109
Authors: Donald Ervin Knuth
Categories: Mathematics
Type: BOOK - Published: 1992 - Publisher: Springer Verlag

"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,
Automated Deduction in Geometry
Language: en
Pages: 211
Authors: Hoon Hong
Categories: Computers
Type: BOOK - Published: 2006-01-25 - Publisher: Springer Science & Business Media

This book constitutes the thoroughly refereed post-proceedings of the 5th International Workshop on Automated Deduction in Geometry, ADG 2004, held at Gainesville, FL, USA in September 2004. The 12 revised full papers presented were carefully selected from the papers accepted for the workshop after careful reviewing. All current issues in
Graph Drawing and Network Visualization
Language: en
Pages: 666
Authors: Therese Biedl, Andreas Kerren
Categories: Computers
Type: BOOK - Published: 2018-12-17 - Publisher: Springer

This book constitutes the refereed proceedings of the 26th International Symposium on Graph Drawing and Network Visualization, GD 2018, held in Barcelona, Spain, in September 2018. The 41 full papers presented in this volume were carefully reviewed and selected from 85 submissions. They were organized in topical sections named: planarity
Theorem Proving in Higher Order Logics
Language: en
Pages: 347
Authors: Victor A. Carreno, César A. Muñoz, TPHOLs 2002, Sofiene Tahar
Categories: Computers
Type: BOOK - Published: 2002-08-07 - Publisher: Springer Science & Business Media

awidespectrumofareasintheoreticalcomputerscience,formalmethods,and softwareengineering. ThevenueoftheTPHOLsconferencetraditionallychangescontinenteach yearinordertomaximizethelikelihoodthatresearchersfromallovertheworld willattend. Startingin1993,theproceedingsofTPHOLsanditspredecessor workshopshavebeenpublishedinthefollowingvolumesoftheSpringer-Verlag LectureNotesinComputerScienceseries: 1993(Canada) 780 1998(Australia)1479 1994(Malta) 859 1999(France) 1690 1995(USA) 971 2000(USA) 1869 1996(Finland)1125 2001(UK) 2152 1997(USA) 1275 VI Preface The2002conferencewasorganizedbyateamfromNASALangleyResearch Center,theICASEInstituteatLangleyResearchCenter,andConcordiaU- versity. FinancialsupportcamefromIntelCorporation. Thesupportofallthese organizationsisgratefullyacknowledged. August2002 V´?ctorA. Carreno ˜ C´esarA. Muno ˜z VII Organization TPHOLs2002isorganizedbyNASALangleyandICASEincooperationwith ConcordiaUniversity. Organizing Committee ConferenceChair: V´?ctorA. Carren˜o(NASALangley) ProgramChair: C´esarA.