Representing Geometric Configurations

  • Walter Whiteley
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 14)

Abstract

How should we represent a geometric configuration? Building on artificial intelligence investigations of ‘knowledge representation’ and research on constrained diagrams in CAD, criteria are presented for an ‘adequate representation’ of a discrete geometric set. Dependence on both the level of geometry (Euclidean, similarity, and projective) and on the sources of the geometric data are considered. The criteria are illustrated with representations for a finite set of ‘geometric points and lines’ in the plane. Appropriate constructions and representations are translated from classical and from modern geometric practice. The sample representations use coordinates, distances, angles, incidences, orientations and projections.

Keywords

Terion 

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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Walter Whiteley
    • 1
  1. 1.Department of Mathematics and StatisticsYork UniversityNorth YorkCanada

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