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Projective Relations

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Encyclopedia of GIS

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Historical Background

Starting from the 1990s, a number of formal models for qualitative spatial reasoning (QSR) were developed mainly based on topological and direction/orientation relations. Such models emphasized qualitative aspects by opposition to metric aspects based on Euclidean geometry. However, there was a gap to be filled to cover many other spatial relations that can be studied by considering geometric aspects that are in between topology and metrics. Projective geometry is more restrictive than topology, since it preserves the collinearity between three points, but more general than Euclidean geometry, since it disregards metric properties and is independent from Euclid’s parallel axiom. Projective geometry can be used to build a comprehensive model that covers intermediate relations between topology and metrics. The appropriateness of projective geometry is supported by studies in cognitive science, such as in Piaget’s work on the cognitive development of children...

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Author information

Authors and Affiliations

  1. Department of Industrial and Information Engineering and Economics, University of L’Aquila, L’Aquila, Italy

    Eliseo Clementini

  2. Geomatics Unit, Department of Geography, University of Liege, Liege, Belgium

    Roland Billen

Authors
  1. Eliseo Clementini
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  2. Roland Billen
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Correspondence to Eliseo Clementini .

Editor information

Editors and Affiliations

  1. University of Minnesota, Minneapolis, MN, USA

    Shashi Shekhar

  2. Management Science and Information Systems Department, Rutgers Business School, Rutgers, The State University of New Jersey, Newark, NJ, USA

    Hui Xiong

  3. Department of Management Sciences, Tippie College of Business, University of Iowa, Iowa City, IA, USA

    Xun Zhou

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Clementini, E., Billen, R. (2017). Projective Relations. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_1540

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