True Grid

  • Barry Smith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2205)


The Renaissance architect, moral philosopher, cryptographer, mathematician, Papal adviser, painter, city planner and land surveyor Leon Battista Alberti provided the theoretical foundations of modern perspective geometry. Alberti’s work on perspective exerted a powerful influence on painters of the stature of Albrecht Dürer, Leonardo da Vinci and Piero della Francesca. But his Della pittura of 1435-36 contains also a hitherto unrecognized ontology of pictorial projection. We sketch this ontology, and show how it can be generalized to apply to represantive devices in general, including maps and spatial and non-spatial databases.


Linear Perspective Objective Array Target Grid Transparent Grid Fiat Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Alberti, Leon Battista ca. 1435–1436 De pictura praestantissima, origina (Latin) edition: Basel 1540 (reprinted Portland, Oregon 1972), Italian translation: Della pittura, Venice 1547. Cited according to the English translation: On Painting, 1956 (complete text available at
  2. Bennett, B., Cohn, A. G., Torrini, P. and Hazarika, S. M. 2000 “A Foundation for Region-Based Qualitative Geometry”, Proceedings of ECAI 2000, Berlin, 204–208.Google Scholar
  3. Bittner, Thomas and Stell, John G. 1998 “A Boundary-Sensitive Approach to Qualitative Location”, Annals of Mathematics and Artificial Intelligence, 24, 93–114.zbMATHCrossRefMathSciNetGoogle Scholar
  4. Bittner, Thomas and Smith, Barry (in this volume) “A Taxonomy of Granular Partitions”.Google Scholar
  5. Collingwood, R. G. 1938 The Principles of Art, Oxford: Oxford University Press.Google Scholar
  6. Edgerton, Samuel Y. 1975 The Renaissance Rebirth of Linear Perspective, New York: Basic Books.Google Scholar
  7. Gibson, James J. 1978 “The Ecological Approach to Visual Perception in Pictures”, Leonardo, 11:3, 227–235.CrossRefMathSciNetGoogle Scholar
  8. Gibson, James J. 1979 The Ecological Approach to Visual Perception, Boston: Houghton-Mifflin.Google Scholar
  9. Gibson, James J. 1980 “A Prefatory Essay on the Perception of Surfaces versus the Perception of Markings on a Surface”, in M. Hagen (ed.), The Perception of Pictures, Volume 1: Alberti’s Window, New York: Academic Press, xi–xvii.Google Scholar
  10. Gibson, James J. 1982 Reasons for Realism. Selected Essays of James J. Gibson, Edward Reed and Rebecca Jones (eds.) Hillsdale, NJ and London: Lawrence Erlbaum.Google Scholar
  11. Husserl, Edmund 1970 Logical Investigations, London: Routledge and Kegan Paul, 1970.Google Scholar
  12. Kennedy, Jon Milles 1974 A Psychology of Picture Perception: Images and Information, San Francisco: Jossey Bass.Google Scholar
  13. Lefevbre, Henri 1974 La Production de L’Espace, Paris: Editions Anthropos.Google Scholar
  14. Millikan, Ruth Garrett 1998 “A Common structure for concepts of individuals, stuffs, and real kinds: More Mama, more milk, and more mouse”, Behavioral and Brain Sciences, 9:1, 55–100.CrossRefGoogle Scholar
  15. Mulligan, Kevin 1995 “Perception” in B. Smith and D. W. Smith, eds., The Cambridge Companion to Husserl, Cambridge and New York: Cambridge University Press, 168–238.CrossRefGoogle Scholar
  16. Panofsky, Erwin 1927 “Die Perspektive als’ symbolische Form’”, Vörtrage der Bibliothek Warburg, 258–330. English translation: Perspective as Symbolic Form, New York: Zone Books, 1991Google Scholar
  17. Pirenne, M. H. 1952 “The Scientific Basis for Leonardo Da Vinci’s Theory of Perspective”, British Journal for the Philosophy of Science, 3:10, 169–185.CrossRefGoogle Scholar
  18. Pylyshyn, Zenon W. 1989 “The Role of Location Indexes in Spatial Perception: A Sketch of the FINST Spatial-Index Model”, Cognition, 32, 65–97.CrossRefGoogle Scholar
  19. Smith, Barry, 2001 “Fiat Objects”, Topoi, 20:2.Google Scholar
  20. Smith, Barry and Brogaard, Berit 2001 “Quantum Mereotopology”, Annals of Mathematics and Artificial Intelligence (in press).Google Scholar
  21. Smith, Barry and Brogaard, Berit 2001a “A Unified Theory of Truth and Reference”, Logique et Analyse, 43 (in press).Google Scholar
  22. Spencer, John R. 1956 “Introduction” to the English translation of Alberti 1435–36, 1–31.Google Scholar
  23. Veltman, Kim H. 1977 Review of Edgerton 1975, The Art Bulletin, 59:2, 281–282.CrossRefGoogle Scholar
  24. Veltman, Kim H. 1986 Linear Perspective and the Visual Dimensions of Science and Art (Leonardo da Vinci Studies I), Munich: Deutscher Kunstverlag, 1986.Google Scholar
  25. Veltman, Kim H. 1999 Continuity and Discovery in Optics and Astronomy (Leonardo da Vinci Studies II), http://www/ See also
  26. Westfall, Carroll William 1974 In This Most Perfect Paradise: Alberti, Nicholas Y, and the Invention of Conscious Urban Planning in Rome, 1447-55, University Park: Pennsylvania State University Press.Google Scholar
  27. Wittgenstein, Ludwig 1961 Tractatus Logico-Philosophicus, with English translation by D. F. Pears and B. F. McGuinness, London: Routledge and Kegan Paul.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Barry Smith
    • 1
  1. 1.Department of Philosophy, Center for Cognitive Science and NCGIAUniversity at BuffaloUSA

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