Modeling Visibility in 3D Space: A Qualitative Frame of Reference

  • Paolo FogliaroniEmail author
  • Eliseo Clementini
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


This paper introduces and formalizes a frame of reference for projective relations in 3D space that can be used to model human visual perception. While in 2D space visibility information can be derived from the concept of collinearity (thus, as ternary relations), in 3D space it can be derived from coplanarity, which calls for quaternary relations. Yet, we can retain ternary relations by anchoring our frame to an ubiquitous reference element: a general sense of vertical direction that, on Earth, can be the expression of gravity force or, in other cases, of the asymmetries of an autonomous agent, either human or robotic, that is, its vertical axis. Based on these observations, the presented frame of reference can be used to model projective and visibility information as ternary relations. Granularity and complexity of the models can be adjusted: we present two differently detailed realizations and discuss possible applications in Geographic Information Systems.


Direction Vector Reference Object Aggregation Rule Projective Relation Shadow Zone 
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.


  1. Abbott EA (1884) Flatland: a romance of many dimensions. Dover Publications Inc., New York (republished in 1992)Google Scholar
  2. Bartie P, Reitsma F, Clementini E, Kingham S (2011) Referring expressions in location based services: the case of the ‘opposite’ relation. In: Advances in conceptual modeling. Recent developments and new directions. LNCS. Springer, pp 231–240Google Scholar
  3. Billen R, Clementini E (2004) A model for ternary projective relations between regions. In: Advances in database technology. LNCS. Springer, pp 537–538Google Scholar
  4. Billen R, Clementini R (2006) Projective relations in a 3D environment. In: Geographic information science. Springer, pp 18–32Google Scholar
  5. Chazelle B (1984) Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm. SIAM J Comput 13(3):488–507CrossRefGoogle Scholar
  6. Clementini E, Skiadopoulos S, Billen R, Tarquini F (2010) A reasoning system of ternary projective relations. IEEE Trans Knowl Data Eng 22(2):161–178CrossRefGoogle Scholar
  7. Cohn AG, Renz J (2008) Qualitative spatial representation and reasoning. In: Handbook of knowledge representation, foundations of artificial intelligence. Elsevier, pp 551–596Google Scholar
  8. De Felice G, Fogliaroni P, Wallgrün JO (2010) Qualitative reasoning with visibility information for environmental learning. In: Proceedings of the 6th international conference on geographic information science (GIScience 2010)Google Scholar
  9. Fogliaroni P, Wallgrün JO, Clementini E, Tarquini F, Wolter D (2009) A qualitative approach to localization and navigation based on visibility information. In: Proceedings of the 9th international conference on spatial information theory. LNCS. Springer, pp 312–329Google Scholar
  10. Frank AU (1991) Qualitative spatial reasoning with cardinal directions. In: Proceedings of the 7th austrian conference on artificial intelligence. ÖGAI. Springer, pp 157–167Google Scholar
  11. Franklin N, Tversky B (1990) Searching imagined environments. J Exp Psychol Gen 119(1):63CrossRefGoogle Scholar
  12. Freksa C (1992) Using orientation information for qualitative spatial reasoning. In: Theories and methods of spatio-temporal reasoning in geographic space, vol 639. LNCS. Springer, pp 162–178Google Scholar
  13. Galton A (1994) Lines of sight. AI Cogn Sci 94:103–113Google Scholar
  14. Hernandez D, Clementini E, Di Felice P (1995) Qualitative distances. In: Spatial information theory a theoretical basis for GIS, vol 988. LNCS. Springer, pp 45–57Google Scholar
  15. Köhler C (2002) The occlusion calculus. Cognitive vision workshopGoogle Scholar
  16. Randell D, Cui Z, Cohn AG (1992) A spatial logic based on regions and connection. In: Principles of knowledge representation and reasoning: proceedings of the 3rd international conference (KR’92). Morgan Kaufmann, Massachusetts, pp 165–176Google Scholar
  17. Randell D, Witkowski M, Shanahan M (2001) From images to bodies: modelling and exploiting spatial occlusion and motion parallax. In: IJCAI, pp 57–66Google Scholar
  18. Raubal M, Winter S (2002) Enriching way finding instructions with local landmarks. In: Geographic Information Science. LNCS. Springer, pp 243–259Google Scholar
  19. Tarquini F, De Felice G, Fogliaroni P, Clementini E (2007) A qualitative model for visibility relations. In: KI 2007: advances in artificial intelligence, pp 510–513Google Scholar
  20. Tassoni S, Fogliaroni P, Bhatt M, De Felice G (2011) Toward a qualitative model of 3D visibility. 25th international workshop on qualitative reasoning (IJCAI 2011) (position paper)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department for Geodesy and GeoinformationVienna University of TechnologyViennaAustria
  2. 2.Department of Industrial and Information Engineering and EconomicsUniversity of L’AquilaL’AquilaItaly

Personalised recommendations