Projective Relations in a 3D Environment

  • Roland Billen
  • Eliseo Clementini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4197)


This paper presents a model for positional relations among bodies of arbitrary shape in three dimensions. It is based on an existing model for projective relations among regions in two dimensions. The motivation is to provide a formal qualitative spatial relations model for emerging 3D applications. Two sets of relations are defined: ternary projective relations based on the concept of collinearity between a primary object and two reference objects and quaternary projective relations based on the concept of coplanarity between a primary object and three reference objects. Four sets of JEPD relations are defined for points and bodies in R 3.


Convex Hull Augmented Reality Tangent Plane Projective Geometry Reference Object 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roland Billen
    • 1
  • Eliseo Clementini
    • 2
  1. 1.Geomatics UnitUniversity of LiegeLiegeBelgium
  2. 2.Dept. of Electrical and Information EngineeringUniversity of L’AquilaL’AquilaItaly

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