Euler Operators and Navigation of Multi-shell Building Models

  • Pawel BoguslawskiEmail author
  • Christopher Gold
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


This work presents the Dual Half Edge (DHE) structure and the associated construction methods for 3D models. Three different concepts are developed and described with particular reference to the Euler operators. All of them allow for simultaneous maintenance of both the primal and dual graphs. They can be used to build cell complexes in 2D or 3D. They are general, and different cell shapes such as building interiors are possible. All cells are topologically connected and may be navigated directly with pointers. Our ideas may be used when maintenance of the dual structure is desired, for example for path planning, and the efficiency of computation or dynamic change of the structure is essential.


3D Data Models 3D Data Structures Building Interior Models Emergency Response Disaster Management Topology CAD Quad-Edge 3D Dual Graph 3D Graph navigation Euler Operators 


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This research is supported by the Ordnance Survey and EPSRC funding of a New CASE award.


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Computing and MathematicsUniversity of GlamorganWalesUK
  2. 2.Department of GeoinformaticsUniversiti Teknologi Malaysia (UTM)SkudaiMalaysia

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