Journal of Logic, Language and Information

, Volume 24, Issue 4, pp 375–408 | Cite as

Drawing Interactive Euler Diagrams from Region Connection Calculus Specifications



This paper describes methods for generating interactive Euler diagrams. User interaction is needed to improve the aesthetic quality of the drawing without writing tedious formal specifications. More precisely, the user can modify the diagram’s layout on the fly by mouse control. We prove that the satisfiability problem is in \({\textsf {PSPACE}}\) and we provide two syntactic fragments such that the corresponding restricted satisfiability problem is already \({\textsf {NP}}\)-hard. We describe (1) an improved local search based approach, (2) a method inspired from the gradient method and a hybrid method mixing both (1) and (2). A software tool was implemented and its implementation is described. We also experimentally compare the different methods. We first see that the improved local search and the hybrid method outperforms the local search from the literature and the gradient method for generating a diagram. Concerning interaction, the local search approach is not suitable but hybrid method and gradient method give both good results in terms of quality of drawings and stability. Specifications are written using region connection calculus (\({\mathbf{RCC-8 }}\)), radius constraints and disjunctions. Euler diagrams are described as set of circles.


Euler diagrams Region connection calculus  Satisfiability problem Local search 



We still wish to thank the three JELIA reviewers for their critical comments and pointers to relevant studies. We also thank the reviewers of this journal version. We thank users who accepted to perform the user study. We thank also Benjamin Boutin for the example in Footnote 2.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.ENS RennesBruzFrance
  2. 2.IRISARennesFrance

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