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Drawing Interactive Euler Diagrams from Region Connection Calculus Specifications

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Abstract

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.

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Notes

  1. The correct term should be ‘disks’ instead of ‘circles’ since a disk of radius r and center C also contain point whose distance from C are smaller than r. But we use here the term ‘circles’ as in our JELIA paper (Schwarzentruber et al. 2014) and related work (Stapleton et al. 2010).

  2. For instance, let us consider the set of all bounded functions \(f: \mathbb {R}\rightarrow \mathbb {R}^+\) and the topology defined by the uniform norm. Let b be the subset of functions bounded by 1 in the neighborhood of \(\pm \infty \) and a be the subset of functions that converge to 0 in \(\pm \infty \). As the boundary of b is the set of bounded functions that converge to 1 in \(\pm \infty \), we should have the constraint \( NTPP (a, b)\).

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Acknowledgments

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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Authors and Affiliations

  1. ENS Rennes, Campus de Ker Lann, Avenue Robert Schumann, 35170, Bruz, France

    François Schwarzentruber

  2. IRISA, 263 Avenue Général Leclerc, 35000, Rennes, France

    François Schwarzentruber

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  1. François Schwarzentruber
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Correspondence to François Schwarzentruber.

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Schwarzentruber, F. Drawing Interactive Euler Diagrams from Region Connection Calculus Specifications. J of Log Lang and Inf 24, 375–408 (2015). https://doi.org/10.1007/s10849-015-9230-7

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