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### Drawing Graphs in Euler Diagrams [chapter]

Paul Mutton, Peter Rodgers, Jean Flower
2004 Lecture Notes in Computer Science
The system described here links graph drawing and Euler diagram drawing into a system for drawing graph-enhanced Euler diagrams.  ...  In any drawing, the nodes are required to be included in the corresponding zone. We are, in effect, embedding graphs in Euler diagrams.  ...  Drawing Euler Diagrams Enhanced With Graphs In this section we describe our three stage generic method for laying out graphs in Euler diagrams. The software system has been implemented in Java.  ...

### Drawing Euler diagrams with circles and ellipses

G. Stapleton, P. Rodgers
2011 2011 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)
In this paper, we present a novel approach to Euler diagram drawing that draws diagrams with circles, ellipses and curves in general.  ...  Previous research on automated Euler diagram drawing has used various different approaches, each of which had their own problems, including: (a) failure to draw a diagram in all cases, (b) poor diagram  ...  Euler diagrams are associated with various graphs. In this paper, we are interested in three of these associated graphs, all of which are defined in  .  ...

### Visualise Undrawable Euler Diagrams

Paolo Simonetto, David Auber
2008 2008 12th International Conference Information Visualisation
Euler diagram characteristics might collide with the sets relationships to depict, making it impossible to outline a correct draw.  ...  We aim to introduce methods and constructions to produce a clear representation, as close as possible to Euler diagrams, even for sets that are not formally drawable in that way.  ...  Drawing Euler diagrams is a difficult task.  ...

### Towards a General Solution to Drawing Area-Proportional Euler Diagrams

Stirling Chow, Frank Ruskey
2005 Electronical Notes in Theoretical Computer Science
We present a deterministic algorithm for drawing Euler diagrams using n simple polygons so that the regions have a prescribed area.  ...  . , n}, the algorithm can still be applied, but will sometimes create an Euler diagram where the curves are self-intersecting.  ...  Figure 4 shows the Euler Graph and Dual of the Euler diagram in Figure 3 .  ...

### Fully Automatic Visualisation of Overlapping Sets

Paolo Simonetto, David Auber, Daniel Archambault
2009 Computer graphics forum (Print)
In this paper, we present an approach for the automatic generation of Euler-like diagrams.  ...  Euler diagrams, one of the most natural ways of depicting intersecting sets, may provide a solution to these problems.  ...  Therefore, a drawing of the intersection graph decides positions and shapes of the zones and classes in the Euler diagram.  ...

### A general method for drawing area-proportional Euler diagrams

Gem Stapleton, Peter Rodgers, John Howse
2011 Journal of Visual Languages and Computing
In this paper, we considerably advance the state-of-the-art in area-proportional Euler diagram drawing by presenting the first method that is capable of generating such a diagram given any area-proportional  ...  Area-proportional Euler diagrams have many applications, for example they are often used for visualizing data in medical and biological domains.  ...  Acknowledgements The authors are supported by the EPSRC for the Visualization with Euler diagrams project (EP/E011160/1 and EP/E010393/1).  ...

### An Heuristic for the Construction of Intersection Graphs

Paolo Simonetto, David Auber
2009 2009 13th International Conference Information Visualisation
The final Euler diagram can be constructed by drawing the sets boundaries around the nodes of the intersection graph, either manually or automatically.  ...  A planar drawing of this graph will then indicate how to draw the sets in order to depict all the set intersections.  ...  Recent studies on automatically drawing Euler diagrams have been facing these problems.  ...

### A survey of Euler diagrams

Peter Rodgers
2014 Journal of Visual Languages and Computing
They first appeared several hundred years ago, however, there has been a resurgence in Euler diagram research in the twenty-first century.  ...  It also overviews application areas and the ways in which Euler diagrams have been extended.  ...  An Euler graph is shown in Figure 12 . It is the Euler graph of the Euler diagram given in Figure 11 .  ...

### Drawing Euler Diagrams for Information Visualization [chapter]

John Howse, Peter Rodgers, Gem Stapleton
2010 Lecture Notes in Computer Science
Euler diagrams have numerous applications in information visualization as well as logical reasoning.  ...  There have been a number of techniques devised for the automated drawing of Euler diagrams, each of which has its own advantages and disadvantages.  ...  Euler diagrams have numerous applications in information visualization as well as logical reasoning.  ...

### Drawing Euler Diagrams with Circles [chapter]

Gem Stapleton, Leishi Zhang, John Howse, Peter Rodgers
2010 Lecture Notes in Computer Science
Euler diagrams are a popular and intuitive visualization tool which are used in a wide variety of application areas, including biological and medical data analysis.  ...  As with other data visualization methods, such as graphs, bar charts, or pie charts, the automated generation of an Euler diagram from a suitable data set would be advantageous, removing the burden of  ...  Dual Graph Methods: With these methods, a so-called dual graph of the required Euler diagram is identified and embedded in the plane. Then the Euler diagram is formed from the dual graph.  ...

### Drawing Euler Diagrams from Region Connection Calculus Specifications with Local Search [chapter]

François Schwarzentruber, Jin-Kao Hao
2014 Lecture Notes in Computer Science
Euler diagrams are described as set of circles.  ...  This paper describes a local search based approach and a software tool to approximate the problem of drawing Euler diagrams. Specifications are written using RCC-8-constraints and radius constraints.  ...  Tulip displays the graph and extracts an Euler diagram from it.  ...

### Subdivision Drawings of Hypergraphs [chapter]

Michael Kaufmann, Marc van Kreveld, Bettina Speckmann
2009 Lecture Notes in Computer Science
In this paper we study two new types of subdivision drawings which are more general than concrete Euler diagrams and more restricted than vertex-based Venn diagrams.  ...  Vertex-based Venn diagrams and concrete Euler diagrams are both subdivision drawings.  ...  This research was initiated during the Bertinoro Workshop on Graph Drawing, 2008.  ...

### Embedding Wellformed Euler Diagrams

Peter Rodgers, Leishi Zhang, Gem Stapleton, Andrew Fish
2008 2008 12th International Conference Information Visualisation
The method in this paper achieves an embedding of any wellformed Euler diagram. The method first triangulates the dual graph.  ...  Finally, the process attempts to embed the Euler diagram from the dual graph. This paper describes a method for embedding wellformed Euler diagrams from dual graphs.  ...  In these diagrams, the dual graph is shown with dotted lines to more easily distinguish it from the Euler diagram.  ...

### Generating Euler Diagrams [chapter]

Jean Flower, John Howse
2002 Lecture Notes in Computer Science
The work makes use of properties of the dual graph of an abstract diagram to identify which abstract diagrams are "drawable" within given wellformedness rules on concrete diagrams.  ...  This article describes an algorithm for the automated generation of any Euler diagram starting with an abstract description of the diagram.  ...  Related work There is much work on graph-drawing algorithms, see e.g.  . Euler diagrams are similar to the hypergraphs discussed in  .  ...

### Changing euler diagram properties by edge transformation of euler dual graphs

John Howse, Peter Rodgers, Gem Stapleton
2009 2009 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)
Recently, various techniques for automated Euler diagram drawing have been proposed, contributing to the Euler diagram generation problem: given an abstract description, draw an Euler diagram with that  ...  In this paper we define transformations of the dual graph that allow us to alter the properties that the generated diagram possesses.  ...  Acknowledgements This work is supported by the UK EP-SRC grants EP/E011160/1 and EP/E010393/1 for the Visualization with Euler Diagrams project.  ...
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