# Drawing Euler Diagrams with Circles: The Theory of Piercings

@article{Stapleton2011DrawingED, title={Drawing Euler Diagrams with Circles: The Theory of Piercings}, author={Gem Stapleton and Leishi Zhang and John Howse and Peter J. Rodgers}, journal={IEEE Transactions on Visualization and Computer Graphics}, year={2011}, volume={17}, pages={1020-1032} }

Euler diagrams are effective tools for visualizing set intersections. They have a large number of application areas ranging from statistical data analysis to software engineering. However, the automated generation of Euler diagrams has never been easy: given an abstract description of a required Euler diagram, it is computationally expensive to generate the diagram. Moreover, the generated diagrams represent sets by polygons, sometimes with quite irregular shapes that make the diagrams less…

## 41 Citations

### Drawing Euler diagrams with circles and ellipses

- Computer Science2011 IEEE Symposium on Visual Languages and Human-Centric Computing (VL/HCC)
- 2011

This paper presents a novel approach to Euler diagram drawing that draws diagrams with circles, ellipses and curves in general and can enforce wellformedness properties as chosen by the user.

### Drawing Euler Diagrams with Circles and Ellipses Gem

- Computer Science

This paper presents a novel approach to Euler diagram drawing that draws diagrams with circles, ellipses and curves in general and can enforce wellformedness properties as chosen by the user.

### On the drawability of 3D Venn and Euler diagrams

- Computer Science, MathematicsJ. Vis. Lang. Comput.
- 2014

### Drawing Interactive Euler Diagrams from Region Connection Calculus Specifications

- Computer ScienceJ. Log. Lang. Inf.
- 2015

The improved local search and the hybrid method outperforms the local search from the literature and the gradient method for generating a diagram and both good results in terms of quality of drawings and stability are seen.

### Introducing 3D Venn and Euler Diagrams

- Computer ScienceED@Diagrams
- 2012

3D Venn and Euler diagrams are considered, for the first time, as the first to consider these diagrams as set-theoretic notions of intersection, containment and disjointness, and it is demonstrated that some data can be visualized with wellformed 3D diagrams that cannot be visualization with well formed 2D diagrams.

### The efficacy of Euler diagrams and linear diagrams for visualizing set cardinality using proportions and numbers

- Computer SciencePloS one
- 2019

This paper presents the first empirical investigation that compares Euler and linear diagrams when they are used to represent set cardinality and suggests that area-proportional Euler diagrams with numerical annotations most effectively supports task performance and so should be used to visualize set cardinalities.

### Stapleton , Gem ( 2012 ) Introducing 3 D Venn and Euler Diagrams

- Computer Science, Mathematics

3D Venn and Euler diagrams are considered, for the first time, to comprise of labelled, orientable closed surfaces and it is demonstrated that some data can be visualized with wellformed 3D diagrams that cannot be visualization with well formed 2D diagrams.

### Visualizing set relations and cardinalities using Venn and Euler diagrams

- Computer Science
- 2013

Novel automatic drawing methods for different types of Euler diagrams are presented and a user study of how such diagrams can help probabilistic judgement is studied, to facilitate data analysis and reasoning about the sets.

### Tactical Diagrammatic Reasoning

- Computer ScienceUITP
- 2016

An interactive proof assistant for Euler diagrams, Speedith, is taken and tactics are added to its reasoning engine, providing a level of automation in the construction of proofs, and designed to not only prove the theorem, but also to support explanation.

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