Visual Mathematics: Diagrammatic Formalization and Proof
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
General Euler Diagram Generation
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
Diagrams '08 Proceedings of the 5th international conference on Diagrammatic Representation and Inference
A graph theoretic approach to general Euler diagram drawing
Theoretical Computer Science
Efficient on-line algorithms for Euler diagram region computation
Computational Geometry: Theory and Applications
Drawing euler diagrams with circles
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Coloured euler diagrams: a tool for visualizing dynamic systems and structured information
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Drawing area-proportional Venn-3 diagrams with convex polygons
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Blocks of hypergraphs: applied to hypergraphs and outerplanarity
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
A general method for drawing area-proportional Euler diagrams
Journal of Visual Languages and Computing
Automatically drawing Euler diagrams with circles
Journal of Visual Languages and Computing
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
Fully automatic visualisation of overlapping sets
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
An interactive visualization interface for studying egocentric, categorical, contact diary datasets
Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining
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An Euler diagram C = {c 1, c2, . . . , cn} is a collection of n simple closed curves (i.e., Jordan curves) that partition the plane into connected subsets, called regions, each of which is enclosed by a unique combination of curves. Typically, Euler diagrams are used to visualize the distribution of discrete characteristics across a sample population; in this case, each curve represents a characteristic and each region represents the sub-population possessing exactly the combination of containing curves' properties. Venn diagrams are a subclass of Euler diagrams in which there are 2n regions representing all possible combinations of curves (e.g., two partially overlapping circles). In this dissertation, we study the Euler Diagram Generation Problem (EDGP), which involves constructing an Euler diagram with a prescribed set of regions. We describe a graph-theoretic model of an Euler diagram's structure and use this model to develop necessary-and-sufficient existence conditions. We also use the graph-theoretic model to prove that the EDGP is NP-complete. In addition, we study the related Area-Proportional Euler Diagram Generation Problem (ω-EDGP), which involves constructing an Euler diagram with a prescribed set of regions, each of which has a prescribed area. We develop algorithms for constructing area-proportional Euler diagrams composed of up to three circles and rectangles, as well as diagrams with an unbounded number of curves and a region of common intersection. Finally, we present implementations of our algorithms that allow the dynamic manipulation and real-time construction of area-proportional Euler diagrams.