Generating and drawing area-proportional Euler and Venn diagrams
| dc.contributor.author | Chow, Stirling Christopher | |
| dc.contributor.supervisor | Ruskey, Frank | |
| dc.date.accessioned | 2007-06-11T17:50:45Z | |
| dc.date.available | 2007-06-11T17:50:45Z | |
| dc.date.copyright | 2007 | en_US |
| dc.date.issued | 2007-06-11T17:50:45Z | |
| dc.degree.department | Department of Computer Science | |
| dc.degree.level | Doctor of Philosophy Ph.D. | en_US |
| dc.description.abstract | An Euler diagram C = {c_1, c_2,..., c_n} 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 2^n 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 (w-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. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/128 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | Venn Diagrams | en_US |
| dc.subject | Euler Diagrams | en_US |
| dc.subject | Computational Geometry | en_US |
| dc.subject | Information Visualization | en_US |
| dc.subject | Computational Complexity | en_US |
| dc.subject | Area-Proportional | en_US |
| dc.subject | Logic Diagrams | en_US |
| dc.subject.lcsh | UVic Science Index::Sciences and Engineering::Applied Sciences::Computer science | en_US |
| dc.title | Generating and drawing area-proportional Euler and Venn diagrams | en_US |
| dc.type | Thesis | en_US |