%0 Journal Article %1 flower2008euler %A Flower, J. %A Fish, A. %A Howse, J. %D 2008 %J Journal of Visual Languages & Computing %K algorithm diagram euler visualization math mathematics %N 6 %P 675--694 %R 10.1016/j.jvlc.2008.01.004 %T Euler diagram generation %U http://www.sciencedirect.com/science/article/pii/S1045926X08000049 %V 19 %X Euler diagrams form the basis of many diagrammatic notations used to represent set theoretic relationships in a wide range of contexts including: file system information, statistical data representation, object-oriented modeling, logical specification and reasoning systems, and database search queries. An abstract Euler diagram is a formal abstract description of the information that is to be displayed as a concrete (or drawn) Euler diagram. If the abstract diagram can be visualized, whilst satisfying certain desirable visual properties (called well-formedness conditions), then we say the diagram is drawable. We solve the drawability problem for a given set of well-formedness conditions, identifying the properties which classify a diagram as drawable or undrawable. Furthermore, we present a high level algorithm which enables the generation of a concrete diagram from an abstract diagram, whenever it is drawable.

@article{flower2008euler, abstract = {Euler diagrams form the basis of many diagrammatic notations used to represent set theoretic relationships in a wide range of contexts including: file system information, statistical data representation, object-oriented modeling, logical specification and reasoning systems, and database search queries. An abstract Euler diagram is a formal abstract description of the information that is to be displayed as a concrete (or drawn) Euler diagram. If the abstract diagram can be visualized, whilst satisfying certain desirable visual properties (called well-formedness conditions), then we say the diagram is drawable. We solve the drawability problem for a given set of well-formedness conditions, identifying the properties which classify a diagram as drawable or undrawable. Furthermore, we present a high level algorithm which enables the generation of a concrete diagram from an abstract diagram, whenever it is drawable.}, added-at = {2020-08-18T11:57:06.000+0200}, author = {Flower, J. and Fish, A. and Howse, J.}, biburl = {https://www.bibsonomy.org/bibtex/24e16ac969ca4a9d91585ca1d2fb30534/jaeschke}, doi = {10.1016/j.jvlc.2008.01.004}, interhash = {3b7d30b9325287fb6a979a84cb51f7bb}, intrahash = {4e16ac969ca4a9d91585ca1d2fb30534}, issn = {1045-926X}, journal = {Journal of Visual Languages & Computing}, keywords = {algorithm diagram euler visualization math mathematics}, number = 6, pages = {675--694}, timestamp = {2020-08-18T11:57:31.000+0200}, title = {Euler diagram generation}, url = {http://www.sciencedirect.com/science/article/pii/S1045926X08000049}, volume = 19, year = 2008 }