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.
%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
}