Document Detail

Drawing Euler Diagrams with Circles: The Theory of Piercings.
MedLine Citation:
PMID:  20855916     Owner:  NLM     Status:  Publisher    
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 which make the diagrams less comprehensible. In this paper we address these two issues by developing the theory of piercings, where we define single piercing curves and double piercing curves. We prove that if a diagram can be built inductively by successively adding piercing curves under certain constraints then it can be drawn with circles, which are more aesthetically pleasing than arbitrary polygons. The theory of piercings is developed at the abstract level. In addition, we present a Java implementation that, given an inductively pierced abstract description, generates an Euler diagram consisting only of circles within polynomial time.
Gem Stapleton; Leishi Zhang; John Howse; Peter Rodgers
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Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2010-9-8
Journal Detail:
Title:  IEEE transactions on visualization and computer graphics     Volume:  -     ISSN:  1077-2626     ISO Abbreviation:  -     Publication Date:  2010 Sep 
Date Detail:
Created Date:  2010-9-21     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  9891704     Medline TA:  IEEE Trans Vis Comput Graph     Country:  -    
Other Details:
Languages:  ENG     Pagination:  -     Citation Subset:  -    
University of Brighton, Brighton.
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