The Online Abstraction Problem for Euler Diagrams

3rd International Workshop on Euler Diagrams; 7th International Conference on the Theory and Application of Diagrams (Diagrams 2012)

Gennaro Cordasco1 ; Rosario De Chiara2 ; Andrew Fish3 ; 2 ISISLab ; Dipartimento di Informatica – Universita` di Salerno ; ITALY ; 3 School of Computing ; Engineering and Mathematics – University of Brighton ; UK

Others  :  http://ceur-ws.org/Vol-854/paper5.pdf
PID  :  43056

来源: CEUR

【 摘 要 】

A Euler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Efficient algorithms to quickly compute the abstract regions of an Euler diagram upon curve addition and removal have been developed, but a strict set of drawing conventions (called wellformedness conditions) were enforced, meaning that some abstract diagrams are not representable as concrete diagrams. We present a variation and extension of the methodology which enables region computations for Euler diagrams under the relaxation of several drawing conventions. We provide complexity analysis and compare with the previous methodology. The algorithms are presented for generic curves, allowing for specialisations such as utilising fixed geometric shapes for curves that often occur in applications.