Euler Diagram Encodings

Euler Diagrams are a well-known visualisation of set-based relationships, used in many application areas and at the basis of more complex notations. We propose a static code for concrete Euler Diagrams, which enables efficient storage (vs. storage of concrete diagrams), and transformations preserving concrete-level structure, hence the viewer’s mental map. We provide the theoretical underpinnings of the encoding, examples and deductions, and an indication of their utility. For use in an interactive setting, we provide algorithms to update the code upon curve addition and removal. Independently, we show that the code identifies minimal regions, enabling the computation of the abstract zone set.