Goodness of fit
Not every set of region sizes can be drawn exactly, so eunoia reports a few scalars that summarize how faithfully the fitted geometry reproduces the requested set relationships. These appear under Goodness of fit in the App, and are returned on the layout for programmatic callers.
Metrics
- stress: a scale-invariant measure due to Wilkinson (2012),
popularized by
venneuler. Lower is better. - diagError: the largest absolute discrepancy between a fitted
region’s share of the total area and its requested share. Defined by Micallef & Rodgers (2014); values below
0.01generally indicate a faithful diagram. - regionError: the same quantity as
diagError, but reported per region rather than as the maximum across all of them.
When a diagram can’t be drawn exactly
Not every set of region areas can be represented faithfully with circles, or even with ellipses. A classic example:
A=5, B=3, C=1, A&B=2, A&B&C=2No two-dimensional Euler diagram with circles can satisfy these
constraints exactly. In such cases diagError will be large, and the
geometry eunoia returns is the best compromise the optimizer found. The
metrics above are how you tell a faithful diagram apart from a forced
one; always check them before trusting a layout.
References
- Wilkinson, L. (2012). Exact and approximate area-proportional circular Venn and Euler diagrams. IEEE Transactions on Visualization and Computer Graphics, 18(2), 321–331.
- Micallef, L., & Rodgers, P. (2014). eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses. PLOS ONE, 9(7), e101717.