Fitter pipeline

Fitting a diagram turns a set of region sizes into concrete shapes (circles, ellipses, squares, or rectangles) whose overlaps reproduce those sizes as closely as possible. Eunoia runs this in four stages.

The widget below records a real fit of a three-set spec and lets you play it back step by step. Initial layout runs the MDS stage: the shapes start at random positions and spread out so overlapping sets sit near each other. Final layout then runs the optimizer, refining every shape to minimize the loss. Each button plays its stage and stops on the result; Re-run draws a fresh random start, and you can switch between circles and ellipses.

1. Initial layout (MDS)

An initial arrangement is computed with positional multidimensional scaling. Each shape’s size is fixed up front from the requested set areas, and only the center (x, y) of every shape is solved for, which is why the shapes move into place at a fixed size during this stage in the animation. Target pairwise distances come from inverting each shape’s own overlap formula, so the warm start already places overlapping sets near each other and disjoint sets apart.

2. Optimizer encoding

The MDS positions are converted into the per-shape parameter encoding the optimizer works in. An ellipse, for example, is optimized over [x, y, ln a, ln b, φ] rather than its raw semi-axes. The log encoding keeps widths and heights positive and balances the scales of the parameters so a single solver setting works across positions, radii, and angles.

3. Final optimization

The shape parameters are refined by minimizing a loss that measures the discrepancy between the fitted region areas and the requested ones. This is the final stage in the animation, where the shapes resize and shift to tighten the fit. The optimizer and the loss are both selectable; circles and ellipses use analytical gradients where the loss allows, and a global-escape stage can kick in when a plain local solve stalls on a hard layout.

A single fit actually runs this two-phase pipeline several times (ten by default) from independent random starts and keeps the lowest-loss result. Pressing Re-run above shows one such start, and you can see how different starts converge differently.

4. Normalization

The fitted layout is post-processed for a stable, consistent appearance: disconnected clusters are separated, the diagram is rotated to a canonical orientation, centered, and the clusters are packed together. The result is a layout you can polygonize, label, and render. (The animation shows the optimizer’s own raw coordinates, before this cosmetic step.)

How faithfully the result reproduces the requested sizes is summarized by a few scalar metrics; see Goodness of fit.

For the authoritative details (optimizers, losses, gradients, and the shape-specific encodings) see the Architecture section in CONTRIBUTING.md.