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Stage 10 of 14

Putting back the symmetry the pipeline quietly broke

Many logos are mirror-symmetric by design, and drawn that way exactly. This stage finds that exact symmetry early, while it is still easy to prove, and restores it at the very end — after every other stage has had its turn and had the chance to nudge one side very slightly out of step with the other.

Technical reference: 10-symmetry.md

The artist was exact. The tracer, quietly, was not.

A great many real logos are mirror-symmetric on purpose, and the artist's own symmetry is essentially perfect: rendering one such icon and comparing it against its own mirror image gives a difference of around one part in a hundred thousand — floating-point rounding, nothing more.

Before this stage existed, the tracer's own traced output came back roughly two to four hundred times worse than that — a difference around four in a thousand. That sounds small, but it is exactly the kind of error a person notices at a glance and a colour-difference measurement barely registers at all: one bar of a three-bar mark ending up a tenth of a pixel wider than the other two, so the mark reads as slightly lopsided even though every individual measurement looks fine on its own.

The striking part is where that error does not come from. Measured all the way through the pipeline, the input picture itself is symmetric to within one part in a million, and the very first per-pixel colour-label map this pipeline produces is symmetric exactly — not almost, exactly. Every bit of the eventual mismatch is introduced afterwards, by genuine coin-flips scattered through the rest of the pipeline: which of two equally valid pixels a boundary crack gets filed under, which direction a chain of points happens to be walked in, which of two equally good candidates a search happens to reach first. None of those choices is wrong by itself. There are simply thousands of them, and which one flips which way differs from icon to icon and from stage to stage — there is no single place to go and fix.

Rather than chase down every tie-break individually across a pipeline this size, symmetry is restored once, structurally, as its own dedicated pass at the very end.

Finding the mirror, exactly, while it is still easy

This stage looks for symmetry twice, at two different moments, for two different reasons.

First, immediately after the shapes and their connections are settled — before any point has moved even slightly off the exact pixel grid — it checks whether the picture has a vertical or horizontal mirror line running through its exact centre. The test has no tolerance whatsoever: a candidate mirror is accepted only if every single pixel on one side matches the corresponding pixel's ink on the other side. There is no near-enough. This is deliberate: a looser test could be fooled into "discovering" symmetry in a logo the artist genuinely drew slightly asymmetric, which would be a worse mistake than missing a real symmetry occasionally is.

Because this check runs while every boundary point still sits on an exact grid position, matching one side against its mirror is simple exact arithmetic — no rounding, no near-misses to argue about. That is precisely why it has to happen this early: once later stages start moving points to their true sub-pixel positions, the same comparison would need a tolerance, and a tolerance is exactly the kind of judgement call this test is built to avoid.

Restoring it once every tie has already been broken

The second moment is the very last thing this pipeline does, after every stage that could nudge a point asymmetrically has already run — moving points to their sub-pixel positions, resolving junctions, any later boundary adjustment, deciding exactly how each region gets filled. Only then does this stage act on the mirror it found earlier: every boundary point that has a matching mirrored partner is replaced by the exact midpoint of itself and that partner's reflection.

Replacing both sides with their average, rather than simply picking one side to win, is the whole point. Neither side is more correct than the other — they were built from identical evidence and differ only because of an arbitrary tie broken one way on one side and the other way on the other. The midpoint is the position both sides actually support.

Before and after averaging a mirrored pair Before — a tie broken differently on each side mirror axis two points, close but not equal After — both replaced by their shared midpoint one point, exactly on the axis
Both mirrored points were honest measurements. Averaging them does not favour either one — it removes only the disagreement between them, which was never evidence about the shape in the first place.

The concrete case this exists for: a glyph made of three bars that should all be the same width can come back from fitting at, say, 21.3, 21.4 and 21.3 pixels — each bar fitted on its own, with the middle one straddling the mirror axis and absorbing a small independent error on each side of itself. This stage is what makes that middle bar come back exactly as wide as its two neighbours, because it is, structurally, required to.

Anything nudged in between gets flattened back

Because the final averaging step treats both sides identically and has no way to prefer one over the other, any stage that runs between the two moments — the detection and the restoration — and treats a mirrored pair of points asymmetrically has that asymmetric adjustment erased at the very end, regardless of whether it was an improvement or not. This is simply how the averaging works, not a special case it watches for. A stage inserted into that window either has to respect the mirror itself, or accept that whatever it did differently on the two sides will be pulled back into agreement afterwards.

What this does not fix

Restoring symmetry to the underlying points does not automatically make the curves fitted through them identical, because the process that turns a chain of points into a smooth curve can walk one mirrored boundary in one direction and its partner in the other, and reach a slightly different curve even from perfectly mirrored points. That is handled separately, downstream: rather than fit both halves of a symmetric pair independently and hope they agree, only one edge of each mirrored pair is fitted at all, and its result is reflected directly onto its partner — which is both exactly consistent and roughly half the fitting work for anything the mirror covers.

What this stage will not attempt

Only two candidate mirrors are ever considered: a single vertical line and a single horizontal line, each running through the exact centre of the image, because a short argument shows those are the only lines a pixel grid's own edges can possibly support without going out of bounds. A diagonal mirror, a shape with four-fold rotational symmetry, or a symmetry that only holds within one part of a larger picture rather than across the whole canvas are all outside what this stage looks for. And because the pixel-level test has no tolerance at all, a logo with even one pixel of genuine, deliberate hand-drawn asymmetry is correctly found to have no mirror at all — which is the intended behaviour, not a shortcoming: this stage would rather miss a symmetry than manufacture one that was never really there.