Four numbers. The straight figure is Chiodo's: nine triangles whose corners all fall where they must, built from four heights a, b, c, d on the vertical diameter. Everything else follows by ruler and compass — a circle through three points, the meeting of two lines — so the sliders move the construction rather than nudging the drawing towards it.
What is exact about it. The seven places where an apex has to land on another triangle's base, and the twelve triples of lines that have to meet at one point, hold to machine precision at every setting of the four sliders. They are steps of the construction, not conditions being satisfied.
The held conditions. Each switch above the sliders asks for one more thing — the innermost triangle centred on the bindu, or equilateral, or D3's corners on the rim — and solves the remaining freedom for it. Four heights carry at most four conditions, so the switches compete: turn on a fourth and something has to give.
Twelve points, eighteen numbers. The arc figures are built from twelve seed points, and every side is a single circular arc rather than a spline through the nodes — so the curvature of a side is constant by construction, and a straight side is just the zero-curvature case. The eighty-eight incidences hold because each one is a step of the construction.
The grown rings. Outside the nine triangles the figure grows two rings of cells. Ring 1 held Ring 2 held keeps that ring's tips exactly on a circle, which costs six or seven of the eighteen numbers; the sliders then move only what is left. No rings holds neither, so all eighteen are free — it opens on the ring-two figure and lets go from there.
Principal directions. The eighteen seeds are a fine basis and poor dials: moving one moves the picture by an amount that has nothing to do with moving another. The principal directions are the same space in an order — each scaled so a full slider moves the worst-placed node the same distance, and each one the figure can actually take, since they are found in the null space of whatever ring is held.
The bindu. The dot at the centre is the point the innermost triangle is measured against, not an ornament: on the straight figure one of the switches puts it exactly at the centroid.
Note. Every figure here is a construction. There is no solver running and nothing is being fitted — what the sliders move are the numbers the drawing is made from.