Context

Every body the renderer drew was a sphere. Formally it was a unit sphere scaled by the equatorial radius and squashed along the spin axis by polarRadius / radius, which is a spheroid — the right shape for anything hydrostatic equilibrium got hold of, and a genuinely important one. Saturn is 9.8% oblate and reads as wrong long before anybody can say why.

It is not the right shape for the rest of the Solar System.

Phobos is 27 × 22 × 18 km with Stickney, a nine-kilometer crater, taken out of one end. Bennu is a spinning top with a ridge round its equator that its own rotation raised. 216 Kleopatra is a dog bone 217 km long. 1P/Halley is a black peanut. Draw any of those as a sphere and you have not simplified the body, you have drawn a different object — and docs/design/art.md is explicit that what a player can check has to be true.

The pressure to fix it came from adding the bodies. packages/universe/src/solar carried eight planets and twenty moons, every one of them round. It now carries those plus fifty-nine dwarf planets, asteroids and comets, and forty-two more moons — twenty-one of the planets' that are rocks, and twenty-one going round something that is not a planet. Ninety-two of Sol's hundred and twenty-nine bodies are not spheroids, and — because generated moons below the rounding threshold are not either — neither is a large fraction of every other system in the galaxy.

Decision

A body carries a figure when it is not a spheroid, and null when it is. Null means round; it does not mean unknown. BodyFigure holds the second equatorial half-extent (radius is a, polarRadius is c, this is b), a key naming a shipped shape model, and a residual roughness for the generated case.

A shape model is a latitude/longitude grid of radii, shipped as a small binary in data/shapes/, and the renderer builds a mesh from it in exactly the layout Three.js's SphereGeometry uses.

The generated case and the measured case are the same case. A body with no model gets a radius grid out of its own address seed, on its measured half-extents, through the same mesh builder. The renderer has one code path for "not a sphere" and it does not know which kind it is holding.

Alternatives rejected

A triangle mesh per body. More general — it can hold an overhang, which a radius grid cannot. Rejected because the generality is unused and the costs are not:

Every surface map in this project is equirectangular and was written for a sphere with a known UV layout. A grid mesh is that sphere with the radii moved, so Phobos takes an albedo map through the same material as Mars, seam and poles included. An arbitrary mesh needs a parameterization invented for it and a seam split done by hand.
Level of detail is subsampling. Take every second row and column, and the coarse mesh is the fine one's own samples rather than a decimation with its own error. A body may not change size when it crosses a tier.
The file is the data. Sixteen bytes of header and one uint16 per sample: Phobos at 256 × 129 is 65 KB, and the whole set of twenty-five is 937 KB. A mesh needs positions, indices and normals.
The sources are mostly already grids. Peter Thomas's satellite models and Philip Stooke's small-body atlas both publish latitude, longitude and a radius, one sample per line.

The cost is real and is named: a radius grid cannot represent a surface that is not star-shaped about the body's center. Every published model run through the ingest is — including the bilobate ones, because a neck is a saddle rather than a roof — and the ingest measures it, comparing the reconstructed volume against the source mesh's own and refusing anything that loses more than 6%. Kleopatra, the shape most likely to break it, reconstructs to 100.6%.

A displacement in the shader, on the existing sphere. Cheaper still, and wrong for the reason every displacement map is wrong: the vertex normals stay the sphere's, so a crater shades exactly as if it were not there. Recomputing normals in the shader means differencing the height field per fragment, which is three extra texture samples on a body that is forty pixels across.

Keeping figure out of the core and doing it all in the renderer. The figure of a body is a measurement — it is where the surface is — and it sits beside radius and polarRadius for the same reason those do. What is presentation is the seed the generated field is drawn from, and that stays in the renderer.

Consequences

A third radius exists and three files have to agree about it. radius is a, figure.intermediateRadius is b, polarRadius is c, sorted. The half-extents of a body with a shipped model are measured off that model by the ingest rather than transcribed beside it, so the number the renderer scales by and the geometry it scales cannot drift apart.

flattening must not be applied to a body with a figure. The mesh already carries the polar squash; applying both squashes it twice. This is the one place the renderer branches, and it is one line in render/bodyUniforms.ts: the mesh and every shell around it read the same shellFlattening, which is 1 for a body with a figure.

A body may be round and still have a figure. Haumea is a Jacobi ellipsoid — 1050 × 840 × 537 km, in hydrostatic equilibrium, and tri-axial because it turns once every 3.9 hours. It is the one body where "round" and "spheroid" come apart, and it is named in the test that checks the rest of the rule.

The roughness of a generated body is calibrated, not chosen. Across the twenty-five shipped models the residual radial deviation about each body's own best-fit ellipsoid runs 0.023 to 0.61 with a median of 0.090, and irregularFigure draws from that. The first version of the noise delivered 0.03 when asked for 0.18, because an fBm's standard deviation is a sixth of its range and nothing divided it out; the property test that would have caught it now exists.

Orbit traces had to learn what a small body is. The planetarium drew a subject's siblings for context, which was eight ellipses and is now a hundred and twenty-nine lines with the subject somewhere behind them. OrbitPath gained a kind and rubble is drawn only when it is the subject.

SYSTEM_ALGORITHM went to 3. Generated systems now contain six to eighteen small bodies each. Nothing a save could already point at moved — that is what issue ordinals (ADR-0009) are for — but a system contains things it did not, and the manifest has to say so.