← report · parts, clean 10k (renders of A and B) · middle slices

Fitted contours on point clouds: A vs B

2026-10-28 · clean 10k clouds (pointclouds/*_clean_10000.ply) · prototypes in scripts/ringfit.py, package untouched · slices: scripts/compare_slices.py, tables: report/ringfit_table_clean_10000.txt.

What the two do

Both replace the slicer's traced polylines with contours fitted to the points: for every layer, the points within a spacing of the plane are moved onto it along the surface (a point is used only when that move is under ¾ spacing, so slanted and near-horizontal surfaces count only near the plane), each contour is x(t), y(t) with N_eff = min(16, (n/3 − 1)/2) harmonics for its n points (regularised by the point count, plus a light ridge on the high harmonics), and each point's t comes from its projection on the current fit (4 rounds). The fitted contours then go through the package's tracking, cuts and atom selection unchanged.

• A, slicer topology: the slicer's rings decide how many contours a layer has, which are holes, and which points belong to each (nearest ring, on its face by the oriented normal); only the shape is refitted.
• B, point sheets: no slicer field. Points within 3 spacings whose normals do not face opposite ways are joined into sheets (a thin wall's two faces stay apart); a sheet that closes around its centre (angular gap under 120°) becomes a contour, parametrised first by the angle around its centre; solid or hole from whether its normals point away from or towards the centre.

Results, clean 10k

tracks / parts / mean distance over the diagonal (×10⁻³). Mesh parts for reference. Red: error ≥ 2× the package's.

B's lower part counts on the loaf pan (36) and the elephant (17) are not progress: they come from layers it lost, not from better tracking — the errors show it.

What the slices show

Each comparison page shows, per layer, the slicer's rings, A and B over GT (black) and the slab's points (grey): GSO bowl · loaf pan · battery · dino · shoe.

A: clean shapes, the slicer's topology

• It removes the hooks. Where the slicer's ring is right but ragged, A's ring is smooth and lies on GT: GSO bowl layer 114, loaf pan 13, 29 and 44, battery 85 and 100 (the latch step is kept). This is what the ring fit was for: N follows the points, not 512 resamples of a traced line.
• It inherits every topology error. Where the slicer opens the loaf pan's wall into a C (layer 60), A fits one ring to both faces: a twisted C. Where the slicer fragments the bowl's rim (118) or the battery's top (122), A fits each fragment. Tracks are the slicer's, so the parts barely move.
• It adds a few artefacts. A spike at the bowl's 116 and the loaf pan's 99: points assigned to the wrong ring (the nearest-ring assignment fails where the slicer's rings are themselves wrong). Corners are slightly rounded (battery), as N ≤ 16 always does. Net: error +0–15 %, mostly from these spikes.

B: the right idea, a fragile implementation

• When the sheet is closed and roughly convex, it is excellent. GSO bowl layers 20–100 (both faces of the wall, as two clean contours), battery 20, 60, 115: as good as A, with no slicer at all.
• Failure 1, lost layers. A sheet broken by a gap wider than the link, or with a few wrongly oriented normals, does not close and is dropped: the loaf pan's 13 and 44 and the bowl's rim (114–118) have no contour at all. A layer with no contour is a hole in the object, hence the large errors.
• Failure 2, wild contours. The angle around the centre is a poor first parameter when the sheet is not star-shaped around its centre, is elongated, or has stray points: battery 85 (the step) and 100, loaf pan 29, 60 and 99 show loops far outside the object.
• Failure 3, thin crescents. The rim's section is a thin crescent: an outer arc and an inner arc that close only together. B's sheets are the two arcs, neither closes, both are dropped.
• Failure 4, false holes. On non-convex sections the mean of n·(p − c) can come out negative and a solid becomes a hole (dino, mug, shoe: 9–18 holes against 0–8).

Which is more promising

B, but not as it stands. Everything A can do is bounded by the slicer's topology, and the topology is the problem: at 10k the excess parts are tracks (GSO bowl 18 against 3, loaf pan 56 against 2), which no fitting of shapes removes. B is the only one of the two that can fix them, and on the layers where its sheets close it already does. Its four failures are all in the parts I simplified, not in the idea:

1. the order of a sheet's points: replace the angle around the centre by a real curve reconstruction of the slab's points with normals (e.g. the nearest-neighbour crust, or a shortest cycle through the sheet's k-NN graph), which handles non-convex, elongated and stepped sections;
2. open sheets: pair the two faces of a thin wall (opposite normals, a wall's width apart) into one ring (the crescent), and close a sheet across a gap under a few spacings instead of dropping it;
3. solid or hole from the orientation of the reconstructed curve (signed area against the normals), not from the centre;
4. a fallback per layer to A (the slicer's topology) where B's contours do not explain the points, so B can never lose a layer.

The honest risk: at 10k some walls are thinner than the spacing (47 % of the loaf pan's surface). There even a perfect reconstruction relies on the normals alone to separate the faces, and where the slicer's normals are wrong, B is wrong too. A's fitting step is worth keeping either way: it is the right last stage for whichever topology wins.