Point-cloud slicing: what each approach is good for, and what to combine

Findings, from the 1 980 runs below (10 objects × 18 cloud types × 11 configurations) and the gallery.

The idea that unifies what works: the encoder works at one scale ε, the finest detail the input supports, ε = max(point spacing, 4σ) with the noise σ given as an encoder parameter (0 for a clean cloud). Surfaces closer than ε merge, loops smaller than ε² vanish, and a part is cut only where one smooth height fit fails to explain the points (configuration eps: eps.py). On a clean cloud ε is the spacing and this is the package's slicer with the point test.

1. Per-point noise: eps turns the explosion into a description at the noise level. 10k points, all objects, against the mesh's 139 parts: 0.6 % noise 1 385 → 314 parts, error 0.85× the package's; 1.2 % noise 3 277 → 153 parts, error 0.57×. At 2 048 points and 1.2 %: 742 → 185 parts, error 1.17× (thin limbs are below ε there). Measured on the way: the slicer's support, band and inlier distance must scale with ε and the minimum loop with ε² (ε or a fixed loop leave the specks); the cut margin and the thin-wall rule must not (scaled by ε they delete geometry). C = 4 (report/eps_*.txt).
2. The point test is the cut rule (also inside eps). Everywhere about 10 % fewer parts at the same error at 10k and within 5 % at 2 048; on some organic shapes it keeps pieces the mesh cuts (dress, dino at 10k).
3. Thin walls are an orientation failure. A wall thinner than about a spacing is oriented as one sheet, so the inner face reads the cavity as inside: the slicer's inside band sits beside the wall and its zero line breaks (field pages). The thin-wall band (thinwall.py) fixes part of it at 10k (loaf pan 74 → 57 parts, error 16.6 → 9.9; shoe 30 → 26) and leaves thick objects unchanged, but it overthickens walls at 2 048 and the wall is not always closed (thinwall.html). The gated hybrid repairs the same rings from neighbouring layers at 5× the cost.
4. Ring refitting (A, the hybrid) gives cleaner rings, not fewer parts, and costs accuracy at 2 048 (8–14 %).
5. Variable density: the same idea per point. No global scale fits a cloud whose density varies (a global ε from the 90th-percentile spacing roughly halves the parts, report/eps_density.txt). With ε measured per point, ε_i = max(local spacing_i, 4σ), setting that point's RIMLS support, band, plane-fit inlier distance and the minimum loop around it (configuration local, surf_local.py, CPU): gradient density at 10k 927 → 274 parts at 0.53× the package's error, striped 1 362 → 637 at 0.85×, gradient at 2 048 564 → 264 at 0.88×; per-point noise as global ε (0.6 %: 315 parts at 0.73×; 1.2 %: 168 at 0.67×); clean and mesh-noise clouds about the package's. One measured detail: the flood's balls follow the local spacing, not ε (it seals sampling gaps, and noise opens none; scaling it by 4σ cost up to 50 % error at 1.2 % noise, report/local_flood.txt). Weak spot: per-point noise at 2 048 points (0.6 %: 1.13× the package's error).
6. Noise estimation is not solved. A local quadric fit reads thick shapes' noise (horse 0.55 % for 0.6 %) but takes a thin wall's two faces for noise (clean mug 0.84 %), and at 2 048 everything reads high: σ is a parameter, not estimated (report/sigma_estimators.txt).
7. 2 048 points is past the sampling limit for this set: about twice the mesh's parts in every configuration, some features gone.

Since then: the GWN slicer beats every prototype above (another agent's, ../../fcp_2810_gwn; checked here: its numbers reproduce exactly on 25 clouds, it uses no ground truth, the same clouds and metric; report/gwn_check.txt). Inside / outside from the mollified generalized winding number of the oriented, area-weighted points, mollifier ε_i = max(0.5 local spacing_i, 3σ): the same one-scale idea with a better field. Against the mesh's 134 parts: clean 10k 135 parts at 0.96× the package's error (local 179, 1.01×); 0.6 % noise 284 at 0.60×; density stripes 273 at 0.38×; clean 2 048 181 at 0.88×. GWN + point test (configuration gwn+pointtest): 8–17 % fewer parts again at 1–6 % more error, but below the mesh's count on clean clouds (median 0.79) and at 1.2 % noise (0.50): with GWN's clean rings the coefficient cut rule no longer over-cuts, and the point test's 2-spacing margin (set for ragged rings) keeps pieces the mesh cuts. GWN alone is the closest to the mesh's parts; the point test helps where GWN still over-cuts (sparse and variable-density clouds at 2 048); its margin for GWN (about 1 spacing) is not measured yet (report/gwn_combo_summary.txt).

Test set change: the ObjectFolder loaf pan (its mesh all slivers: its noisy versions reached only 0.21–0.27 % noise) is replaced by open_box (scripts/make_openbox.py): the loaf pan's size, rounded corners, 6 mm walls and floor, marching cubes of its signed distance (well-shaped triangles; the noisy versions reach 0.20 / 0.53 / 0.94 %). Its mesh route has 2 parts; clean 10k: package 37, local 25, GWN 19 (error 4.5 → 3.6 ×10⁻³); 0.6 % noise: 331 → 111. The tables count only the current test set (the loaf pan's rows stay in the CSV).

Recommended, in the paper's words: "Every point carries the resolution the input supports there, ε = max(a fraction of its local spacing, a multiple of the noise σ). Inside and outside come from the winding number of the oriented, area-weighted points mollified at ε, so the field neither sees the density nor resolves anything finer than ε; loops smaller than ε² are dropped, and a part is cut where one smooth fit along the height fails." In the package: the GWN slicer (with a fast evaluation: it is a direct sum, 1.6–3.5 s at 10k and 11–54 s at 50k), a noise= parameter, and the cut rule chosen for GWN's rings (the package's, or the point test with its margin measured for them). Later: thin walls (the open box still has 19 parts against 2), and an estimate of σ that does not read thin walls as noise.

The package is untouched; every prototype is in scripts/. A change to the package is a decision for api/DECISIONS.md, with these tables.