Partition: degree sweep

2026-10-29 10:58 · fcp v5.31 (CUDA), package untouched (KAPPA patched in the process) · scripts/degree_sweep.py → report/degree_sweep.csv (360 rows, 10 objects) · Chamfer: mean of both directions, % of the diagonal; >30°: share of decoded-surface samples whose face normal is over 30° from the nearest clean-mesh sample's (unsigned)

Question. Keep tracked-fit (decision 22: tracking, the fit cut, the step rule that puts the cut on the event) but cut only where a part really breaks (a ledge, a joint), and let a higher height degree follow the rest. Step 1: the same rule against the degree cap, M and KAPPA (largest condition number of the Chebyshev basis on a part's layer centres; at 1e2 the degree is at most 11 / 17 / 25 / 35 on 16 / 32 / 64 / 128 layers). A higher cap lets one fit follow more, so the rule cuts less by itself. The SDF decode reads a part only at its layer centres, so a higher degree cannot wobble between layers there. Meshes only (exact slices, no slicer noise), 128 layers, up = +z, decoded on the SDF default at 128. (tracked, no cuts, is in the CSV but not shown: it is the old rule and loses the joints.)

The 2x2 (below): the stored degree alone changes nothing (high basis on the default parts: 1.000 / 1.000 / 0.998 Chamfer); the cuts a high cap removes are what cost (default basis on those parts: 1.13 at every budget, normals 1.4-3.5 times; bowl_of 1.4, shoe 1.3-1.5, horse 1.2). Cuts removed by a higher degree are not the unneeded ones.

Step 1, so far. A higher cap removes cuts (134 parts over the ten at the default, 121 at κ 1e3, 108 at κ 1e4) at the same Chamfer at 6144 atoms, but worse at 256 / 1024 (up to 1.13 / 1.05 times) and with more normals over 30° (up to 1.4 / 1.6 times). The renders show which cuts go.

Summary: geometric mean over the objects of the ratio to the default

Default row shaded (tracked-fit, κ 1e2, M 24). Green: 2 % better, red: 2 % worse. Parts and encode time summed over the objects; longest deg: the largest degree any part reached.

rule	κ	M	objects	parts	longest deg	Chamfer × 256	Chamfer × 1024	Chamfer × 6144	>30° × 256	>30° × 1024	>30° × 6144	encode s
tracked-fit	100	24	10	134	24	1.000	1.000	1.000	1.000	1.000	1.000	3.95
tracked-fit	100	35	10	132	34	1.006	1.001	1.000	1.052	1.079	1.035	3.46
tracked-fit	100	50	10	132	34	1.006	1.001	1.000	1.052	1.079	1.035	3.42
tracked-fit	100	80	10	132	34	1.006	1.001	1.000	1.052	1.079	1.035	3.40
tracked-fit	1000	24	10	123	24	1.103	1.032	1.001	1.281	1.398	1.120	3.28
tracked-fit	1000	35	10	122	35	1.075	1.029	1.001	1.180	1.311	1.025	4.01
tracked-fit	1000	50	10	121	41	1.107	1.030	1.000	1.277	1.437	1.067	3.98
tracked-fit	1000	80	10	121	41	1.107	1.030	1.000	1.277	1.437	1.067	3.74
tracked-fit	10000	24	10	110	24	1.106	1.049	1.001	1.355	1.500	1.217	3.13
tracked-fit	10000	35	10	110	35	1.123	1.051	1.001	1.388	1.585	1.066	4.18
tracked-fit	10000	50	10	108	47	1.125	1.052	1.001	1.363	1.580	1.045	4.19
tracked-fit	10000	80	10	108	47	1.125	1.052	1.001	1.363	1.579	1.044	4.39

The two effects apart: the cut decision and the stored basis

scripts/split_2x2.py: tracked-fit's cut decision with the default or a high cap (fewer cuts), and the stored height basis with the default or a high cap (higher degrees). Ratios to default / default (shaded).

cut decision	stored basis	objects	parts	Chamfer × 256	Chamfer × 1024	Chamfer × 6144	>30° × 256	>30° × 1024	>30° × 6144
default (κ 1e2, M 24)	default	10	134	1.000	1.000	1.000	1.000	1.000	1.000
default (κ 1e2, M 24)	high	10	134	1.000	1.000	0.998	1.000	1.026	0.982
high (κ 1e4, M 50)	default	10	108	1.131	1.137	1.137	1.442	2.714	3.484
high (κ 1e4, M 50)	high	10	108	1.125	1.052	1.001	1.363	1.580	1.045

object	parts cut lo	parts cut hi	Chamfer % lo/lo 256	Chamfer % lo/lo 6144	Chamfer % lo/hi 256	Chamfer % lo/hi 6144	Chamfer % hi/lo 256	Chamfer % hi/lo 6144	Chamfer % hi/hi 256	Chamfer % hi/hi 6144
battery_stepped	4	4	0.25864	0.25864	0.25864	0.25864	0.26519	0.26319	0.26134	0.25938
dress	17	13	0.35159	0.15516	0.35159	0.15498	0.37309	0.16067	0.37748	0.15484
elephant	27	22	0.78699	0.23325	0.78699	0.23303	0.73605	0.24164	0.73539	0.23336
bowl_of	5	3	0.20927	0.19665	0.20927	0.19689	0.3102	0.27931	0.29625	0.1972
bowl_gso	6	4	0.21864	0.19861	0.21864	0.19864	0.25738	0.2145	0.25407	0.1983
mug	8	6	0.28218	0.22037	0.28218	0.219	0.33674	0.23137	0.34094	0.22004
dino	25	21	0.40409	0.13395	0.40409	0.13293	0.41297	0.14586	0.41297	0.13404
shoe	22	18	0.43926	0.19044	0.43926	0.18977	0.58311	0.29357	0.57616	0.19142
open_box	2	2	0.25683	0.25655	0.25683	0.25663	0.25683	0.25655	0.25683	0.25663
horse	18	15	0.37328	0.14231	0.37328	0.14223	0.4457	0.1738	0.44793	0.14256

Why the elephant is cut so much

17 tracks, 27 parts: every extra part comes from one track, the body (layers 6-99), cut into 11 slabs. Three or four of its cuts sit on real events (a step of 0.2-0.5 in the ring coefficients, a jump of the perimeter: legs at 13, the leg tops at 26-30, the head at 50-51, the trunk at 91). The others (19, 36, 61, 70, 77, 85) sit on smooth stretches (steps 0.01-0.05). There the cut test, the fit's worst miss in coefficients, is 2.5-4 times the miss in shape (nearest-point RMS between the fitted ring and the sliced ring): 14-26 0.029 against 0.0072, 31-50 0.0115 against 0.0038, 61-89 0.031 against 0.0096 (tolerance 0.01). The rest is the parametrization sliding along the ring (tangential drift of the arc-length start), which moves no surface. Across the head (36-89) both are large (0.149 / 0.045): a real cut. A higher degree removes some of these cuts only by following the drift too.

scripts/body_track.py elephant → report/elephant_body.txt (per layer: rings in the slice, area, perimeter, coefficient step; then the coefficient and shape misses of the stretches).

Step 2: the fit test in shape, not in coefficients

scripts/shape_test.py: tracked-fit unchanged (tracking, cut search, step rule, tolerance 0.01, default cap) except that a fit follows its part when every ring is within the tolerance in shape (nearest-point RMS between the fitted and the sliced ring, both ways) instead of in coefficients. Green / red: shape better / worse than coef. Renders: shape-fit images in each object's section.

object	parts coef	parts shape	Chamfer % coef 256	Chamfer % shape 256	Chamfer % coef 1024	Chamfer % shape 1024	Chamfer % coef 6144	Chamfer % shape 6144	>30° % coef 256	>30° % shape 256	>30° % coef 1024	>30° % shape 1024	>30° % coef 6144	>30° % shape 6144
battery_stepped	4	4	0.2586	0.2586	0.2586	0.2586	0.2586	0.2586	3.04	3.04	3.04	3.04	3.04	3.04
dress	17	16	0.3516	0.3532	0.1852	0.1845	0.1552	0.1549	42.65	41.98	31.49	31.42	26.85	26.41
elephant	27	23	0.7870	0.7507	0.3720	0.3667	0.2333	0.2351	59.85	52.89	42.52	39.47	16.53	17.83
bowl_of	5	5	0.2093	0.2093	0.1976	0.1976	0.1966	0.1966	4.80	4.80	0.30	0.30	0.32	0.32
bowl_gso	6	5	0.2186	0.2234	0.1984	0.1999	0.1986	0.1992	7.44	8.84	1.10	2.09	0.99	1.83
mug	8	8	0.2822	0.2822	0.2249	0.2249	0.2204	0.2204	12.68	12.68	0.96	0.96	0.52	0.52
dino	25	25	0.4041	0.4041	0.1943	0.1943	0.1340	0.1340	37.36	37.36	18.05	18.05	7.28	7.28
shoe	22	17	0.4393	0.4251	0.2511	0.2514	0.1904	0.1908	33.74	31.68	26.47	24.52	7.57	8.35
open_box	2	2	0.2568	0.2568	0.2567	0.2567	0.2566	0.2566	1.00	1.00	1.01	1.01	1.10	1.10
horse	18	17	0.3733	0.3835	0.1851	0.1868	0.1423	0.1425	27.84	28.10	10.95	10.53	2.89	3.14
all (geometric mean of shape / coef)	134	122		× 0.997		× 1.000		× 1.001		× 0.998		× 1.046		× 1.089

Step 2, result. (After a fix: the first run measured to the nearest sample of the other ring, which leaves a floor of up to half a sample spacing, about the tolerance on a big ring, and cut more; now to the polyline.) The shape test cuts less (124 parts against 134: elephant 27 → 23, shoe 22 → 17, dress 17 → 16, horse 18 → 17, bowl_gso 6 → 5) at the same Chamfer (× 0.997 / 1.000 / 1.001 at 256 / 1024 / 6144). Normals: better at 256 on the elephant and the shoe, worse at 6144 (elephant, shoe, horse about +9 %; bowl_gso × 1.9). The bowl shows why: the foot (6-14) and the waist (15-26) become one part, and its fit leaves horizontal ripples at the foot, still at 6144 atoms. Every ring is within 0.01 in shape, but 0.01 is 0.64 of a layer height (2 / 128): a miss that alternates from layer to layer at that size tilts the surface by tens of degrees. A tolerance on distance alone allows it; the coefficient test caught it by being stricter for another reason. Next: a slope test besides the distance (the change of the miss between neighbouring rings, against the layer height).

Which parts fit their shape

scripts/fit_audit.py: per part, the worst shape distance over its layers between the sliced ring and the ring given back at the layer centre, in layer heights (0.0172 canonical; the cut tolerance 0.01 is 0.58 of one). Counts of parts by their worst miss. "full fit": all degrees of the part's height basis (what the cut test judges). Images: per object and cut test, the four parts that miss most: equivalent radius sqrt(area / pi) along the part (sliced, full fit, 6144, 1024 atoms) and the miss per layer.

What it shows. 6144 atoms give back the full fit (the budget is not what limits a part there); 1024 does not (elephant parts 0.5-2 layer heights off). Most parts fit to under a tenth of a layer. The waves are where a part holds a corner or a step: the polynomial rings around it with a period of two or three layers across the whole part (bowl_gso, shape test: the foot, layers 6-26, holds the bottom edge at layers 6-8, the radius 5 → 27 layer heights in two layers, then a gentle flare; its miss alternates 0.1 / 0.28 up to layer 26 and peaks at 0.52 at the corner. The corner cannot be cut off: it is two layers from the end and pieces are at least FIT_MIN = 4). With the coefficient test every part of the ten stays within 0.38 of a layer (dino 0.38, dress 0.31, the rest 0.25 or less); the shape test at the same 0.01 lets elephant, bowl_gso and shoe parts go to 0.5 (a step at the head, the leg tops, the foot). The coefficient test is, in shape, about three times stricter than its number: it cuts the corners and steps, and the smooth drifting stretches too. So the knob is the tolerance in shape: a fraction of a layer.

object	cut test	parts	6144: ≤ 0.1	6144: 0.1-0.25	6144: 0.25-0.5	6144: > 0.5	6144 worst	1024: ≤ 0.1	1024: 0.1-0.25	1024: 0.25-0.5	1024: > 0.5	1024 worst	full fit worst
battery_stepped	coef	4	4	0	0	0	0.00	4	0	0	0	0.00	0.00
battery_stepped	shape	4	4	0	0	0	0.00	4	0	0	0	0.00	0.00
dress	coef	17	9	6	2	0	0.30	0	0	3	14	1.18	0.31
dress	shape	16	7	7	2	0	0.30	0	0	2	14	1.46	0.31
elephant	coef	27	21	6	0	0	0.20	0	0	3	24	1.97	0.18
elephant	shape	23	18	3	1	1	0.55	0	0	3	20	2.34	0.54
bowl_of	coef	5	5	0	0	0	0.07	3	2	0	0	0.16	0.07
bowl_of	shape	5	5	0	0	0	0.07	3	2	0	0	0.16	0.07
bowl_gso	coef	6	6	0	0	0	0.10	2	3	1	0	0.36	0.10
bowl_gso	shape	5	4	0	0	1	0.52	1	2	1	1	0.52	0.52
mug	coef	8	7	1	0	0	0.15	0	2	6	0	0.43	0.15
mug	shape	8	7	1	0	0	0.15	0	2	6	0	0.43	0.15
dino	coef	25	18	6	1	0	0.38	0	4	5	16	1.27	0.38
dino	shape	25	18	6	1	0	0.38	0	4	5	16	1.27	0.38
shoe	coef	22	8	14	0	0	0.25	0	0	0	22	2.17	0.23
shoe	shape	17	5	8	3	1	0.51	0	0	0	17	2.37	0.51
open_box	coef	2	2	0	0	0	0.01	2	0	0	0	0.02	0.01
open_box	shape	2	2	0	0	0	0.01	2	0	0	0	0.02	0.01
horse	coef	18	13	5	0	0	0.20	0	0	5	13	1.13	0.19
horse	shape	17	11	6	0	0	0.22	0	0	5	12	1.19	0.22

battery_stepped

dress

elephant

bowl_of

bowl_gso

mug

dino

shoe

open_box

horse

The dino's body part: the height polynomial

scripts/part_profile.py dino 1e4 50 and dino 1e2 24: the largest part, the sliced rings at the layer centres (dots) and the stored polynomial drawn continuously at 1024 and 6144 atoms (equivalent radius, five single coefficients, the shape miss at the centres).

With the ground truth (grey: the mesh sectioned at 10 heights per layer, the part's ring; bottom panel, lines: the polynomial against it at every height, dots: against the sliced rings at the centres). Inside (41-65) the true section is smooth and the 6144 polynomial follows it to about 0.12 of a layer between the centres too (0.05-0.08 at them); at 1024 it is 0.4-0.65 everywhere: the budget, not the partition. The top end (66-70) is a real event: the true section jumps at 66.4 (radius 16.1 → 17.9 → 16.7, x centroid -5 → -9.5 → -7.5) and again at 68.2 (16.5 → 17.6): something joins the body ring, twice, between layers. The part runs on through it in both settings (a cut there would leave 2 layers, FIT_MIN = 4), and no polynomial follows a step: 1.5 layer heights off between the centres at 6144, though 0.07 at them. The bottom end (39-40) is smooth in truth; with KAPPA 1e4 the polynomial swings there anyway (more than 2 layers off between the first centres; beyond the end centres up to 193 layer heights of radius): the ill-conditioning KAPPA 1e2 prevents. The default follows it. Note: the SDF decode does not read the polynomial between the centres (it interpolates the rings' signed distance), so the lines between the dots are the polynomial's behaviour, not the mesh's.

Why 1024 atoms is wavy, and a smaller dictionary

The cap on the atom count changes nothing below it: the selection is one projection and one sort, so MAX_ATOMS = 2048 and decoding 1024 gives the dino's descriptor and mesh bit for bit as 6144 does. The waves at 1024 are the selection's: it keeps the atoms of largest energy (185 of 1021 values in the dino's body part, scattered over degrees 0-16), so the error left is the sum of the dropped degree polynomials, an oscillation along the height (0.4-0.6 of a layer). A smaller dictionary (scripts/nm_sweep.py; the cut test fits with the same M, so a lower M also cuts more): lowering N loses the angular detail (8 / 8: Chamfer 1.07-1.17 times, normals 1.6-1.8 times at 1024 / 2048; the battery and the open box worst); the dino's body at N 8, M 8 is smooth along the height at 1024 (degrees up to 4 kept) but 0.35-0.55 of a layer off the ground truth, and 0.25-0.5 still at 6144: 8 harmonics cannot draw its section (the dots there are the N 8 rings, not the truth). Keeping N 16 and lowering M only: Chamfer within 0.4 % at every budget; normals over 30° 8 % fewer at 256 (M 12 or 8), 4-10 % more at 1024 / 2048; elephant better (42.5 → 37.2 % at 1024, M 8), dress worse. A lower degree trades the waves for more parts; at 1024 the error stays about the same size.

N	M	parts	Chamfer × 256	Chamfer × 1024	Chamfer × 2048	>30° × 256	>30° × 1024	>30° × 2048
16	24	134	1.000	1.000	1.000	1.000	1.000	1.000
16	16	138	0.997	0.999	1.000	0.997	1.012	1.012
16	12	139	0.997	1.000	1.000	0.920	1.045	1.045
16	8	154	1.003	0.996	0.998	0.921	1.101	1.096
12	16	137	1.011	1.026	1.040	1.016	1.131	1.182
8	12	139	1.061	1.117	1.169	1.077	1.606	1.703
8	8	154	1.067	1.112	1.169	1.088	1.634	1.775
6	6	178	1.168	1.307	1.403	1.150	2.116	2.367
4	4	198	1.294	1.607	1.767	1.452	3.075	3.748

Step 3: the fewest parts for a tolerance

scripts/dp_split.py: each track partitioned by dynamic programming into the fewest pieces (at least FIT_MIN = 4 layers) whose full fit misses no ring by more than the tolerance; among those the least total squared miss (cuts on the events). dp-coef: the package's measure and tolerance (coefficients, 0.01), so its difference from greedy (the package) is the search alone; dp-shape-t: the miss in shape, the tolerance t layer heights. Worst part miss: over all parts of all objects, the full fit's worst ring, in shape (layer heights). Ratios to greedy. Renders at 1024 atoms below the tables (6144 in img/).

partition	parts	worst part miss (layer heights)	parts over 0.25 layer	Chamfer × 256	Chamfer × 1024	Chamfer × 6144	>30° × 256	>30° × 1024	>30° × 6144
greedy	134	0.38	3	1.000	1.000	1.000	1.000	1.000	1.000
dp-coef	128	0.38	4	1.099	1.036	1.001	1.204	1.258	1.052
dp-shape-0.1	145	0.97	1	1.097	1.053	1.000	1.186	1.173	1.019
dp-shape-0.15	137	0.15	0	1.101	1.039	0.999	1.215	1.232	1.017
dp-shape-0.2	131	0.20	0	1.093	1.040	0.998	1.209	1.239	1.015
dp-shape-0.3	126	0.28	1	1.101	1.045	0.999	1.218	1.251	1.013

object	greedy parts / worst	dp-coef parts / worst	dp-shape-0.1 parts / worst	dp-shape-0.15 parts / worst	dp-shape-0.2 parts / worst	dp-shape-0.3 parts / worst
battery_stepped	4 / 0.00	4 / 0.00	4 / 0.00	4 / 0.00	4 / 0.00	4 / 0.00
dress	17 / 0.31	16 / 0.31	19 / 0.97	19 / 0.15	18 / 0.17	16 / 0.24
elephant	27 / 0.18	25 / 0.31	28 / 0.05	25 / 0.15	24 / 0.20	24 / 0.20
bowl_of	5 / 0.07	5 / 0.07	5 / 0.07	5 / 0.07	5 / 0.07	5 / 0.07
bowl_gso	6 / 0.10	5 / 0.28	5 / 0.10	5 / 0.10	5 / 0.10	5 / 0.10
mug	8 / 0.15	8 / 0.14	9 / 0.03	8 / 0.14	8 / 0.14	8 / 0.14
dino	25 / 0.38	25 / 0.38	28 / 0.10	27 / 0.13	27 / 0.13	26 / 0.24
shoe	22 / 0.23	21 / 0.23	24 / 0.09	23 / 0.11	21 / 0.20	19 / 0.28
open_box	2 / 0.01	2 / 0.01	2 / 0.01	2 / 0.01	2 / 0.01	2 / 0.01
horse	18 / 0.19	17 / 0.19	21 / 0.10	19 / 0.14	17 / 0.19	17 / 0.19

Step 4: cut where the shape jumps between neighbouring rings

scripts/ring_steps.py: along each track (before any cut), the shape change from one ring to the next (each ring evaluated at 256 points from its Fourier series, the RMS distance of each one's points to the other's polyline, both ways: no fit, and no dependence on where a ring starts), log scale, with the package's cuts (red). scripts/spike_split.py: a cut where that step is at least 2.5 times the median of the steps within 4 layers on either side and at least one layer height; pieces down to 2 layers. spike: nothing else; spike+fit: then the package's cut search inside any piece whose fit still misses by more than 0.25 of a layer in shape.

The events stand out as spikes over a slowly varying baseline (0.02-1.5 layer heights). The dino's long track is cut by the package on its spikes already (11.5, 29.5, 38.5, 68.5; 66.5 not, as it would leave 2 layers). The elephant's body has spikes at 8, 13, 26, 30, 50-51, 64, 89, 91, 96, and the package cuts on some (13, 51, 91), between 26 and 30, and on flat stretches at 19, 36, 61, 70, 77; 64, 89, 96 not. The bowl's wall is smooth from 9 to 114 (falling from 1 to 0.02 as it turns vertical); its spikes are the bottom edge (6-8, up to 15 layer heights) and the rim (115+), and the package's cuts at 14.5 and 26.5 sit on the smooth stretch, fencing off the bottom edge that is too close to the end to cut. First three objects: spikes alone leave the bowl's bottom edge inside (between the track's first two rings: a cut would leave one ring; 14.8 layer heights off) and an elephant piece at 0.47; with the check: elephant 27 parts (0.21), bowl 5 (0.10, one fewer than the package), dino 28 (0.24 against the package's 25 at 0.38: the two-layer pieces at its joins).

partition	parts	worst part miss (layer heights)	parts over 0.25 layer	Chamfer × 256	Chamfer × 1024	Chamfer × 6144	>30° × 256	>30° × 1024	>30° × 6144
greedy	134	0.38	3	1.000	1.000	1.000	1.000	1.000	1.000
spike	127	14.79	12	1.012	1.043	1.062	0.857	1.435	1.658
spike+fit	142	0.24	0	0.958	0.978	0.999	0.669	0.907	1.011

object	greedy parts / worst	spike parts / worst	spike+fit parts / worst
battery_stepped	4 / 0.00	4 / 0.00	4 / 0.00
dress	17 / 0.31	17 / 2.68	22 / 0.24
elephant	27 / 0.18	25 / 0.47	27 / 0.21
bowl_of	5 / 0.07	4 / 0.81	5 / 0.07
bowl_gso	6 / 0.10	4 / 14.79	5 / 0.10
mug	8 / 0.15	9 / 0.15	9 / 0.15
dino	25 / 0.38	28 / 0.24	28 / 0.24
shoe	22 / 0.23	18 / 0.64	23 / 0.23
open_box	2 / 0.01	2 / 0.01	2 / 0.01
horse	18 / 0.19	16 / 0.70	17 / 0.22

Step 5: cut only when coefficients AND shape miss

scripts/and_test.py: the package's cut search unchanged; a piece is cut only when its fit misses a ring by more than 0.01 in coefficients (the points at the same t) and by more than t layer heights in shape (closest points). Sliding along the ring (large in coefficients, small in shape) no longer cuts.

It changes little: 134 parts → 133 (t = 0.15, 0.2), 129 (0.25), 128 (0.3); Chamfer within 0.2 % at every budget, normals within 1.5 %. Only a handful of the package's cuts come from sliding: the rest are misses of more than 0.3 of a layer in shape, real changes the polynomial does not follow. With the cut test as the lever, there is little room to make parts bigger at the same accuracy.

Why so little (scripts/and_scatter.py: every piece the package's cut search tests, its fit's worst miss in coefficients and in shape). 144 pieces tested on the ten meshes, 60 cut. The shape miss is about half the coefficient miss (median 0.48; 10-90 % 0.27-0.73), and the points sit close to that line: a piece that fails the coefficient test (over 0.58 of a layer) is almost always over 0.3 of a layer in shape too. Of the 60 cuts, the shape miss is under 0.15 for 1, under 0.25 for 5, under 0.3 for 6, under 0.4 for 9, under 0.58 (the same number as the coefficient tolerance) for 12. AND spares only those; the rest are real shape misses.

partition	parts	worst part miss (layer heights)	parts over 0.25 layer	Chamfer × 256	Chamfer × 1024	Chamfer × 6144	>30° × 256	>30° × 1024	>30° × 6144
greedy	134	0.38	3	1.000	1.000	1.000	1.000	1.000	1.000
and-0.15	133	0.38	3	0.998	1.000	1.000	0.997	0.998	0.997
and-0.2	133	0.38	3	0.998	1.000	1.000	0.997	0.998	0.997
and-0.25	129	0.38	3	0.998	1.000	1.000	0.990	0.991	1.007
and-0.3	128	0.38	4	1.000	1.000	1.000	0.986	0.986	1.012

object	greedy parts / worst	and-0.15 parts / worst	and-0.2 parts / worst	and-0.25 parts / worst	and-0.3 parts / worst
battery_stepped	4 / 0.00	4 / 0.00	4 / 0.00	4 / 0.00	4 / 0.00
dress	17 / 0.31	17 / 0.31	17 / 0.31	16 / 0.31	16 / 0.31
elephant	27 / 0.18	27 / 0.18	27 / 0.18	25 / 0.21	25 / 0.21
bowl_of	5 / 0.07	5 / 0.07	5 / 0.07	5 / 0.07	5 / 0.07
bowl_gso	6 / 0.10	6 / 0.10	6 / 0.10	6 / 0.10	6 / 0.10
mug	8 / 0.15	8 / 0.15	8 / 0.15	8 / 0.15	8 / 0.15
dino	25 / 0.38	25 / 0.38	25 / 0.38	25 / 0.38	25 / 0.38
shoe	22 / 0.23	21 / 0.23	21 / 0.23	21 / 0.23	20 / 0.28
open_box	2 / 0.01	2 / 0.01	2 / 0.01	2 / 0.01	2 / 0.01
horse	18 / 0.19	18 / 0.19	18 / 0.19	17 / 0.22	17 / 0.22

The mug's handle: where coefficients and shape part ways

scripts/mug_handle.py mug: along the body track, the step between neighbouring rings in coefficients (points at the same t: what the fit sees) and in shape (closest points), with the package's cuts; below, the rings around the four largest steps (start point dotted; the slice's other rings, the handle, in grey).

Layers 28-38: the handle's root grows out of the body ring as a lobe; the coefficient step (about 3 layer heights) is 2.7 times the shape step (1.1): the lobe adds length and every point slides. The package does not cut there: the fit follows it, and the body part 6-38 holds the whole root. 38 → 39: the lobe pinches off and becomes its own ring (the handle hole appears): the body ring loses a lobe of about 8 layer heights in one layer, shape step 7.8 (19 in coefficients), and the package cuts exactly there. 94 → 95 and 101 → 102: the handle joins from above in one layer (4.3) and pinches off again (5.6): cuts at 93 and 102. The rim (119 → 121): 47 in coefficients against 5 in shape (the start point jumps), then a real jump of 31: cut at 113. The cuts are on real jumps of the outline, which both measures see; where only the coefficients jump, the fit follows, or a real jump is next to it. To keep the handle region in the body's part, the part would have to hold a lobe that vanishes within one layer: no height polynomial can, whatever the cut rule. The way out is the tracking: the lobe as its own part from where it starts to grow (a ring split at its neck).

Step 6: rings split at their necks before tracking (prototype)

scripts/neck_split.py mug: every solid ring cut at its narrowest neck (the pair of points with the least chord / shorter arc, under 0.3, chord inside, both pieces at least 3 % of the area), then the package's tracking, Fourier and cut rule unchanged.

Mug: 4 tracks → 12, 8 parts → 16 (worst part miss 0.15 → 0.18 of a layer). The handle becomes three parts (lower root 33-39, handle 40-95, upper root 96-100), but the body is still cut at 33 and 96: the neck forms only once the lobe is longer than it is wide, so the body ring still holds the short bump at 28-32 and loses it at 33 (a smaller jump, still cut). The rim's thin lip (120-121) is shredded into 7 parts. To work, a split found at one layer would have to be carried down the track to the layers where the lobe is still a bump (two passes), and thin rings (rims, walls) kept whole. Not run on the other objects.

Step 7: momentum, the body goes on and the lobe is peeled off (prototype, mug)

scripts/momentum.py mug: after tracking, a long solid track is fitted along the height on the layers it follows; at the others the clean body is interpolated (PCHIP per coefficient) from the undisturbed layers on either side. Where a ring is the clean ring plus a lobe (reaching 2 layer heights out, meeting the clean ring along at most 40 % of it), the track keeps ring AND clean ring and the lobe (widened 1.5 layer heights into the body, so the parts overlap) goes to the track it touches (the handle). Then the package's cut rule.

The body is one part from the base to layer 96, through the lower handle attachment (the package: 6-38, 39-92, 93-101); the lower root joins the handle's track (one cut left at 39, where the handle hole opens: a real ledge). The upper attachment only partly (the body flares towards the rim there; the body cut at 97). 9 parts against 8, worst part miss 0.14 against 0.15. Accuracy: Chamfer 0.296 / 0.228 / 0.223 against 0.282 / 0.225 / 0.220 at 256 / 1024 / 6144; normals over 30° 13.8 / 2.8 / 1.9 % against 12.7 / 0.96 / 0.52 %. The overlap costs it: the decoder's signed distance at a layer is to the nearest ring edge, the lobe's edges inside the body included, and near the junction those inner edges bend the field. Parts that overlap are inside for the decoder, but its distance assumes rings that do not. Making this pay would take a union distance in the decoder (each part's own distance, then the largest), on NumPy, numba and CUDA, bit for bit.

With the union distance in the decoder (worktree ../fcp_devel_union, branch union-sdf)

Decoder: the distance at a layer is measured only to segments on the region's boundary (a segment whose midpoint the other rings put inside the region on both of its sides is left out; the parity unchanged); one host flag table, the same on NumPy, numba and CUDA; disjoint or nested rings unchanged; all 281 tests pass. On the mug the flags work (the buried segments at the lower root, 28-38) and the bad normals there are gone. What is left is the upper attachment (95-101), right where the body flares towards the rim: the clean body predicted from below does not flare, so part of what is peeled is a band around the rim, not the handle. Peeled patchily (95, 100, 101): 9 parts, normals over 30° 2.8 / 2.0 % at 1024 / 6144 against 0.97 / 0.57; peeled whole (95-101): 8 parts with the body 6-102 one part, but Chamfer 0.75 against 0.22 (the band, drawn with 16 harmonics, wanders into the cavity). The lower attachment shows the idea works where the body is predictable; near the rim it does not yet.

The v6 work (the evaluation on meshes and clouds, the short-track filter, atoms="auto", lobe parts) has its own report: fcp_2910_v6/report/index.html.

Per object

Green / red: better / worse than the default row by 2 % (Chamfer) or 5 % (normals).

battery_stepped

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	4	24	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	100	35	4	27	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	100	50	4	27	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	100	80	4	27	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	1000	24	4	24	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	1000	35	4	33	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	1000	50	4	33	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	1000	80	4	33	29.0	0.2586	0.2586	0.2586	3.04	3.04	3.04	0.5573
tracked-fit	10000	24	4	24	29.0	0.2613	0.2594	0.2594	4.88	3.47	3.47	0.5599
tracked-fit	10000	35	4	35	29.0	0.2613	0.2594	0.2594	4.88	3.47	3.47	0.5599
tracked-fit	10000	50	4	37	29.0	0.2613	0.2594	0.2594	4.88	3.47	3.47	0.5599
tracked-fit	10000	80	4	37	29.0	0.2613	0.2594	0.2594	4.88	3.47	3.47	0.5599

dress

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	17	16	12.6	0.3516	0.1852	0.1552	42.65	31.49	26.85	0.3459
tracked-fit	100	35	17	16	12.6	0.3516	0.1852	0.1552	42.65	31.49	26.85	0.3459
tracked-fit	100	50	17	16	12.6	0.3516	0.1852	0.1552	42.65	31.49	26.85	0.3459
tracked-fit	100	80	17	16	12.6	0.3516	0.1852	0.1552	42.65	31.49	26.85	0.3459
tracked-fit	1000	24	16	18	13.4	0.3829	0.2021	0.1545	43.83	33.60	26.53	0.34353
tracked-fit	1000	35	16	18	13.4	0.3829	0.2021	0.1545	43.83	33.60	26.53	0.34353
tracked-fit	1000	50	16	18	13.4	0.3829	0.2021	0.1545	43.83	33.60	26.53	0.34353
tracked-fit	1000	80	16	18	13.4	0.3829	0.2021	0.1545	43.83	33.60	26.53	0.34353
tracked-fit	10000	24	13	24	16.5	0.3775	0.2077	0.1548	43.90	34.66	26.96	0.34397
tracked-fit	10000	35	13	24	16.5	0.3775	0.2077	0.1548	43.90	34.66	26.96	0.34397
tracked-fit	10000	50	13	24	16.5	0.3775	0.2077	0.1548	43.90	34.66	26.96	0.34397
tracked-fit	10000	80	13	24	16.5	0.3775	0.2077	0.1548	43.90	34.66	26.96	0.34397

elephant

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	27	15	6.2	0.7870	0.3720	0.2333	59.85	42.52	16.53	0.487
tracked-fit	100	35	27	15	6.2	0.7870	0.3720	0.2333	59.85	42.52	16.53	0.487
tracked-fit	100	50	27	15	6.2	0.7870	0.3720	0.2333	59.85	42.52	16.53	0.487
tracked-fit	100	80	27	15	6.2	0.7870	0.3720	0.2333	59.85	42.52	16.53	0.487
tracked-fit	1000	24	24	18	7.0	0.7421	0.3604	0.2335	54.96	39.87	17.02	0.48851
tracked-fit	1000	35	24	18	7.0	0.7421	0.3604	0.2335	54.96	39.87	17.02	0.48851
tracked-fit	1000	50	24	18	7.0	0.7421	0.3604	0.2335	54.96	39.87	17.02	0.48851
tracked-fit	1000	80	24	18	7.0	0.7421	0.3604	0.2335	54.96	39.87	17.02	0.48851
tracked-fit	10000	24	23	20	7.3	0.7221	0.3658	0.2332	56.52	40.09	16.53	0.48691
tracked-fit	10000	35	23	20	7.3	0.7221	0.3658	0.2332	56.52	40.09	16.53	0.48691
tracked-fit	10000	50	22	20	7.6	0.7354	0.3720	0.2334	55.45	41.03	16.46	0.48816
tracked-fit	10000	80	22	20	7.6	0.7354	0.3720	0.2334	55.45	41.03	16.46	0.48816

bowl_of

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	5	24	44.6	0.2093	0.1976	0.1966	4.80	0.30	0.32	0.44587
tracked-fit	100	35	4	33	55.8	0.2170	0.1978	0.1966	6.55	0.34	0.31	0.44556
tracked-fit	100	50	4	33	55.8	0.2170	0.1978	0.1966	6.55	0.34	0.31	0.44558
tracked-fit	100	80	4	33	55.8	0.2170	0.1978	0.1966	6.54	0.34	0.31	0.44556
tracked-fit	1000	24	4	24	55.8	0.2756	0.2001	0.1979	20.29	1.66	0.82	0.44991
tracked-fit	1000	35	4	35	55.8	0.2192	0.1978	0.1971	7.39	0.50	0.33	0.44785
tracked-fit	1000	50	3	41	74.3	0.2963	0.1998	0.1972	16.29	1.56	0.61	0.44762
tracked-fit	1000	80	3	41	74.3	0.2962	0.1998	0.1973	16.28	1.56	0.62	0.4477
tracked-fit	10000	24	4	24	55.8	0.2756	0.2001	0.1979	20.29	1.66	0.82	0.44991
tracked-fit	10000	35	4	35	55.8	0.2974	0.2008	0.1973	19.19	1.51	0.34	0.44806
tracked-fit	10000	50	3	47	74.3	0.2963	0.2001	0.1972	16.29	1.68	0.33	0.4473
tracked-fit	10000	80	3	47	74.3	0.2962	0.2001	0.1972	16.28	1.68	0.33	0.44727

bowl_gso

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	6	24	36.2	0.2186	0.1984	0.1986	7.44	1.10	0.99	0.44427
tracked-fit	100	35	5	30	43.4	0.2236	0.1997	0.1994	9.09	1.94	1.57	0.44426
tracked-fit	100	50	5	30	43.4	0.2236	0.1997	0.1994	9.09	1.94	1.57	0.44426
tracked-fit	100	80	5	30	43.4	0.2236	0.1997	0.1994	9.09	1.94	1.57	0.44426
tracked-fit	1000	24	5	24	43.4	0.2234	0.1996	0.1991	8.84	1.21	0.93	0.44472
tracked-fit	1000	35	4	35	54.2	0.2541	0.2005	0.1991	12.33	1.96	1.28	0.44625
tracked-fit	1000	50	4	40	54.2	0.2541	0.2004	0.1987	12.33	1.56	0.97	0.44269
tracked-fit	1000	80	4	40	54.2	0.2541	0.2003	0.1987	12.33	1.56	0.97	0.44266
tracked-fit	10000	24	5	24	43.4	0.2234	0.1991	0.1986	8.84	1.17	0.99	0.44347
tracked-fit	10000	35	4	35	54.2	0.2541	0.2005	0.1991	12.33	1.96	1.28	0.44625
tracked-fit	10000	50	4	46	54.2	0.2541	0.2000	0.1983	12.33	1.67	1.03	0.4428
tracked-fit	10000	80	4	46	54.2	0.2541	0.2000	0.1983	12.33	1.67	1.03	0.44273

mug

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	8	24	35.2	0.2822	0.2249	0.2204	12.68	0.96	0.52	0.49436
tracked-fit	100	35	8	32	35.2	0.2822	0.2249	0.2205	12.68	0.96	0.51	0.4946
tracked-fit	100	50	8	32	35.2	0.2822	0.2249	0.2205	12.68	0.96	0.51	0.4946
tracked-fit	100	80	8	32	35.2	0.2822	0.2249	0.2205	12.68	0.96	0.51	0.49452
tracked-fit	1000	24	7	24	40.3	0.3485	0.2302	0.2209	20.51	2.51	0.57	0.49818
tracked-fit	1000	35	7	35	40.3	0.3357	0.2303	0.2204	18.13	2.55	0.50	0.4975
tracked-fit	1000	50	7	39	40.3	0.3357	0.2303	0.2205	18.13	2.55	0.53	0.49696
tracked-fit	1000	80	7	39	40.3	0.3357	0.2303	0.2205	18.13	2.55	0.53	0.49694
tracked-fit	10000	24	6	24	47.0	0.3493	0.2309	0.2204	20.58	2.82	1.04	0.49603
tracked-fit	10000	35	6	35	47.0	0.3409	0.2316	0.2201	17.20	2.94	0.55	0.49727
tracked-fit	10000	50	6	45	47.0	0.3409	0.2316	0.2200	17.20	2.94	0.58	0.49639
tracked-fit	10000	80	6	45	47.0	0.3409	0.2316	0.2200	17.20	2.94	0.58	0.49647

dino

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	25	19	11.6	0.4041	0.1943	0.1340	37.36	18.05	7.28	0.28603
tracked-fit	100	35	25	19	11.6	0.4041	0.1943	0.1340	37.36	18.05	7.28	0.28603
tracked-fit	100	50	25	19	11.6	0.4041	0.1943	0.1340	37.36	18.05	7.28	0.28603
tracked-fit	100	80	25	19	11.6	0.4041	0.1943	0.1340	37.36	18.05	7.28	0.28603
tracked-fit	1000	24	24	23	12.0	0.4112	0.2019	0.1332	36.84	19.93	6.95	0.28514
tracked-fit	1000	35	24	23	12.0	0.4112	0.2019	0.1332	36.84	19.93	6.95	0.28514
tracked-fit	1000	50	24	23	12.0	0.4112	0.2019	0.1332	36.84	19.93	6.95	0.28514
tracked-fit	1000	80	24	23	12.0	0.4112	0.2019	0.1332	36.84	19.93	6.95	0.28514
tracked-fit	10000	24	21	24	13.8	0.4059	0.2113	0.1341	34.41	21.58	7.01	0.28433
tracked-fit	10000	35	21	25	13.8	0.4130	0.2175	0.1340	35.94	23.06	6.84	0.28514
tracked-fit	10000	50	21	25	13.8	0.4130	0.2175	0.1340	35.94	23.06	6.84	0.28514
tracked-fit	10000	80	21	25	13.8	0.4130	0.2175	0.1340	35.94	23.06	6.84	0.28514

shoe

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	22	15	10.1	0.4393	0.2511	0.1904	33.74	26.47	7.57	0.41043
tracked-fit	100	35	22	15	10.1	0.4393	0.2511	0.1904	33.74	26.47	7.57	0.41043
tracked-fit	100	50	22	15	10.1	0.4393	0.2511	0.1904	33.74	26.47	7.57	0.41043
tracked-fit	100	80	22	15	10.1	0.4393	0.2511	0.1904	33.74	26.47	7.57	0.41043
tracked-fit	1000	24	20	18	11.2	0.5811	0.2726	0.1912	43.60	30.94	9.13	0.41068
tracked-fit	1000	35	20	18	11.2	0.5049	0.2631	0.1910	40.91	29.60	8.27	0.41268
tracked-fit	1000	50	20	18	11.2	0.5049	0.2631	0.1910	40.91	29.60	8.27	0.41268
tracked-fit	1000	80	20	18	11.2	0.5049	0.2631	0.1910	40.91	29.60	8.27	0.41268
tracked-fit	10000	24	17	21	13.1	0.6183	0.2789	0.1914	43.89	32.48	9.55	0.41005
tracked-fit	10000	35	18	21	12.4	0.5762	0.2751	0.1914	44.94	33.49	9.58	0.41281
tracked-fit	10000	50	18	21	12.4	0.5762	0.2751	0.1914	44.94	33.49	9.58	0.41281
tracked-fit	10000	80	18	21	12.4	0.5762	0.2751	0.1914	44.94	33.49	9.58	0.41281

open_box

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	2	24	112.0	0.2568	0.2567	0.2566	1.00	1.01	1.10	0.55454
tracked-fit	100	35	2	34	112.0	0.2568	0.2565	0.2565	1.00	1.05	1.02	0.55368
tracked-fit	100	50	2	34	112.0	0.2568	0.2565	0.2565	1.00	1.05	1.02	0.55368
tracked-fit	100	80	2	34	112.0	0.2568	0.2565	0.2565	1.00	1.06	1.02	0.55381
tracked-fit	1000	24	2	24	112.0	0.2568	0.2567	0.2566	1.00	1.01	1.10	0.55454
tracked-fit	1000	35	2	35	112.0	0.2568	0.2566	0.2566	1.00	1.05	1.02	0.55425
tracked-fit	1000	50	2	41	112.0	0.2568	0.2566	0.2566	1.00	1.05	1.02	0.55426
tracked-fit	1000	80	2	41	112.0	0.2568	0.2566	0.2566	1.00	1.05	1.02	0.55438
tracked-fit	10000	24	2	24	112.0	0.2568	0.2567	0.2566	1.00	1.01	1.10	0.55454
tracked-fit	10000	35	2	35	112.0	0.2568	0.2566	0.2566	1.00	1.05	1.02	0.55425
tracked-fit	10000	50	2	47	112.0	0.2568	0.2566	0.2566	1.00	1.05	1.02	0.55426
tracked-fit	10000	80	2	47	112.0	0.2568	0.2566	0.2566	1.00	1.05	1.02	0.55438

horse

rule	κ	M	parts	longest deg	mean length	Chamfer % 256	Chamfer % 1024	Chamfer % 6144	>30° % 256	>30° % 1024	>30° % 6144	p95 % 6144
tracked-fit	100	24	18	24	20.7	0.3733	0.1851	0.1423	27.84	10.95	2.89	0.29711
tracked-fit	100	35	18	24	20.7	0.3733	0.1851	0.1423	27.84	10.95	2.89	0.29711
tracked-fit	100	50	18	24	20.7	0.3733	0.1851	0.1423	27.84	10.95	2.89	0.29711
tracked-fit	100	80	18	24	20.7	0.3733	0.1851	0.1423	27.84	10.95	2.89	0.29711
tracked-fit	1000	24	17	24	21.9	0.4318	0.2034	0.1424	33.90	15.02	2.91	0.29755
tracked-fit	1000	35	17	29	21.9	0.4406	0.2081	0.1431	35.25	16.17	2.89	0.29982
tracked-fit	1000	50	17	29	21.9	0.4406	0.2081	0.1431	35.25	16.17	2.89	0.29982
tracked-fit	1000	80	17	29	21.9	0.4406	0.2081	0.1431	35.25	16.17	2.89	0.29982
tracked-fit	10000	24	15	24	24.9	0.4366	0.2153	0.1423	38.04	20.85	2.86	0.29715
tracked-fit	10000	35	15	33	24.9	0.4479	0.2132	0.1426	41.09	19.74	2.98	0.29767
tracked-fit	10000	50	15	33	24.9	0.4479	0.2132	0.1426	41.09	19.74	2.98	0.29767
tracked-fit	10000	80	15	33	24.9	0.4479	0.2132	0.1426	41.09	19.74	2.98	0.29767

Partition: longer parts, higher height degree

Summary: geometric mean over the objects of the ratio to the default

The two effects apart: the cut decision and the stored basis

Why the elephant is cut so much

Step 2: the fit test in shape, not in coefficients

Which parts fit their shape

battery_stepped

dress

elephant

bowl_of

bowl_gso

mug

dino

shoe

open_box

horse

The dino's body part: the height polynomial

Why 1024 atoms is wavy, and a smaller dictionary

Step 3: the fewest parts for a tolerance

Step 4: cut where the shape jumps between neighbouring rings

Step 5: cut only when coefficients AND shape miss

The mug's handle: where coefficients and shape part ways

Step 6: rings split at their necks before tracking (prototype)

Step 7: momentum, the body goes on and the lobe is peeled off (prototype, mug)

With the union distance in the decoder (worktree `../fcp_devel_union`, branch `union-sdf`)

v6

Per object

battery_stepped

dress

elephant

bowl_of

bowl_gso

mug

dino

shoe

open_box

horse

Partition: longer parts, higher height degree

Summary: geometric mean over the objects of the ratio to the default

The two effects apart: the cut decision and the stored basis

Why the elephant is cut so much

Step 2: the fit test in shape, not in coefficients

Which parts fit their shape

battery_stepped

dress

elephant

bowl_of

bowl_gso

mug

dino

shoe

open_box

horse

The dino's body part: the height polynomial

Why 1024 atoms is wavy, and a smaller dictionary

Step 3: the fewest parts for a tolerance

Step 4: cut where the shape jumps between neighbouring rings

Step 5: cut only when coefficients AND shape miss

The mug's handle: where coefficients and shape part ways

Step 6: rings split at their necks before tracking (prototype)

Step 7: momentum, the body goes on and the lobe is peeled off (prototype, mug)

With the union distance in the decoder (worktree ../fcp_devel_union, branch union-sdf)

v6

Per object

battery_stepped

dress

elephant

bowl_of

bowl_gso

mug

dino

shoe

open_box

horse

With the union distance in the decoder (worktree `../fcp_devel_union`, branch `union-sdf`)