id int32 0 26 | label int64 0 26 | mesh.vertices listlengths 31.1k 51.2k | mesh.faces listlengths 62.3k 102k | mean_width float32 0.07 0.08 | diameter float32 0.09 0.09 | roundness float32 0.37 0.45 | aspect_ratio float32 0.71 1 | volume float32 0 0 | concavity float32 1 1 |
|---|---|---|---|---|---|---|---|---|---|
0 | 0 | [[-0.02681674063205719,-0.026891404762864113,-0.02687367983162403],[-0.02681674063205719,-0.02689140(...TRUNCATED) | [[13971,14519,556],[28814,28823,27009],[24902,24901,24903],[24903,24901,24895],[22849,22850,26921],[(...TRUNCATED) | 0.078751 | 0.090001 | 0.422211 | 0.973903 | 0.000161 | 1 |
1 | 1 | [[-0.02662353403866291,-0.0262486319988966,-0.026379860937595367],[-0.02662353403866291,-0.026248631(...TRUNCATED) | [[1,163,477],[17176,33861,17177],[13521,13522,17174],[29773,33960,29772],[37183,16936,16937],[16935,(...TRUNCATED) | 0.077394 | 0.090004 | 0.406408 | 0.906669 | 0.000155 | 1 |
2 | 2 | [[-0.026620853692293167,-0.026257408782839775,-0.02673051878809929],[-0.026620853692293167,-0.026257(...TRUNCATED) | [[10197,400,556],[240,162,10196],[29884,13524,13523],[10204,400,10201],[400,10199,10201],[400,10197,(...TRUNCATED) | 0.077393 | 0.090003 | 0.406365 | 0.890922 | 0.000155 | 1 |
3 | 3 | [[-0.026642169803380966,-0.02657686173915863,-0.02639899030327797],[-0.026642169803380966,-0.0265768(...TRUNCATED) | [[32116,23263,32115],[477,13631,13603],[13603,13631,23263],[13603,32116,16968],[23263,32116,13603],[(...TRUNCATED) | 0.077563 | 0.090003 | 0.406924 | 0.844579 | 0.000155 | 1 |
4 | 4 | [[-0.02664078399538994,-0.026577986776828766,-0.017486220225691795],[-0.02664078399538994,-0.0265779(...TRUNCATED) | [[6851,82,6537],[27637,10297,27773],[27773,27636,27637],[27637,6536,10297],[17333,333,17343],[6539,1(...TRUNCATED) | 0.077564 | 0.090004 | 0.406891 | 0.844332 | 0.000155 | 1 |
5 | 5 | [[-0.02712458185851574,-0.02656751126050949,-0.02686859667301178],[-0.02712458185851574,-0.026567511(...TRUNCATED) | [[1,84,398],[32588,20235,32587],[4884,3878,4852],[20107,3878,4884],[8,3060,9],[32586,32585,34820],[3(...TRUNCATED) | 0.078243 | 0.090001 | 0.421349 | 0.757604 | 0.000161 | 1 |
6 | 6 | [[-0.026802152395248413,-0.026428937911987305,-0.026371978223323822],[-0.026802152395248413,-0.02642(...TRUNCATED) | [[37099,26404,26405],[26405,37098,37099],[10284,32857,10283],[36874,20188,36876],[36876,20188,10280](...TRUNCATED) | 0.077313 | 0.090004 | 0.406457 | 0.941992 | 0.000155 | 1 |
7 | 7 | [[-0.026801809668540955,-0.026428598910570145,-0.017511241137981415],[-0.026801809668540955,-0.02642(...TRUNCATED) | [[36970,36971,20186],[35067,32817,32816],[84,398,1],[38634,37054,38623],[28018,32890,32862],[20259,3(...TRUNCATED) | 0.077312 | 0.090003 | 0.406458 | 0.941408 | 0.000155 | 1 |
8 | 8 | [[-0.026801809668540955,-0.017390968278050423,-0.026548869907855988],[-0.026801809668540955,-0.01739(...TRUNCATED) | [[3,400,635],[38767,37060,38763],[13278,13279,20187],[36874,35252,20191],[20190,36874,20191],[20191,(...TRUNCATED) | 0.077312 | 0.090003 | 0.406457 | 0.779719 | 0.000155 | 1 |
9 | 9 | [[-0.026772432029247284,-0.026407847180962563,-0.01719314232468605],[-0.026772432029247284,-0.026407(...TRUNCATED) | [[15456,6636,6637],[242,6639,1],[13276,319,241],[6638,15456,6637],[18146,18187,18219],[18146,18106,1(...TRUNCATED) | 0.07714 | 0.090001 | 0.405942 | 0.922668 | 0.000155 | 1 |
Filleted cubes, four edges of twelve
27 classes. Each class is a cube whose twelve edges carry one of two fillet radii: four edges at 0.36 of the half-edge (9.75 mm on the 54 mm cube that fits a 9 cm caliper diameter), eight at 0.02 (0.54 mm). The fillets run the full length of every edge and blend at the corners, so the surface is smooth everywhere and the solid is convex -- exactly, volume/hull-volume 1.000000, which keeps it on the loader's exact-hull path and away from VHACD.
A rolling-ball fillet of a convex solid is convex at every radius. OCCT does not quite deliver that at this radius: where two large fillets meet a small one its mixed-radius vertex blend dips below the ideal surface, costing 0.17% of volume and putting the as-built solid at 0.9983, under the loader's threshold. The hull is the intended shape and the dip is the artifact, so the meshes shipped here are hulled. The audit does not move either way.
The 27 classes are the orbits of the four-edge subsets of a cube under the cube's rotation group, so no rigid rotation carries one class onto another. Nine of them are chiral pairs; reflections are not quotiented out, because a mirror image is a genuinely different object to a hand.
Episodes randomise scale on a grid of 50 rungs, so absolute size carries nothing and what has to be controlled is the scale-invariant shape. All classes share one largest caliper width to 0.004%, and reading a scale-invariant descriptor to 2 percent and taking the nearest class gives: worst inertia eigenvalue/d^2 4.28x chance, volume/d^3 4.09x, area/d^2 3.65x, sphericity 1.11x. For comparison the set this replaces, abc20cyl, was solved to 0.775 against 0.05 chance -- 15.5x -- by height-over-diameter alone.
This is the deliberately deeper point on the relief/leak frontier: at r_big 0.18 the same construction audits at 3.2x but carries only 1.76 mm of relief contrast, which is marginal for an Allegro fingertip read through joint angles. Here the contrast is 3.81 mm and the leak is 4.3x. Fillet relief sets both quantities and they track each other at correlation 0.988, so on a cube the trade cannot be avoided, only chosen.
Meshes are watertight single bodies in metres, scaled so the largest caliper width
is 0.090 m. id is the class index.
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