#jJ HdZddlZddlZddlZddlZddlZddlmZddlZ eej dej dz Z ejdee ejdeeejeejjZedz Zej dz Zej dz Zej d z Zed z ed z ed z ed z edz edz edz edz edz edz edz edz d ZgdZdddZgdZdZd*dZd+d Zd!Z d"Z!d#Z"d$Z#d%Z$d&Z%e&d'kr1ej'd(d)vr$e e$e#e%d)ej'd(dSdSdS),aConvex hull from the descriptor (fcp_hull.py) against qhull on the source mesh, for the report section "hull". cd ~/code/data/meshes/fcp_3010_hull env -u PYTHONPATH ~/code/fcp_devel/.venv/bin/python scripts/hull.py run # out/hull.csv (per object and setting) env -u PYTHONPATH ~/code/fcp_devel/.venv/bin/python scripts/hull.py make # figures, data.csv, section.html Objects: the collision section's 12 (fcp_2910_collision/scripts/common.py). Encode: the package at FCP_API (default ~/code/fcp_devel/api), defaults except the layers and atoms of each setting. Times: median of 21 after one warm-up, one thread (scipy's qhull and the numba kernel are both serial). 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Convex hull straight from the descriptor

Package v5.31 (commit db3e6ceb; the working tree only raises MAX_ATOMS to 12288; defaults: parts="tracked-fit", interp="poly"), the 12 objects of the collision section, encoded at 128 layers (1024 or 6144 atoms) and at 256 layers (6144 atoms). The hull is built from the descriptor without a decode grid, a mesh or qhull: the solid rings are evaluated from the Fourier and Chebyshev coefficients (holes are inside the solid and never touch the hull), each part's end rings are held to the part's outer edges, and per level (a layer centre or a part edge) one numba kernel takes the 2D hull of the ring samples and its support point in M directions. In each direction a hull vertex must lie on the upper concave envelope of (height, support) over the levels; neighbouring directions' envelopes are joined by height and the end levels capped, which gives a closed triangle surface in O(levels × M). Reference: scipy's qhull on the source mesh's vertices, and the route through the decoded mesh (fcp.decode, then qhull). CPU: rGu, one thread for both (median of 21 runs; the decode route of 7). Distances in % of the source mesh's diagonal, from 20k points on the source mesh's hull to the descriptor's hull; volume relative to the source mesh's hull.

z\
layersatomsdirections MFCP hull, ms (median)qhull on the mesh, ms (median) decode + qhull, ms (median)FCP faster than qhullspeed-up, median (min–max) volume / true hull, median (min)gap, mean % diaggap, max % diag non-convex dent, max % diaghulls with no over-shared edge

Time: at 128 layers and M = 64 the descriptor's hull takes z ms, against uK ms for qhull on these meshes (2.3k–38k vertices): about even, faster on z of 12 (z, z ), at most zA×. The gain is in not having the mesh: the decode route is z ms, a× slower. qhull's cost grows with the hull it outputs, and the descriptor's hull has more vertices than the mesh's (the rings are dense where the mesh is coarse), so a large source mesh is where the descriptor wins outright (a 222k-vertex dress outside this set: 3.5 ms against 39 ms); the knot and spring, with many parts per level, are the slowest descriptor hulls. M = 128 and 256 layers cost z × and z;× the time (medians). Accuracy: the volume is z. of the true hull at 128 layers, the mean gap z % of the diagonal, the largest z % (zv). Nearly all of it is the encoding, not the hull: the decoded mesh's hull (qhull) is as far from the true hull (mean z %, max up to z0 %), and the descriptor's hull is within a mean z % of it (max zh %, the spring and knot at the top: 64 directions are too few there; M = 128 lowers their max gap, knot z → z %, spring z % (decoded mesh's hull: z %)). A flat top or bottom also moves: a part ends at a layer edge, so a cap sits up to half a layer from the true one (the mug's top: z % of the diagonal). 256 layers lower the gap only where the layers were the limit (horse, mug ace, spring); elsewhere it is the rings' own error. Defects: the surface is convex only up to the M directions (dents up to z% % of the diagonal at M = 64, on the u); and where one pair of support points lies on the envelopes of two non-neighbouring directions, the bands on both sides use that edge: no open edge on any of the 48 hulls, but 0–11 edges shared by four triangles (a fold, not a hole; the volume is unaffected). A final qhull over the descriptor hull's own vertices would remove both (1–6 ms on 500–2400 such vertices in the first trials), giving up most of the gain. Prototype, not in the package.

u
object (128 layers, 6144 atoms, M = 64)mesh verticesatoms heldFCP hull, ms qhull, msdecode + qhull, msFCP hull verticestrue hull verticesvolume / true gap, mean %gap, max %decoded mesh's hull: gap, mean %its gap, max % FCP hull to decoded hull, mean %
Six objects: the source mesh inside the descriptor's hull (top) and the descriptor's hull coloured by its distance to the mesh's hull (bottom)
Top: the source mesh (grey) inside the hull built from the descriptor (orange edges). Bottom: the descriptor's hull, each triangle coloured by the distance of its centre to the source mesh's hull (0–0.5 % of the diagonal); 128 layers, 6144 atoms, M = 64. The brightest triangles are the flat tops (caps) of the mug and the dog bowl: long fans whose centres lie below the true rim.
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