5jCdZddlZddlZddlZddlmZddlZejdZ ejddge_ej de ee jddlmZee jjZedz edz ed z cZZZejd z ZddlZeejd d Zeejd dZddgZeefdkrdned krdendedeZgdZ d"dZ!dZ"dZ#dZ$gdZ%dZ&dZ'dZ(e)dkr&e#e$e&e(d e d!dSdS)#aVolume: exact (the mesh), FCP from the mesh, FCP from a 20k point cloud, screened Poisson from the same cloud (true normals, and normals estimated from the points). 128 layers, 2048 atoms. For the report section "volume". cd ~/code/data/meshes/fcp_3010_hull F=~/code/fcp_devel/.venv/bin/python; O=~/code/data/meshes/fcp_2910_collision/.venv/bin/python env -u PYTHONPATH $F scripts/volume_pc.py points # out/pc/.npz: 20k area-uniform points, seed 3, true normals env -u PYTHONPATH $F scripts/volume_study.py fcp # out/vs_fcp.csv, out/vs_render/_fcp_*.npz env -u PYTHONPATH OMP_NUM_THREADS=1 $O scripts/volume_study.py poisson # out/vs_poisson.csv, out/vs_render/_poisson_*.npz env -u PYTHONPATH $O scripts/volume_study.py render # sections/hull/volume_fig_renders.png (Open3D decimates for drawing) env -u PYTHONPATH $F scripts/volume_study.py section # sections/hull/{volume_data.csv, volume_objects.csv, volume_section.html} Times: median of 5 (encode, Poisson) or of 2000 (volumes) after a warm-up. FCP's CPU encode uses numba's threads (12); Poisson runs on one thread (Open3D's threaded Poisson was 1.5-4x slower on this CPU). N)Pathx)OBJECTSoutzout/pcz out/vs_renderz)code/data/meshes/fcp_report/sections/hull FCP_LAYERS FCP_ATOMS)_6144fcp6144z128 layers, 6144 atoms) _L256_6144fcpL256z256 layers, 6144 atoms)r r __L)mugbowl_dogshoedinohorseknotc|g}t|D]H}tj}||tj|z Idt t j|zS)N@@)rangetime perf_counterappendfloatnpmedian)fntrt0s A/home/joao/code/data/meshes/fcp_3010_hull/scripts/volume_study.pymedr('s~ACCC A 1XX++     "$$r)**** ry||$$ $$c ||dddf||dddf||dddf}}}ttjd|tj||dz S)Nrrzij,ij->)r r!einsumcross)VFabcs r' mesh_volumer41sj!!!Q$j!AaaadG*a!!!Q$j!qA 9a!Q881< = ==r)c < ddl}ddl}ddlddlmddlmtddg}tj D]\}}| |d}tj |jtjtj |jtjc  }tjtj t&|dz d tj}t+|t- |d t/ fd d z }d|fd|ffD]&\} t2t4d|d| d<d t/fdd z|d| d<t/fd|d| d<t/fd|d| d<j|d| d<t2t4d} | |d| d<|t8vrMt:sFd} tjt|d| dz | j| j(|t8vr)t:s"tjt|dz | |tCd | Dd!|"|#tHd"t:d#z d$%dS)&Nr)volume_atoms_fast)vol_nbTparentsexist_okmesh)force.npzPrcSN)F0V0r7sr'zfcp_step..EsRXRXY[]_R`R`r)i)objfacesexactexact_uspointscpuatomslayersdevicefcp__volcSr@rA)dr6sr'rDzfcp_step..Is7H7H7K7Kr)_vol_uscJttdS)NrJrKencodeATOMSLAYERSfcpgeosr'rDzfcp_step..JsSZZ5Y_hmZ5n5nr) _enc_cpu_mscJttdS)NcudarKrUrYsr'rDzfcp_step..KscjjEZ`ioj6p6pr) _enc_cuda_ms_bytesr^ _vol_cuda)rN_fcp_r/r0 _mesh.npzcdi|]-\}}|t|trt|dn|.S)) isinstancer round).0kvs r' zfcp_step..Us9UUU41aq*Q"6"6=5A;;;AUUUr)flushvs_fcp.csvFindex)%pandastrimeshrZ volume_atomsr6 volume_sotar7RDmkdirritemsloadr!ascontiguousarrayverticesfloat64rFint64asarrayPCfloat32dictlenr(rVrWrXnbytesRENDERTAGdecodesavezrprint DataFrameto_csvOUT)pdrtrowsnamepathmrGr>rsrcdcdmrBrCrRrZr[r7r6s @@@@@@@r'fcp_stepr6stNNNJJJ......""""""HHTDH))) Dmoocc d LLVL , ,%aj"*==r?STUT[]_]e?f?fBr2 JrwrtMMM12237 D D TRcJ`J`J`J`J`J`bfFgFg@g h h h !xm4 R RHC 3eF5 IIA"3"3A"6"6AS %(3/K/K/K/K/KT+R+R%RA!S!!! "),-n-n-n-n-n)o)oA%S%%% &*-.p.p.p.p.p*q*qA&S&&& '$%HA S   !CuVFKKB'8'8'<'>#> HRT,,,,b 9 9 9 9 A UU17799UUU]abbbbbLLc$6S$6$6$66eDDDDDr)c  ddl ddl}g}tD]}}tjt |dz  t |}dD]! fd jj dd\}}tj |j tj |j ctt|d d <t||d d <t# fd d |d d<dt#fddz|d d<|t$vr%tjt(|d dz #||t-|d||t2dz ddS)Nrr=)rE)trueestcTjjd}dkr&jd|_nB|jd|d|S)Nr>rN)geometry PointCloudutilityVector3dVectornormalsestimate_normalsKDTreeSearchParamKNN'orient_normals_consistent_tangent_plane)pckindo3dzs r'buildzpoisson_step..buildbs\,,S[-G-G#-O-OPP6>>!$!;!;AcF!C!CBJJ'' (I(I"(M(MNNN>>rBBB r)rdepth n_threadspoisson_rP _watertightchjjdkr nddS)Nrrrr)r TriangleMeshcreate_from_point_cloud_poisson)rrrrsr'rDzpoisson_step..ps=#,2K2k2k5==bQ3l3H3Hr)_msrc$tSr@)r4)r0r/sr'rDzpoisson_step..rsK1O Q QD **cCIIosS[[/@A* B BCV$$004 WRT,,,, - -CQCQBR1}rBwmmoo11 #A&( 0 0OA|U00s000011A ))#+*D*DQsV*L*LckNhNhijknioNpNpqqA1S6{{U""11%88 & & ( ( (j,,bj.E.ErzRSRdGeGe!qAbfQY////BVc$iiSYY9JQ9N[_``B    0 01"%111d7 VXV^_cdg_hViViHiBjw} ~ ~ ~    KK!q!A$( + + + KK!q!A$( + + + KK!q!A$( + + +   i ( ( ( LLS ! ! ! OO    F]]''3sV|3D0M0M0M0MCAvv UR 000 IIc4qAvvDLLc$:$:!C!Cc!C!C!CSVbdbn!B  0 0 0 0' 0*QaT!AaPPP MM$M...KK22gKNNNNNr)c8ddl}|tdz |tdz d}gd}tD]\}}}td|dz rr|td|dz }|dgd |Dz|fd  }||d}||d z|d zgz }|D]!}d||dz|jz dz z||dz<"|S)Nrz vs_fcp.csvrrE)on)rrrrrorpc<g|]}|d|S)rO) startswith)rir3s r' ztable..s)BBB1Q\\&-A-ABQBBBr)c6|d|dzdS)NrOrrr)r3pres r'rDztable..s6fgfofopvx{ByBDEgFgFr))columns_mesh_pointsdrPrr)rsread_csvrmergeVARIANTSexistsrenamerG)rr%keystagr!rr2rjs r'rrsg C,&''--bkk#@P:P.Q.QV[-\\A D D DD55 S! $3$$$ $ , , . . 5 C"43"4"4"4455A5'BBBBBBCJJadTFTFTFJGGAe$$A S7]C)O4 4D <<qV}qw6:;!f* Hr)cttdz ddAdfd}ddddjfd d jjd d jfd djj d d j fddj ddj zdz fddj djfg}gg}}|D]\}}}}}|r ||nd} |r@t|dzdknt%} |d|d|sdn| d d|sdn| dd| dt%d|dn |d |sdnd|dd|dd |t)|pd| d | d| ||!!d dl} | |td"z ddfd#D} |d |d|d|df\} }}}jd$kd%d&}d'd(t7|j|jD}dgd)d|d*| dd+| d d,|dd-|d d.|d d/|dd0t%|d1t%d2|d3j d dj d d4jd djd d5tj jkd1t%d6jjjkj jd z dd7j dz ddj dz dd8jdz dd9j dz dd:j dz dd;| d<}td=z |d>}td?z !}|"|vr8td?z |#d@d@z|zdSdS)BNzvolume_objects.csvFrqr+c"||krdn|d|dS)N–.r#rA)rkr$s r'rDzsection_step..sAFFyy1 q r)c|dz|dzfS)Nr)rr"r)rjr%s r'rDzsection_step..sLAa&jM%%''..00!AJ-2C2C2E2E2I2I2K2KLr)z+exact: tetrahedron sum over the source meshrz1FCP from the mesh (encode 2048 atoms, 128 layers)rrz ms on CUDAz-FCP from 20k points (same encode, no normals)rz8screened Poisson (depth 8) from 20k points, true normalsrz1 threadrz^screened Poisson from 20k points, normals estimated (30 neighbours, tangent-plane orientation)rz1 thread, normals included)r2rr rGz / r/z () )method err_med_pct err_max_pct within_1pctbuild_ms_medianvolume_us_medianzvolume_data.csvc3K|]}d|jddd|jd|jd|jd|jd|jd|jdd|jdd|j dd|j dd|j dd|j dd|j ddVdS)r3rrr4rr6N)rErrF fcp_mesh_errfcp_points_errpoisson_true_errpoisson_est_errrHfcp_points_vol_usfcp_mesh_enc_cpu_msfcp_points_enc_cpu_msfcp_points_enc_cuda_mspoisson_true_mspoisson_est_ms)rirr#s r' zsection_step..s!!   }15==c+B+B } }QW } }q   } }+,1Q-=+>+> } }IJ1K]I^I^ } }ijijklk|i}i} } }qQ } }*+!A,?*C*C } }NOaPQPeghNiNi } }tutuvwwNPQuRuR } }q)1-- } }9:!:KQ8O8O } }[\Z[\]\lnoZpZp } } }!!!!!!r)rrA) ascendingz, c3VK|]$\}}|ddd|ddV%dS)rrz+.0frNr )rires r'rHzsection_step..sHiitq!!))C--::::::iiiiiir)aR

Volume straight from the descriptor

Package v5.31 (commit db3e6ceb; the working tree only raises MAX_ATOMS), defaults (parts="tracked-fit", interp="poly", the gwn point slicer), 128 layers, 2048 atoms; the 12 objects of the collision section. The exact volume is the source mesh's (tetrahedra over its faces). From each mesh, 20k area-uniform surface points (seed 3) with the true normals; every point method gets the same points. FCP's volume is one contraction of the stored atoms: a ring's area is π Σk k (ax,kby,k − bx,kay,k) in its Fourier coefficients, and the height atoms are orthonormal on a part's layer centres, so the sum of the ring areas over the layers is the same expression in the atom vectors: V = dz · ∏scale · π Σparts sign · |Σk k (⟨ax,k, by,k⟩ − ⟨bx,k, ay,k⟩)| (the midpoint rule over the layers; no ring is evaluated, no grid, no mesh; one numba loop). Standard route from points: screened Poisson reconstruction (Open3D 0.20, depth 8), then its mesh's volume, with the true normals (the best case) and with normals estimated from the points (what a scan gives). CPU: Intel i5-10400F; FCP's encode on numba's 12 threads and on a GTX 1650; Poisson on one thread (its threaded run was slower here). Times are medians over the objects.

z9
methodvolume error, median |%|max |%|objects within 1 % building the representation, msthe volume, µs

Accuracy: FCP is within z- % of the exact volume from the mesh (median z %) and within z % from the points (median zH %), without normals; Poisson with the true normals is as close (median z %, max z? %). With estimated normals Poisson is off by more than 5 % on z of z objects (z): on the thin-walled ones the orientation flips across a wall and the surface closes over the opening (renders). Time: once encoded, FCP's volume takes zN µs, about the cost of the tetrahedron sum over the source mesh itself (z µs, numba): faster on z= objects, the gain growing with the mesh (spring, 77k faces: z-×); the volume of a Poisson mesh takes z1 ms (NumPy). The cost from points is the encode: z s on the CPU and z s on CUDA (median), against aA s for Poisson on one thread; the descriptor, once made, also answers the other queries of this report. Caveats: clean, complete, uniformly sampled points; Poisson's meshes are not watertight by Open3D's strict test (the volume is taken as is, its sign ignored); learned reconstruction is not compared.

aD
objectmesh facesFCP from mesh, error %FCP from points, error % Poisson, true normals, error %Poisson, estimated normals, error %exact volume, µs FCP volume, µsFCP encode from mesh, ms (CPU)FCP encode from points, ms (CPU) FCP encode from points, ms (CUDA)Poisson, true normals, msPoisson, estimated normals, ms
Six objects: the original mesh, FCP decoded from the mesh and from 20k points, Poisson with true and with estimated normals, each with its volume error
The surfaces behind the volumes: the original mesh, the FCP descriptor decoded (from the mesh and from 20k points; the volume itself is computed from the atoms, not from this mesh), and Poisson's reconstruction with the true and with estimated normals; under each, the volume error against the exact volume.
zvolume_section.htmlz volume_*: ~/code/data/meshes/fcp_3010_hull/scripts/volume_study.py (steps in its docstring); volume_data.csv: the first table; volume_objects.csv: per object (errors in %, times in ms / us as named). z README.txt )r+)$rrrrHr"rCfcp_mesh_enc_cuda_msfcp_mesh_vol_usrDrErBrFpoisson_true_vol_usrGpoisson_est_vol_usintrsumrrrrsrjoin itertuplesrA sort_valuesziprErrr write_text read_textstriprstrip)ammethodsrdatarrjrnotevusrKwithinrorowsfmfpptpebadbadtxthtmlreadmer#r%s @@r' section_steprjs  AHHW+ +5H999<<rsk    x{ HQK 33ttH~~,--... tH~~&-UlD8OTO-C R $)++C C RZ^^L# . . / / BJNN; - -.. :>> E E EFCCCBbbb*O*O*OZ    POPOPOf zvHQ]^^bbcgiuiuvvxxxxxr)