MiISrSSKrSSKJrJrJr SSKJr SSK J r J r SSKJ r SSK JrJrJr SS KJrJrJr SSKJr SS KJr SS \S \S\S\4SjjrS S\S\S\\S\S\S \S\4SjjrS!Sjr Sr!Sr"S"Sjr#S#Sjr$S$Sjr%S%Sjr&g!\a4rSS KJr \R8"\5r\R8"\5rSrCNSrCff=f)&za registration.py --------------- Functions for registering (aligning) point clouds with meshes. N)boundstransformationsutil)weighted_vertex_normals) PointCloud plane_fit)transform_points)anglescrossnormals) ArrayLikeIntegerOptional)cKDTree) exceptionssamplesscale icp_first icp_finalc @Sn[R"US5(d [S5eSnUn [R"US5(av[UR5[UR5:a Un SnU"XS9n Un OUn U"XS9n U R (a U R n OZU RR n OC[R"US5(aUn [R"U 5Sn O [S 5eU R (a U R n OU RR n [R"[RRU 5U 5n[R"/S Q/S Q/S Q/S Q/SQ/SQ/SQ/SQ4Vs/sH1n[R "S5[R""US5-PM3 sn5n[R$"[U55[R&-nS/[U5-nU R(n[+U5Hwunn[R"[,R."UU5[RRU55n[1SU U U[3U5US.UD6unnnUUU'UUU'My [1SU U U[R4"U5[3U5US.UD6unnnU[U 5-nU(a#[RRU5nUU4$UnUU4$s snf)a) Align a mesh with another mesh or a PointCloud using the principal axes of inertia as a starting point which is refined by iterative closest point. Parameters ------------ mesh : trimesh.Trimesh object Mesh to align with other other : trimesh.Trimesh or (n, 3) float Mesh or points in space samples : int Number of samples from mesh surface to align scale : bool Allow scaling in transform icp_first : int How many ICP iterations for the 9 possible combinations of sign flippage icp_final : int How many ICP iterations for the closest candidate from the wider search kwargs : dict Passed through to `icp`, which passes through to `procrustes` Returns ----------- mesh_to_other : (4, 4) float Transform to align mesh to the other object cost : float Average squared distance per point c [UR5US- :aG[R"URUR U[UR5- 545$UR U5$)z Return a combination of mesh vertices and surface samples with vertices chosen by likelihood to be important to registration. )lenverticesnpvstacksamplemcounts n/var/www/eduai.edurigo.com/storigo/production/storigo_env/lib/python3.13/site-packages/trimesh/registration.py key_pointsmesh_other..key_pointsFsT qzz?eai (99ajj!((53qzz?3J*KLM M88E? "Trimeshzmesh must be Trimesh object!TFrrz$other must be mesh or (n, 3) points!)rrr)rrr()rr(r)r(rr)r(r(r)r(rr()rr(r()r(r(r(rN)abinitialmax_iterationsr)ris_instance_named ValueErrorrr is_volumeprincipal_inertia_transformbounding_box_orientedis_shaperoriented_boundsrdotlinalginvarrayeyeappendonesinfcentroid enumeratertransform_aroundicpintargmin)meshotherrrrrkwargsr#inversesearchpoints points_mesh points_PIT search_PITsearch_to_pointsdiagcubescosts transformsr?iflipa_to_bmatrix_junkcost mesh_to_others r" mesh_otherrZsR #  ! !$ 2 2788G F eY// t}} ENN 3 3FG$6FKK%7F  $@@J$::VVJ ug & &++F3A6 ?@@77 11MM vvbiimmJ7D HH    FF1I $* *   E" GGCJ "&& (E#e*$JHU#4  , ,T8 < IIMM* +  " y>    t 1 a)$.  299U+,9~   FE4 CKD  f-  $  $  s8Lr+r,weights reflection translation return_costc[R"U[RS9n[R"U[RS9n[R"US5(a[R"US5(d [ S5e[ U5[ U5:wa [ S5eUc[R"[ U55n[R"[R"U[RS9S5n [ U 5[ U5:wa [ S5eXR5- RS5n U SS2S4S :n X{n Xn Xn U(a#X-RSS 9nX-RSS 9nOF[R"U RS 5n[R"U RS 5nU(aY[R"X- S -U -R55n[R"X- S -U -R55nOS nS n[R"X- U- RX- U- 5n[R R#U5unnnU(a[R"UU5nOu[R"[R"U[R$"S S [R R'[R"UU55/55U5nUUU- [R"UU5-- n[R("UU- U-URS S 545n[R*"U[R,"S /URS -S/-5RS S 545nU(a-[/UU5nU UU - S -U -R5nUUU4$U$)a Perform Procrustes' analysis to quickly align two corresponding point clouds subject to constraints. This is much cheaper than any other registration method but only applies if the two inputs correspond in order. Finds the transformation T mapping a to b which minimizes the square sum distances between Ta and b, also called the cost. Optionally filter the points in a and b via a binary weights array. Non-uniform weights are also supported, but won't yield the optimal rotation. Parameters ---------- a : (n,3) float List of points in space b : (n,3) float List of points in space weights : (n,) float List of floats representing how much weight is assigned to each point. Binary entries can be used to filter the arrays; normalization is not required. Translation and scaling are adjusted according to the weighting. Note, however, that this method does not yield the optimal rotation for non-uniform weighting, as this would require an iterative, nonlinear optimization approach. reflection : bool If the transformation is allowed reflections translation : bool If the transformation is allowed translation and rotation. scale : bool If the transformation is allowed scaling return_cost : bool Whether to return the cost and transformed a as well Returns ---------- matrix : (4,4) float The transformation matrix sending a to b transformed : (n,3) float The image of a under the transformation cost : float The cost of the transformation dtyper'points must be (n,3)!z+a and b must contain same number of points!Nrz)weights must have same length as a and b!)r(raxisrrr(?)r asanyarrayfloat64rr5r1rr=maximumsumreshapezerosshapesqrtr7Tr8svdrOdethstackrr:r )r+r,r[r\r]rr^ a_original b_originalww_normnonzero_weights a_nonzero b_nonzeroacenterbcenterascalebscaletargetu_svhRrV transformedrXs r" procrustesrs)jq 3Jq 3J ==W - -T]]:w5W5W011 :#j/)FGG''#j/* 2== ;Q?A 1vQDEE%%'k " "7 +F QTlS(O+I+I  $F%***2%***2((9??1-.((9??1-. I/A5?DDFGI/A5?DDFG VVi)V366):MQW9W YF f%IAr2 FF1bM FF266!RWWaBIIMM"&&B-,H%IJKR P Vf_q'0BBBK YY!+[-@-@Q-GH IF YY#!''!*)=)E F N NqRT UV WF&z6: k/::q@FJOOQ{D(( Mr%c [R"U[RS9n[R"US5(d [ S5eUc[R "S5n[R"US5nU(dU[R"U[RS9n[R"US5(d [ S5e[U5n[X5nUn[Rn [U5Hxn U(aURRU5upn OWRUS5upXn [SX S.UD6unnnUn[R "UU5nU U- U:a OUn Mz UWW4$) aY Apply the iterative closest point algorithm to align a point cloud with another point cloud or mesh. Will only produce reasonable results if the initial transformation is roughly correct. Initial transformation can be found by applying Procrustes' analysis to a suitable set of landmark points (often picked manually). Parameters ---------- a : (n,3) float List of points in space. b : (m,3) float or Trimesh List of points in space or mesh. initial : (4,4) float Initial transformation. threshold : float Stop when change in cost is less than threshold max_iterations : int Maximum number of iterations kwargs : dict Args to pass to procrustes Returns ---------- matrix : (4,4) float The transformation matrix sending a to b transformed : (n,3) float The image of a under the transformation cost : float The cost of the transformation r`r'rbr*r&r)r+r,r/)rrgrhrr5r1r;r0rr r>rangenearest on_surfacequeryrr7)r+r,r- thresholdr.rGis_meshbtree total_matrixold_cost_closest _distance_faces _distancesixrVrrXs r"rBrB?sNB arzz*A ==G $ $011&&)$$Q 2G  MM!2:: .}}Q((45 5  $ALvvH> " )*)=)=a)@ &G"[[A.NJeG%/$H$H$H! T vvfl3 d?Y & H%#( d **r%cv[R"US5(d6[U[5(d![R "U5n[U5nUR URpTURUSSS24- U- UlURUSSS24- U- UlUbX$SSS24- U- nXXE4$)Nr&) rr0 isinstancerrrgr?rr) source_meshtarget_geometrytarget_positionsrr?rs r"_normalize_by_sourcers  ! !/9 = =jGG==1$X.!**K,=,=e'008D!G3DDMK / 8 88D!G;L LPUUO#,a/@@EI h ==r%c,XPR-USSS24-UlXQR-USSS24-UlUbXR-USSS24-n[U[5(a UVs/sHoeU-USSS24-PM nnU$XS-USSS24-nU$s snf)N)rrlist)rrrresultr?rxs r"_denormalize_by_sourcers !#7#77(47:KKK$'?'??(4QR7BSSO# 3htQw6GG&$9?@A!)htQw//@ M(47"33 MAs%Bc Sn Sn SnSnSn[XU5upnn[UR5n[UR5nURR 5nU "US5n[ R "SSSU/5n[R"UU5nU"UR5nU"UR5nU"U5nU"UXU5unnUc/SQ/S Q/S Q/S Q/nU(aU/nUGHunn n!n"U (dU S :aS n![ R"[ R5Rn#[ R"[ R5Rn$S n%U#U$- U:dMU"bU%U":dM[UUU (+U!S :U!S :=(a U U S9n&[ R"U5n'S U'U&SU:'U!S :avSU&;apU&Sn(U (a SU&;aU&Sn(UU-n)[ R""U)U(5n*U (a[ R$"U*S S5O[ R&"U*5n*U'U*U!--n'U "UUU'U&SUUUUUU 5 nUU-nU$n#[ R(R+U&SU- SS9n+U+U'-R-5n$U(aWR/U5 U%S- n%U#U$- U:dGMU"cGM@U%U":aGMIGM U(aWn,OUn,[1XUU,UU5n,U,$)a Non Rigid Iterative Closest Points Implementation of "Amberg et al. 2007: Optimal Step Nonrigid ICP Algorithms for Surface Registration." Allows to register non-rigidly a mesh on another or on a point cloud. The core algorithm is explained at the end of page 3 of the paper. Comparison between nricp_amberg and nricp_sumner: * nricp_amberg fits to the target mesh in less steps * nricp_amberg can generate sharp edges * only vertices and their neighbors are considered * nricp_sumner tend to preserve more the original shape * nricp_sumner parameters are easier to tune * nricp_sumner solves for triangle positions whereas nricp_amberg solves for vertex transforms * nricp_sumner is less optimized when wn > 0 Parameters ---------- source_mesh : Trimesh Source mesh containing both vertices and faces. target_geometry : Trimesh or PointCloud or (n, 3) float Target geometry. It can contain no faces or be a PointCloud. source_landmarks : (n,) int or ((n,) int, (n, 3) float) n landmarks on the the source mesh. Represented as vertex indices (n,) int. It can also be represented as a tuple of triangle indices and barycentric coordinates ((n,) int, (n, 3) float,). target_positions : (n, 3) float Target positions assigned to source landmarks steps : Core parameters of the algorithm Iterable of iterables (ws, wl, wn, max_iter,). ws is smoothness term, wl weights landmark importance, wn normal importance and max_iter is the maximum number of iterations per step. eps : float If the error decrease if inferior to this value, the current step ends. gamma : float Weight the translation part against the rotational/skew part. Recommended value : 1. distance_threshold : float Distance threshold to account for a vertex match or not. return_records : bool If True, also returns all the intermediate results. It can help debugging and tune the parameters to match a specific case. use_faces : bool If True and if target geometry has faces, use proximity.closest_point to find matching points. Else use scipy's cKDTree object. use_vertex_normals : bool If True and if target geometry has faces, interpolate the normals of the target geometry matching points. Else use face normals or estimated normals if target geometry has no faces. neighbors_count : int number of neighbors used for normal estimation. Only used if target geometry has no faces or if use_faces is False. Returns ---------- result : (n, 3) float or List[(n, 3) float] The vertices positions of source_mesh such that it is registered non-rigidly onto the target geometry. If return_records is True, it returns the list of the vertex positions at each iteration. c X2SS2S4-n USL=(a USLn X@-URUSS2S45/n SU-U-S4n U (a-U RX-5 SU-U-URS-S4n [R"[R "U 55n[R "U [RS9nXSU-SU-U-2SS24'U (a)X-USU-U-SU-U-URS-2SS24'[RRURU-URU-5R5nU$)Nr*r)rr`) multiplyr<rmsparse csr_matrixr lil_matrixrfloat32r8spsolverotoarray)M_kron_GDvertices_weightrwsnEnVDlUlwlU use_landmarksA_stackB_shapeABXs r" _solve_system#nricp_amberg.._solve_systems< ag. .$92T> =!**_QW-E"FGr6B;"  NN27 #2v{RXXa[0!4G   fmmG4 5   gRZZ 8'(!b&AFRK ! #$ >@gAa"frkQVb[288A;67: ; MM ! !!##'1337 3 ; ; =r%cURR5S-n[UR5n[R"[R "U5S5nURR 5n[R"SU-[R5nSUSSS2'U(az[RRURURSS2S4URURSS2S4- SS9nU[R"SU- S5-n[R"XdU44X24S9$)Nrrr(rrdrm)edgesmaxrrrepeatarangeflattenr=rr8normrr coo_matrix)rE do_weightrrrowscolsdata edge_lengthss r"_node_arc_incidence)nricp_amberg.._node_arc_incidences ZZ^^  ! _yy2*zz!!#wwq2vrzz*QTT 99>> djjA./$-- 1a4@P2QQXZ*L BIIa,.2 2D  $t !5bXFFr%cP[U5n[R"[R"U5S5n[R"SU-5n[R"U[R "US454SS9R 5n[R"XBU44USU-4S9$)Nr*rr(rdr) rrrr concatenater=rrr)vertex_3d_datarrrrs r" _create_Dnricp_amberg.._create_Ds  yy2*yyR ~~~rwwAw/?@rJRRT  $t !5b!b&\JJr%c[R"[R"S5[R"/SQ/54SS9n[R"XS45$)Nr))rrrrrdr)rrr;r:tile)rX_s r" _create_Xnricp_amberg.._create_X's= ^^RVVAY)(=>Q Gwwr7##r%cSupEUbUcXE4$[U[5(GaOUupgURUnXR5SS24nU=RUR5R [ R"UR55-slURUSS2S4n URUSS2S4n URUSS2S4n UXSS2SS4-- XSS2SS4-- n UXSS2SS4-- XSS2SS4-- n UXSS2SS4-- XSS2SS4-- n[ R"U RSS-S45nXSSS2'XSSS2'XSSS2'XE4$XSS24nUnXE4$)N)NNrrrr)) rtuplefacesrrrrdiffindptrrrlrm)rrsource_landmarksrrr source_tids source_baryssource_tri_vidsx0x1x2Ul0Ul1Ul2s r" _create_Dl_Ul#nricp_amberg.._create_Dl_Ul,s  #'7'?6M & . .(8 %K)// ikr)rrgminrrr _from_pointskdtree proximityr trianglesr face_normalseinsumr) rE input_pointsrreturn_barycentric_coordinatesrrrrGr rrs r"rrs V==.L/3t}}+=>OS_1 MM  KK)+    D(07DT7X4DOT+&V ++DL9Y%)D*? MM$**T&\2 3T)_+  &' '+-99./##DJJtF|$<=,D' ( Kr%c [R"U5n[R"U5n[U[U55n0nUc [ U5nU(aXUS:deUR XS9upxXSS24n [ U 5SUS'U SS2S4US'USS2S4US'USS2S4US 'U$UR U5uUS'US 'XS SS24US'U$) a' Find the the closest points and associated attributes from a set of 3D points. Parameters ----------- target_points : (n, 3) float Points from which the query is performed input_points : (m, 3) float Input query points kdtree : scipy.cKDTree KDTree used for query. Computed if not provided return_normals : bool If True, compute the normals at each nearest point neighbors_count : int The number of closest neighbors to query kwargs : dict Dict to accept other key word arguments (not used) Returns ---------- qres : Dict Dictionary containing : - nearest points (m, 3) with key 'nearest' - distances to nearest point (m,) with key 'distances' - vertex indices of the nearest points (m,) with key 'vertex_indices' - [optional] normals at nearest points (m,3) with key 'normals' Nr))krr rrrvertex_indices)rrgrrrrr ) target_pointsrrrrrGr rindicesrs r"rrsJMM-0M==.L/3}+=>O D ~'!####\\,\J  +#G,Q/Y!!Q$-Y%adO[!(A  K5;LL4N1[4 01'-=(>(ABY Kr%c ^4^5U44Sjm4Sn U44Sjn U44Sjn SnSnU54Sjn[XU5upnn[UR5m5USL=(a USLnUc/S Q/S Q/S Q/S Q/nU "U5unnn[RR U5nU S :Xa UR nO URnU "UUU5unnU "UUUU5unnU"UX5unnUR5nU(aUST5/n [U5GHVun!un"n#n$n%n&UU#-UU$-/n'UU#-UU$-/n(U(a(U'RUU%-5 U(RUU%-5 U!S :dU(GdGU"S :Ga@[UUST5U(+U&S :U=(a U&S :U S9n)U"U)SU[U55un*n+[R"T55n,S U,U)SU:'U&S :dSU);a~U)Sn-U(a SU);aU)Sn-U"UUR5n.[R"U.U-5n/U(a[R "U/S S5O[R""U/5n/U,U/U&--n,U*=R$U,UU*R&-slU+U,US4-n+U'RU*U"-5 U(RU+U"-5 [(R*"U'SS9n0U0R-5 [R."U(5n1[(RR1U0R2U0-R555n2U2R7U0R2U1-5nU(dGMBW RUST55 GMY U(aW n3OUST5n3[9XUU3UU5n3U3$)a Non Rigid Iterative Closest Points Implementation of the correspondence computation part of "Sumner and Popovic 2004: Deformation Transfer for Triangle Meshes" Allows to register non-rigidly a mesh on another geometry. Comparison between nricp_amberg and nricp_sumner: * nricp_amberg fits to the target mesh in less steps * nricp_amberg can generate sharp edges * only vertices and their neighbors are considered * nricp_sumner tend to preserve more the original shape * nricp_sumner parameters are easier to tune * nricp_sumner solves for triangle positions whereas nricp_amberg solves for vertex transforms * nricp_sumner is less optimized when wn > 0 Parameters ---------- source_mesh : Trimesh Source mesh containing both vertices and faces. target_geometry : Trimesh or PointCloud or (n, 3) float Target geometry. It can contain no faces or be a PointCloud. source_landmarks : (n,) int or ((n,) int, (n, 3) float) n landmarks on the the source mesh. Represented as vertex indices (n,) int. It can also be represented as a tuple of triangle indices and barycentric coordinates ((n,) int, (n, 3) float,). target_positions : (n, 3) float Target positions assigned to source landmarks steps : Core parameters of the algorithm Iterable of iterables (wc, wi, ws, wl, wn). wc is the correspondence term (strength of fitting), wi is the identity term (recommended value : 0.001), ws is smoothness term, wl weights the landmark importance and wn the normal importance. distance_threshold : float Distance threshold to account for a vertex match or not. return_records : bool If True, also returns all the intermediate results. It can help debugging and tune the parameters to match a specific case. use_faces : bool If True and if target geometry has faces, use proximity.closest_point to find matching points. Else use scipy's cKDTree object. use_vertex_normals : bool If True and if target geometry has faces, interpolate the normals of the target geometry matching points. Else use face normals or estimated normals if target geometry has no faces. neighbors_count : int number of neighbors used for normal estimation. Only used if target geometry has no faces or if use_faces is False. face_pairs_type : str 'vertex' or 'edge' Method to determine face pairs used in the smoothness cost. 'vertex' yields smoother results. Returns ---------- result : (n, 3) float or List[(n, 3) float] The vertices positions of source_mesh such that it is registered non-rigidly onto the target geometry. If return_records is True, it returns the list of the vertex positions at each iteration. c >[R"/SQS-5T l[U5n[R"T RU5S[R "[R "U5S5--n[R "URS5nURSS9*nURUS5n[R"Xg4SS9R5n[R"XU44SU-U4[S 9$) N)rrrr*r) rrd r()rmra)rr:_rowrrrrflatrjrkrrrrfloat) rVinvsizerrr minus_inv_sum Vinv_flatr_construct_transform_matrixs r"r/1nricp_sumner.._construct_transform_matrixs+-88IM+B#( Yww277._build_tetrahedronss"" ^^AqD ! ^^AqD ! ^^AqD ! 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