l0j8ddlZddlmZddlmZddlmZ ddlZ n(#e $r Z ddlm Z e j e Z YdZ [ ndZ [ wwxYwdZdd Zdd Zd Zejfd efd ZdZddZ ddZddZdS)N)util)log)NDArray) exceptionsct|gd}|8tj|tj|ddd |dddf<|S)a Given the origin and normal of a plane find the transform that will move that plane to be coplanar with the XY plane. Parameters ---------- origin : (3,) float Point that lies on the plane normal : (3,) float Vector that points along normal of plane Returns --------- transform: (4,4) float Transformation matrix to move points onto XY plane )rrrNr) align_vectorsnpdotappend)originnormal transforms S/home/wildlama/miniconda3/envs/lam/lib/python3.11/site-packages/trimesh/geometry.pyplane_transformrsY"fiii00I F9bi.B.BCCBQBGG "1"a% Fctj|tj}tj|tj}|jdks |jdkrt dtj|dd}tj|dd}tj|dkr|dddfxxdzcc<tj|dkr|dddfxxdzcc<tj d }| |j |dd dd f<|rbtj |d|d}tj tj |dd }|d kr|tjz }||fS|S) a Find the rotation matrix that transforms one 3D vector to another. Parameters ------------ a : (3,) float Unit vector b : (3,) float Unit vector return_angle : bool Return the angle between vectors or not Returns ------------- matrix : (4, 4) float Homogeneous transform to rotate from `a` to `b` angle : float If `return_angle` angle in radians between `a` and `b` dtyper zvectors must be (3,)!rrNrr ?gh㈵)r arrayfloat64shape ValueErrorlinalgsvdreshapedeteyer Tarccosclippi)ab return_angleaubumatrixr angles rr r 's, "*%%%A "*%%%Aw$!'T//0111 qyy)) * *1 -B qyy)) * *1 -B y}}R1 111b5 T  y}}R1 111b5 T VAYYFVVBD\\F2A2rr6NfRUBqE"" "'#tS1122 ;; RUNEu} Mrc*tj|tj}|ddgdfd}|rPtjtjt |djd}||fS|S)a Given a list of faces (n,3), return a list of edges (n*3,2) Parameters ----------- faces : (n, 3) int Vertex indices representing faces Returns ----------- edges : (n*3, 2) int Vertex indices representing edges N)rrrr2r)rr2)r rr)r asanyarrayint64r#tilearangelenr&)faces return_indexedges face_indexs rfaces_to_edgesr<\s M% * *E !!!'''' ( 0 0 9 9E!WRYs5zz22F;;=EEbII j  Lrctj|tj}t|dkrtjgSt j|dr|d}n$t j|dstdt j |dddf|dddf}tj |d d }tj tj |}|S) z Find the angles between pairs of unit vectors. Parameters ---------- pairs : (n, 2, 3) float Unit vector pairs Returns ---------- angles : (n,) float Angles between vectors in radians rrr2r )rr2r )rr2r>zpairs must be (n,2,(2|3))!Nrrr) r r3rr7rris_shaper#r diagonal_dotr(absr')pairsdotsangless r vector_anglerEvs M%rz 2 2 2E 5zzQx|| uf % %7 j)) ]5/ 2 275666  U111a4[%1+ 6 6D 74s # #D VBIdOO $ $F Mrreturnct|dkrtjd|S tj||}t|jdkr&|jddkr||St|jdkrR|jddkrAtj|ddgdf|ddgd ff|Sn#t$rYnwxYwtjd |D}tjd |D}d |D}t|dkr(t|dkr||St|dkrtj|}t|dkr.tj|ddgdf|ddgd ff}tj |||g|S) a= Given an array of quad faces return them as triangle faces, also handles pure triangles and mixed triangles and quads. Parameters ----------- quads: (n, 4) int Vertex indices of quad faces. Returns ----------- faces : (m, 3) int Vertex indices of triangular faces.c rrr2rr rNrrr2)r2r rc8g|]}t|dk|Srr7.0is r z%triangulate_quads..s#444!A! A rc8g|]}t|dk|S)rrJrKs rrNz%triangulate_quads..s#5551Q1Qrcg|]@tdkfdttdz DAS)rcJg|]}d|dz|dzg SrH)rLrMfs rrNz0triangulate_quads...s4???!A$!a%!AE( #???rr2)r7range)rLrSs @rrNz%triangulate_quads..sW    q66A:: @???U3q66A:->->??? ::r) r7r zerosrrastypevstackr r vstack_empty)quadsrtriquadpolys rtriangulate_quadsr]s  5zzQx'''' e,,, u{  q U[^q%8%8<<&& & u{  q U[^q%8%89eAAAyyyL15III3FGHHOOPUVV V      (44u444 5 5C 855555 6 6D     D  4yyA~~#d))q..zz%    4yy1}}y 4yy1}}y$qqq)))|,d111iii<.@ABB  c4. / / 6 6u = ==sAC*?A)C** C76C7c tj||}nR#t$rEt jdtj|dd}YnwxYwt||ksJ||ksJtj dtj |dd}tj ||dddfz}|||zdddfk tj  } tjt|t" }||d}|||dk<n#t($rt jd d tj|jtj } |} t/|D]F} tj| | kdd zddd| || || || z<G| ||dk<YnwxYw|S) a Find vertex face indices from the faces array of vertices Parameters ----------- vertex_count : int The number of vertices faces refer to faces : (n, 3) int List of vertex indices faces_sparse : scipy.sparse.COO Sparse matrix Returns ----------- vertex_faces : (vertex_count, ) int Face indices for every vertex Array padded with -1 in each row for all vertices with fewer face indices than the max number of face indices. ) minlengthzcasting failed, falling back!T) return_countsrrNrrzJvertex_faces falling back to slow loop! mesh probably has degenerate facesexc_infor )r bincountflatten TypeErrorrwarninguniquer7maxr cumsumr6rVr4scipysparseidentityintr nonzero BaseExceptionrUsizerTwhere) vertex_countr8 faces_sparsecountsstartspackpaddedrl sorted_facessortflatvs rvertex_face_indicesr|sg,CU]]__ EEE CCC 34445==??$???B C v;;, & & & & 99;; % % % %Yq")F++CRC0 1 1F 9VZZ\\ " "VAAAtG_ 4DD1199"(CC CF#<((U3(??#''1199;;A> +v{  # # #  3    x "(333}}|$$ Z ZA79x 7J7J17MQR7RTXTXVXTX6YDVAY22 3 3"v{ # Ms$(+A A:9A:A)F**B8I%$I%c fd}fd} |}n0#t$r#tjdd|}YnwxYwtj|}|S)a Find vertex normals from the mean of the faces that contain that vertex. Parameters ----------- vertex_count : int The number of vertices faces refer to faces : (n, 3) int List of vertex indices face_normals : (n, 3) float Normal vector for each face Returns ----------- vertex_normals : (vertex_count, 3) float Normals for every vertex Vertices unreferenced by faces will be zero. c\t}n}|}|SN) index_sparser )r/summed face_normalsr8rkrrs r summed_sparsez*mean_vertex_normals..summed_sparse%s6 >!,66FFFL)) rctjdf}tD]\}}||xx|z cc<|SNr )r rUzip)rfacerrr8rrs r summed_loopz(mean_vertex_normals..summed_loop0sS<+,,|44 # #LD& 4LLLF "LLLL r*unable to use sparse matrix, falling back!Tra)rorrfrunitize) rrr8rrkkwargsrrrvertex_normalss ```` rmean_vertex_normalsrs*          @4PPPP \&))N s *A  A cVfd}fd}dzddk}||||sC tj|S#t$rt jdd YnwxYwtj|S) aV Compute vertex normals from the faces that contain that vertex. The contribution of a face's normal to a vertex normal is the ratio of the corner-angle in which the vertex is, with respect to the sum of all corner-angles surrounding the vertex. Grit Thuerrner & Charles A. Wuethrich (1998) Computing Vertex Normals from Polygonal Facets, Journal of Graphics Tools, 3:1, 43-46 Parameters ----------- vertex_count : int The number of vertices faces refer to faces : (n, 3) int List of vertex indices face_normals : (n, 3) float Normal vector for each face face_angles : (n, 3) float Angles at each vertex in the face Returns ----------- vertex_normals : (vertex_count, 3) float Normals for every vertex Vertices unreferenced by faces will be zero. cvt}|S)N)data)rravelr )r/ face_anglesrr8rrs rrz.weighted_vertex_normals..summed_sparsecs7 lE 8I8I8K8KLLLzz,'''rc(tjdftj}tjD]Z}tj|k\}}||f}tj||z |||<[|Sr)r rUrr6rqr sum) r vertex_idx face_idxs inface_idxssurrounding_anglesrrr8rrs rrz,weighted_vertex_normals..summed_loopks<+RZ88)L11  J&(Xez.A%B%B "I{!,Y -C!D !#"%7%;%;%=%==|I?V""F:   rr2r)axisg?rTra)rrrrorrf)rrr8rruse_looprrface_oks```` rweighted_vertex_normalsrDs >((((((((        Q###++c1G 'NE(Lg&K U U< 00 0 U U U KDt T T T T T T U < & &&s A)) B  B ctj|}t|}|d}tjtjt |dd|jdfd}|t |f}|)tjt |t}n/t |t |krtd|| |}tj |||ff||j}|S)am Return a sparse matrix for which vertices are contained in which faces. A data vector can be passed which is then used instead of booleans Parameters ------------ columns : int Number of columns, usually number of vertices indices : (m, d) int Usually mesh.faces Returns --------- sparse: scipy.sparse.coo_matrix of shape (columns, len(faces)) dtype is boolean Examples ---------- In [1]: sparse = faces_sparse(len(mesh.vertices), mesh.faces) In [2]: sparse.shape Out[2]: (12, 20) In [3]: mesh.faces.shape Out[3]: (20, 3) co In [4]: mesh.vertices.shape Out[4]: (12, 3) In [5]: dense = sparse.toarray().astype(int) In [6]: dense Out[6]: array([[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1]]) In [7]: dense.sum(axis=0) Out[7]: array([3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]) rrrNrzdata incorrect length)rr)r r3rmr#r5r6r7ronesboolr rVrjrk coo_matrixr)columnsindicesrrrowcolrr/s rrrsdmG$$G'llG //"  C ' #g,,''001gmA6F2G   gbkkc'll #E |ws3xxt,,, Tc#hh  0111 {{5!!\ $ $dS#J%7uDJ $ W WF Mr)Fr)NN)numpyr r constantsrtypedr scipy.sparserjroErExceptionWrapperrr r<rEr4r]r|rrrrRrrrs++++ (J ' * *EEEEEE +.2222j4@$&87>7>7>7>7>7>t===@1111j>CB'B'B'B'JGGGGGGsA=A