Ti3{ dZddlZddlZddlmZmZmZddlm Z m Z ddl m Z ddl mZmZmZmZmZmZmZmZmZmZmZ ddlmZmZdd lmZnB#e$r:Zej eZej eZej eZYdZ[ndZ[wwxYw ddl!Z"n"#e$rZej eZ"YdZ[ndZ[wwxYwd/d Z#d eefd Z$dZ%dZ&dZ'dZ( d0dedeefdZ) d1de*de*deeded ef dZ+ d2dedefdZ,d3dZ-ded eefdZ.ded ed eeeffd!Z/d4d#Z0d0d$Z1d5d%Z2 d6d'eed(eefd)Z3 d3d ed*eed ee*e*ffd+Z4d,Z5d3d-Z6d3d.Z7dS)7z graph.py ------------- Deal with graph operations. Primarily deal with graphs in (n, 2) edge list form, and abstract the backend graph library being used. Currently uses networkx or scipy.sparse.csgraph backend. N) exceptionsgroupingutil)logtol)faces_to_edges) ArrayLikeGraphEngineTypeIntegerListNDArrayNumberOptionalSequenceTupleUnionint64) coo_matrixcsgraph)cKDTreeFc|+t|d\}}|dn|j}|j}t j|d}t |dkrtjd ||}|dddf|dddfk}||}|d|r>||dddf|}t |t |ksJ||fS|S) a Returns an (n, 2) list of face indices. Each pair of faces in the list shares an edge, making them adjacent. Parameters ----------- faces : (n, 3) int, or None Vertex indices representing triangles mesh : Trimesh object If passed will used cached edges instead of generating from faces return_edges : bool Return the edges shared by adjacent faces Returns ---------- adjacency : (m, 2) int Indexes of faces that are adjacent edges: (m, 2) int Only returned if return_edges is True Indexes of vertices which make up the edges shared by the adjacent faces Examples ---------- This is useful for lots of things such as finding face- connected components: ```python >>> graph = nx.Graph() >>> graph.add_edges_from(mesh.face_adjacency) >>> groups = nx.connected_components(graph_connected) ``` NT) return_indexraxis require_countrz3No adjacent faces detected! Did you merge vertices?) r sort edges_sorted edges_facer group_rowslenrdebug) facesmesh return_edgesedgesr! edge_groups adjacency nondegenerateadjacency_edgess G/DATA/AppData/hermes/venv/lib/python3.11/site-packages/trimesh/graph.pyface_adjacencyr.1s*H |+5tDDDz  !_ %e1===K ;1 GHHH ;'IaaadOyA6M-(INNN* AAAqD 1- @A?##s9~~5555/)) returnc$|j}|j|z}|d||}t j|jdddf|jdddffdt j }|S)a Find faces that share a vertex i.e. 'neighbors' faces. Relies on the fact that an adjacency matrix at a power p contains the number of paths of length p connecting two nodes. Here we take the bipartite graph from mesh.faces_sparse to the power 2. The non-zeros are the faces connected by one vertex. Returns ---------- neighborhood : (n, 2) int Pairs of faces which share a vertex rN)rdtype) faces_sparseTsetdiageliminate_zerostocoonp concatenaterowcolr)r&VTTT neighborhoods r-face_neighborhoodr@s  B BJJqMMM B> 4"&D/*28L r/c tj|jtjdz }|j}t |jjD]\}}|j|}tjtj ||dddf dk||dddf dk}| ddk}d||ddf<|||||f<|S)a Return the vertex index of the two vertices not in the shared edge between two adjacent faces Parameters ---------- mesh : Trimesh object Input mesh Returns ----------- vid_unshared : (len(mesh.face_adjacency), 2) int Indexes of mesh.vertices for degenerate faces without exactly one unshared vertex per face it will be -1 r3rNrr2rrF) r9 zeros_liker.rface_adjacency_edges enumerater5r% logical_not logical_orreshapesum)r& vid_unsharedr(ifidr%unsharedrow_oks r-face_adjacency_unsharedrPs(=!4BHEEEIL  %ED/122223 3> Mqqq!t,,W555qqq!t,,W555    1%%*$&!!!"'/ VQY r/c|jtjdk}tjdtj|j|z}|j|j}tj|dd}|j }tj tj|j|dd}tj |tj ||d|z}tj|}tjt!|jtjz} |||z | |<| |fS)a Compute an approximate radius between adjacent faces. Parameters -------------- mesh : trimesh.Trimesh Returns ------------- radii : (len(self.face_adjacency),) float Approximate radius between faces Parallel faces will have a value of np.inf span : (len(self.face_adjacency),) float Perpendicular projection distance of two unshared vertices onto the shared edge g{Gz?g@rr)r2rC)face_adjacency_anglesr9radiansabssinverticesrPdiffrIrErunitizesubtract diagonal_dotrow_normonesr#r.inf) r&nonzero denominator point_pairsvectorsr( edges_vecperpspanradiis r-face_adjacency_radiusrgs9,(2:d+;+;;G&rvd&@&IJJJKKK- <=Kgk***227;;G  %E RWT]5%9BBBJJ7SSTTI ;$#GY77??HH9T  D =  D GC+,, - - 6E'][0E'N $;r/c`tj}||j|S)a/ Returns a networkx graph representing the vertices and their connections in the mesh. Parameters ---------- mesh : Trimesh object Returns --------- graph : networkx.Graph Graph representing vertices and edges between them where vertices are nodes and edges are edges Examples ---------- This is useful for getting nearby vertices for a given vertex, potentially for some simple smoothing techniques. >>> graph = mesh.vertex_adjacency_graph >>> graph.neighbors(0) > [1, 3, 4] )nxGraphadd_edges_from edges_unique)r&gs r-vertex_adjacency_graphrns+.  AT&''' Hr/ctjt|d}tjt|d}tj||tj}|S)a Given two sets of faces, find the edges which are in both sets. Parameters --------- faces_a : (n, 3) int Array of faces faces_b : (m, 3) int Array of faces Returns --------- shared : (p, 2) int Edges shared between faces rr operation)r9rr r boolean_rows intersect1d)faces_afaces_be_ae_bshareds r- shared_edgesrysZ '.)) 2 2 2C '.)) 2 2 2C  "3r~ F F FF Mr/enginefacet_thresholdc| tj}|j}|j}t jt |t}t j|tj k}||||z dz|k||<t|j |t j t |j d|}|S)an Find the list of parallel adjacent faces. Parameters ----------- mesh : trimesh.Trimesh engine Which graph engine to use facet_threshold : float Threshold for two facets to be considered coplanar Returns --------- facets : sequence of (n,) int Groups of face indexes of parallel adjacent faces. NrBr)nodesmin_lenrz)rr{rgface_adjacency_spanr9r]r#boolrUzeroconnected_componentsr.aranger%)r&rzr{rfreparallelr_ componentss r-facetsr)s(-  &E  #Dws5zz...HfTllSX%Gw$w-7A=OHW& H%iDJ(( J r/Tonly_watertightrepairr*c ||j}|rd}nd}t|tjt |j||}|j|f||d|S)a3 Split a mesh into multiple meshes from face connectivity. If only_watertight is true it will only return watertight meshes and will attempt to repair single triangle or quad holes. Parameters ---------- mesh : trimesh.Trimesh The source multibody mesh to split only_watertight Only return watertight components and discard any connected component that isn't fully watertight. repair If set try to fill small holes in a mesh, before the discard step in `only_watertight. adjacency : (n, 2) int If passed will be used instead of `mesh.face_adjacency` engine Which graph engine to use for the connected components. Returns ---------- meshes : (m,) trimesh.Trimesh Results of splitting based on parameters. Nr)r(r}r~rz)rr)r.rr9rr#r%submesh)r&rrr*rzkwargsr~rs r-splitr\sH' %ryTZ997SYJ 4< $3F  FL  r/r~c fd} fd}tjtjtjt dkrgSt dkr/dkr'tjdSgStjdstd dg}t dkr'| t dkr'|  tj |dz tj t}d |<|d }|tjd |fd |ff} || vr| |S| D]} | cS#t$$rYwxYwt'd)a Find groups of connected nodes from an edge list. Parameters ----------- edges : (n, 2) int Edges between nodes nodes : (m, ) int or None List of nodes that exist min_len : int Minimum length of a component group to return engine : str or None Which graph engine to use (None for automatic): (None, 'networkx', 'scipy') Returns ----------- components : (n,) sequence of (*,) int Nodes which are connected ctj}dkr|dtj|DS)z: Find connected components using networkx rc,g|]}t|Slist.0rLs r- zEconnected_components..components_networkx..s@@@AQ@@@r/)ri from_edgelistadd_nodes_fromr)graphr(r~r}s r-components_networkxz1connected_components..components_networkxsS '' a<<   ' ' '@@!8!?!?@@@@r/ct}tjt}d|<tjtj|t j||}fd|DS)zF Find connected components using scipy.sparse.csgraph ) node_countrBT)r~c g|] }| Srr)rcindexs r-rzDconnected_components..components_csgraph..s---Qa---r/)connected_component_labelsr9zerosrrrrgroup)labels containedrrr(r~rr}s @r-components_csgraphz0connected_components..components_csgraphs ,EjIIIHZt444  % *BH555i@^F9$5wGGG ----*----r/rBNrrrCr2redges must be (n, 2)!Trscipynetworkxzno graph engines available!)r9 asanyarrayruniquer#rItolistris_shape ValueErrorappendmaxrrall collections OrderedDictvalues BaseException ImportError) r(r~r}rzrrcountsmaskedges_okenginesfunctionrs ``` @r-rrsL2 A A A A A A A$ M%rx 0 0 0E } %   5zzQ Uq a<<:eW--4466 6I = ( (20111SF 5zzA~~ eiikk""" 5zzA~~ eiikk"""!#J 8Jd + + +DDKE{A&&H (OE% % &5H(IJG wv   NN$$ 8::       H  3 4 44s G(( G54G5ct||}tj|d\}}|t||ksJ|S)a? Label graph nodes from an edge list, using scipy.sparse.csgraph Parameters ----------- edges : (n, 2) int Edges of a graph node_count : int, or None The largest node in the graph. Returns ---------- labels : (node_count,) int Component labels for each node F)directed) edges_to_coorrr#)r(rmatrix _body_countrs r-rrsO % , ,F!6vNNNK6{{j(((( Mr/ traversalc . tj|dd|ddf tj dddk}|r|g}n%t j|dd} fd |D}tjfd |D}|rJtj |dD]/}tj ||||ddg||<0tj rr|D]o}tjtj|dd|ddfd}|ddksJp|S) a Given a traversal as a list of nodes split the traversal if a sequential index pair is not in the given edges. Useful since the implementation of DFS we're using will happily return disconnected values in a flat traversal. Parameters -------------- traversal : (m,) int Traversal through edges edges_tree : cKDTree A way to reconstruct original edge indices from sorted (n, 2) edge values. This is a slight misuse of a kdtree since one could just hash the tuples of the integer edges, but that isn't possible with numpy arrays easily and this allows a vectorized reconstruction. Returns --------------- split : sequence of (p,) int Traversals split into only connected paths. Nr2rrr绽|=T)r~ only_nonzerocg|]<}tjdddf||dddg=S)Nrr2r)r9r:)rb trav_edges r-rz$_split_traversal..8sX   KLBNIaaadOA. !B%0@0DE F F   r/c g|]a}t|dkoK|d|dko9t|d|dgddkbS)rrr2r)r#querysorted)rs edges_trees r-rz$_split_traversal..?s    FFQJ C!"  C  1qu !6!677:UB   r/) r9 column_stackrrrrblocksarrayanyr_r:rstrict) rrexistsrr needs_closerLr check_edgers ` @r-_split_traversalrs23B3122 ?@@I  bgia888 9 9! ??E!HH zC C CA!CRC&!ABB%!A!AJJJJ$$Z003e;@@BB B BB B Lr/ traversalsr(ctj|d}t|}t|dkr|Sg}|D]&}|t ||'tjd|D}t|dkrK|d|tj ||tj n|}|S)a Convert a traversal of a list of edges into a sequence of traversals where every pair of consecutive node indexes is an edge in a passed edge list Parameters ------------- traversals : sequence of (m,) int Node indexes of traversals of a graph edges : (n, 2) int Pairs of connected node indexes Returns -------------- splits : sequence of (p,) int Node indexes of connected traversals rrr)rrcZg|](}tj|dd|ddf)S)Nr2r)r9rrs r-rz#fill_traversals..ss6!S!S!Sq"/1SbS61QRR5/"B"B!S!S!Sr/rp) r9rrr#copyextendrr vstack_emptyrrr setdiff1d)rr(rsplitsr}includeds r-fill_traversalsrSs& GE " " "EJ :!zz|| FPP &:NNNOOOO !S!SF!S!S!STTH 8}}q 1   h+E8r|TTTUUUU Mr/bfsctj|tj}t|dkrgSt j|dst dt| }|dkr tj }n"|dkr tj }nt d| d t|}tj|}tj|dkd}tj|dkd}g}tjt|dztj}tj||fD]Q} || r ||| d d tj} || d || <R|S) a Given an edge list generate a sequence of ordered depth first search traversals using scipy.csgraph routines. Parameters ------------ edges : (n, 2) int Undirected edges of a graph mode : str Traversal type, 'bfs' or 'dfs' Returns ----------- traversals : (m,) sequence of (p,) int Ordered DFS or BFS traversals of the graph. rBrrzedges are not (n, 2)!rdfsz(traversal mode must be either dfs or bfsrrF)i_startreturn_predecessorsrT)r9rrr#rrrstrlowerstriprbreadth_first_orderdepth_first_orderrrbincountravelr_rbool_r:astyper) r(modefuncrr nodes_leafr}rvisitedstartordereds r-rrs" HU"( + + +E 5zzQ ]5' * *20111 t99??   " " $ $D u}}* (CDDD JJAJ   E{5;;==))HHM**1-J Jx!| $ $Q 'EJhs8}}q(999G U 344    5>  $ 5ee   &    '""" r/ctj|tj}t|dks$t j|dst d||dz}t|}|(tj t|t}t||j f|j ||fS)a Given an edge list, return a boolean scipy.sparse.coo_matrix representing the edges in matrix form. Parameters ------------ edges : (n, 2) int Edges of a graph count : int The total number of nodes in the graph if None: count = edges.max() + 1 data : (n,) any Assign data to each edge, if None will be bool True for each specified edge Returns ------------ matrix: (count, count) scipy.sparse.coo_matrix Sparse COO rBrrrNr)r3shape)r9rrr#rrrrintr]rrr5r3)r(countdatas r-rrs* M%rx 0 0 0E JJ!OOt}UG<.s4;;;T47   Q ( (;;;r/cg|]P}|d|d|d|dfQSrrrs r-rzneighbors..sd   tAw  # #DG , ,iQ.@.D.DT!W.M.M N   r/Nrc:g|]}t|Srr)rrLrs r-rzneighbors.. s% : : :AT)A,   : : :r/)r defaultdictsetrrange)r( max_indexrrrs @r-rrs$',,I ;;;;U;;;;;        IIKK!O : : : :y)9)9 : : :E Lr/$@angle facet_minareacX |tjd}t|jdkr|S|j|k}|j|}g}d}||j |j|z fd|jD}t|dkrztj t|j t}d|tj |<||| d}tj|}n&#t$rt!jd d YnwxYwt%|d | }t|dkr||t|dkr|Stjtj |} t| t|j kratjtjt|j | } || d||dd } || jd<t| j t|j krt!jd| S)az Return a non-watertight version of the mesh which will render nicely with smooth shading by disconnecting faces at sharp angles to each other. Parameters ----------- mesh : trimesh.Trimesh Source geometry angle : float or None Angle in radians face pairs with angles smaller than this will appear smoothed facet_minarea : float or None Minimum area fraction to consider IE for `facets_minarea=25` only facets larger than `mesh.area / 25` will be considered. Returns --------- smooth : trimesh.Trimesh Geometry with disconnected face patches NrcPg|]"}|k |#Sr)rJ)rfareasmin_areas r-rz smooth_shade..As/JJJAa 0I0Ia0I0I0Ir/rBFrrzfailed to calculate facetsT)exc_infor)r~r}rC)rroriginal_componentszface count in smooth wrong!)r9rTr#r.rrS area_facesarearr]r%rhstackrrrrwarningrrrrrIrmetadata)r&rr angle_okr*rr}rrrbrokesmoothrrs @@r- smooth_shaders2 } 2 4 1$$yy{{)E1H#H-IF E 9}, EKJJJJJJJF6{{Qws4:d;;;*/RYv&&'%d9o&9&9q&9&A&AB  ),, E E E K4t D D D D D D E&i%HHHJ 6{{Q&!!! :!yy{{Yry,, - -F 6{{c$*oo%% RYs4:77@@%--00111\\*eD\ I IF-7FO)* 6<C OO++ 1222 Ms5B!D D:9D:r cx|tj|d}tj|d}t t |dzt |k}||dddddfj}t tj| }||fS)ah Parameters ----------- edges : (n, 2) int List of vertex indices edges_sorted : (n, 2) int Pass vertex indices sorted on axis 1 as a speedup Returns --------- watertight : boolean Whether every edge is shared by an even number of faces winding : boolean Whether every shared edge is reversed Nrrrr)r2rrR) r9rrr"rr#rIr5equalr)r(r groups watertightopposingwindings r- is_watertightr!ks(wu1---  Q ? ? ?Fs6{{Q3u::566JV}$$W--aaa1f57H28X&**,,--G w r/cddl}ddl}|5}tjj||j|d|jdg}dddn #1swxYwY|S)z Turn a networkx graph into an SVG string using graphviz `dot`. Parameters ---------- graph: networkx graph Returns --------- svg: string, pictoral layout in SVG format rNdotz-Tsvg) subprocesstempfileNamedTemporaryFileridrawing nx_agraph write_dotname check_output)rr$r%dot_filesvgs r- graph_to_svgr.sOOO  $ $ & &G( &&uhm<<<%%uhmW&EFFGGGGGGGGGGGGGGG JsAA11A58A5c|Ft|t|zdz}|dfg}g}g}t|D]}|dd}||}t|dkr?||t|dkrn|}jd} |D]^} || D]A} | r|| | fd} ||dd| | fgzB_|S)a* For a networkx MultiDiGraph, find all paths from a source node to leaf nodes. This function returns edge instance numbers in addition to nodes, unlike networkx.all_simple_paths. Parameters --------------- G : networkx.MultiDiGraph Graph to evaluate source : hashable Node to start traversal at cutoff : int Number of nodes to visit If None will visit all nodes Returns ---------- traversals : (n,) list of [(node, edge instance index), ] paths Traversals of the multigraph Nrrr2TF)r#r(r}rrpopkeys) Gsourcecutoffcurrentqueuer_ current_nodechildrnodeinstances r-multigraph_pathsr<sn*~aggii..3qwwyy>>1Q6{mG EJ 6]]!H!Hr{1~ , u::??   g & & &5zzQiikkGGE H H %d 0 0 2 2 H HH H h'7888 %  WSbS\dH5E4F%FGGGG H H r/cg}tj|D]^\}}||d|d|d}|||C|||_|S)a\ Given a MultiDiGraph traversal, collect attributes along it. Parameters ------------- G: networkx.MultiDiGraph traversal: (n) list of (node, instance) tuples attrib: dict key, name to collect. If None, will return all Returns ------------- collected: (len(traversal) - 1) list of attributes rr)rpairwiser)r2rattrib collecteduvattribss r-multigraph_collectrDsI i((..1AaD'!A$-!% >   W % % % %   WV_ - - - - r/)NNF)NN)TTNN)rNN)N)r)NF)Nr)8__doc__rnumpyr9rrr constantsrrgeometryr typedr r r r rrrrrrr scipy.sparserr scipy.spatialrrEExceptionWrapperrrir.r@rPrgrnryrrrrrrrrrrrr!r.r<rDrr/r-rOs(((((((((($$$$$$                          000000000%%%%%%%000)j)!,,G)j)!,,G,,Q//JJJJJJ 0 (((( % $Q ' 'BBBBBB( KKKK\wu~2+++\...b   8.OS00!0;CF;K0000j!%)" 333 3 " 3  3 3333nHLf5f5f55Df5f5f5f5R2<<W <<<<~,,,uXwEV?W,,,,^DDDDN$O$O$O$ONFMQVV&!V9A&9IVVVVt;?"" "$,Y$7" 4:""""J.AAAAHs/A B 0BB BB4B//B4