l0jwdZddlZddlZddlZddlmZmZmZddl m Z m Z ddl m Z ddlmZmZmZmZmZmZmZmZ ddlmZmZdd lmZnB#e$r:ZejeZejeZejeZYdZ[ndZ[wwxYw ddlZ n"#e$rZejeZ YdZ[ndZ[wwxYwd*d Z!d eefd Z"dZ#dZ$dZ%dZ&d+deefdZ'd,d efdZ(d-dZ)d.dZ*ded eefdZ+deded eeeffdZ,d/dZ-d+dZ.d0d Z/d!Z0 d1d#eed$eefd%Z1d.d&Z2d'Z3d.d(Z4d.d)Z5dS)2z 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) ArrayLikeListNDArrayNumberOptionalSequenceUnionint64) 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 P/home/wildlama/miniconda3/envs/lam/lib/python3.11/site-packages/trimesh/graph.pyface_adjacencyr+&s*H |+5tDDDz  !_ %e1===K ;1 GHHH ;'IaaadOyA6M-(INNN* AAAqD 1- @A?##s9~~5555/)) returnc$|j}|j|z}|d||}t j|jdddf|jdddffdt j }|S)a Find faces that share a vertex i.e. 'neighbors' faces. Relies on the fact that an adjacency matrix at a power p contains the number of paths of length p connecting two nodes. Here we take the bipartite graph from mesh.faces_sparse to the power 2. The non-zeros are the faces connected by one vertex. Returns ---------- neighborhood : (n, 2) int Pairs of faces which share a vertex rN)rdtype) faces_sparseTsetdiageliminate_zerostocoonp concatenaterowcolr)r#VTTT neighborhoods r*face_neighborhoodr=ts  B BJJqMMM B> 4"&D/*28L r,c tj|jtjdz }|j}t |jjD]\}}|j|}tjtj ||dddf dk||dddf dk}| ddk}d||ddf<|||||f<|S)a Return the vertex index of the two vertices not in the shared edge between two adjacent faces Parameters ---------- mesh : Trimesh object Input mesh Returns ----------- vid_unshared : (len(mesh.face_adjacency), 2) int Indexes of mesh.vertices for degenerate faces without exactly one unshared vertex per face it will be -1 r0rNrr/rrF) r6 zeros_liker+rface_adjacency_edges enumerater2r" logical_not logical_orreshapesum)r# vid_unsharedr%ifidr"unsharedrow_oks r*face_adjacency_unsharedrMs(=!4BHEEEIL  %ED/122223 3> Mqqq!t,,W555qqq!t,,W555    1%%*$&!!!"'/ 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)r/r@)face_adjacency_anglesr6radiansabssinverticesrMdiffrFrBrunitizesubtract diagonal_dotrow_normonesr r+inf) r#nonzero denominator point_pairsvectorsr% edges_vecperpspanradiis r*face_adjacency_radiusrds9,(2:d+;+;;G&rvd&@&IJJJKKK- <=Kgk***227;;G  %E RWT]5%9BBBJJ7SSTTI ;$#GY77??HH9T  D =  D GC+,, - - 6E'][0E'N $;r,c`tj}||j|S)a/ Returns a networkx graph representing the vertices and their connections in the mesh. Parameters ---------- mesh : Trimesh object Returns --------- graph : networkx.Graph Graph representing vertices and edges between them where vertices are nodes and edges are edges Examples ---------- This is useful for getting nearby vertices for a given vertex, potentially for some simple smoothing techniques. >>> graph = mesh.vertex_adjacency_graph >>> graph.neighbors(0) > [1, 3, 4] )nxGraphadd_edges_from edges_unique)r#gs r*vertex_adjacency_graphrks+.  AT&''' Hr,ctjt|d}tjt|d}tj||tj}|S)a Given two sets of faces, find the edges which are in both sets. Parameters --------- faces_a : (n, 3) int Array of faces faces_b : (m, 3) int Array of faces Returns --------- shared : (p, 2) int Edges shared between faces rr operation)r6rr r boolean_rows intersect1d)faces_afaces_be_ae_bshareds r* shared_edgesrvsZ '.)) 2 2 2C '.)) 2 2 2C  "3r~ F F FF Mr,facet_thresholdc| tj}|j}|j}t jt |t}t j|tj k}||||z dz|k||<t|j |t j t |j d|}|S)a Find the list of parallel adjacent faces. Parameters ----------- mesh : trimesh.Trimesh engine : str Which graph engine to use: ('scipy', 'networkx') facet_threshold : float Threshold for two facets to be considered coplanar Returns --------- facets : sequence of (n,) int Groups of face indexes of parallel adjacent faces. Nr?r)nodesmin_lenengine)rrwrdface_adjacency_spanr6rZr boolrRzeroconnected_componentsr+aranger")r#r{rwrcrbparallelr\ componentss r*facetsrs&-  &E  #Dws5zz...HfTllSX%Gw$w-7A=OHW& H%iDJ(( J r,Tc ||j}|rd}nd}t|tjt |j||}|j|fd|i|}|S)a# 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 only_watertight: bool Only return watertight components adjacency : (n, 2) int Face adjacency to override full mesh engine : str or None Which graph engine to use Returns ---------- meshes : (m,) trimesh.Trimesh Results of splitting Nr)r%ryrzr{only_watertight)r+rr6rr r"submesh)r#rr'r{kwargsrzrmeshess r*splitrPs}0' %ryTZ997SYJT\* P Po P P PF Mr,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$$rYwxYwt'd)a Find groups of connected nodes from an edge list. Parameters ----------- edges : (n, 2) int Edges between nodes nodes : (m, ) int or None List of nodes that exist min_len : int Minimum length of a component group to return engine : str or None Which graph engine to use (None for automatic): (None, 'networkx', 'scipy') Returns ----------- components : (n,) sequence of (*,) int Nodes which are connected ctj}dkr|dtj|DS)z: Find connected components using networkx rc,g|]}t|Slist.0rIs r* zEconnected_components..components_networkx..s@@@AQ@@@r,)rf from_edgelistadd_nodes_fromr)graphr%rzrys r*components_networkxz1connected_components..components_networkxsS '' a<<   ' ' '@@!8!?!?@@@@r,ct}tjt}d|<tjtj|t j||}fd|DS)zF Find connected components using scipy.sparse.csgraph ) node_countr?T)rzc g|] }| Srr)rcindexs r*rzDconnected_components..components_csgraph..s---Qa---r,)connected_component_labelsr6zerosr}rrrgroup)labels containedrrr%rzrrys @r*components_csgraphz0connected_components..components_csgraphs ,EjIIIHZt444  % *BH555i@^F9$5wGGG ----*----r,r?Nrrr@r/redges must be (n, 2)!Trscipynetworkxzno graph engines available!)r6 asanyarrayruniquer rFtolistris_shape ValueErrorappendmaxrr}all collections OrderedDictvalues BaseException ImportError) r%rzryr{rrcountsmaskedges_okenginesfunctionrs ``` @r*rrxsL. A A A A A A A$ M%rx 0 0 0E } %   5zzQ Uq a<<:eW--4466 6I = ( (20111SF 5zzA~~ eiikk""" 5zzA~~ eiikk"""!#J 8Jd + + +DDKE{A&&H (OE% % &5H(IJG wv   NN$$ 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. Nr/rrr绽|=T)rz only_nonzerocg|]<}tjdddf||dddg=S)Nrr/r)r6r7)rb trav_edges r*rz$_split_traversal..sX   KLBNIaaadOA. !B%0@0DE F F   r,c g|]a}t|dkoK|d|dko9t|d|dgddkbS)rrr/r)r querysorted)rs edges_trees r*rz$_split_traversal..#s    FFQJ C!"  C  1qu !6!677:UB   r,) r6 column_stackrrrrblocksarrayanyr\r7rstrict) rrexistsrr needs_closerIr 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)Nr/r)r6rrs r*rz#fill_traversals..Ws6!S!S!Sq"/1SbS61QRR5/"B"B!S!S!Sr,rm) r6rrr copyextendrr vstack_emptyrro setdiff1d)rr%rsplitsryincludeds r*fill_traversalsr7s& GE " " "EJ :!zz|| FPP &:NNNOOOO !S!SF!S!S!STTH 8}}q 1   h+E8r|TTTUUUU Mr,bfsc:tj|tj}t|dkrgSt j|dst dt| }|dkr tj }n"|dkr tj }nt d| d t|d }t!|}g}t|dkr}|}|||d d tj}||||t|dk}|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. r?rrzedges are not (n, 2)!rdfsz(traversal mode must be either dfs or bfsrrr/F)i_startreturn_predecessorsr)r6rrr rrrstrlowerstriprbreadth_first_orderdepth_first_orderrsetrFrpopastyperdifference_update)r%modefuncryrrstartordereds r*rrfs|" HU"( + + +E 5zzQ ]5' * *20111 t99??   " " $ $D u}}* (CDDD JJAJ  b!! " "E   EJ e**q.. $ 5ee   &    '""" ((( e**q.. r,ctj|tj}t|dks$t j|dst d||dz}t|}|(tj t|t}t||j f|j ||f}|S)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 r?rrrNr)r0shape)r6rrr rrrrintrZr}rr2r0)r%countdatars 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)rrIrs r*rzneighbors..s% : : :AT)A,   : : :r,)r defaultdictrrrange)r% max_indexrrrs @r*rrs$',,I ;;;;U;;;;;        IIKK!O : : : :y)9)9 : : :E Lr,cRtjdtdt|i|S)zA DEPRECATED: use `trimesh.graph.smooth_shade(mesh, ...)` zu`trimesh.graph.smoothed` is deprecated and will be removed in March 2024: use `trimesh.graph.smooth_shade(mesh, ...)`r)category stacklevel)warningswarnDeprecationWarning smooth_shade)argsrs r*smoothedr s= M 8#   ( ( ((r,$@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)rG)rfareasmin_areas r*rz smooth_shade..&s/JJJAa 0I0Ia0I0I0Ir,r?Frrzfailed to calculate facetsT)exc_infor)rzryr@)rroriginal_componentszface count in smooth wrong!)r6rQr r+rrP area_facesarearrZr"r}hstackrrrrwarningrrrrrFrmetadata)r#r r angle_okr'rryrrrbrokesmoothrrs @@r*rrs2 } 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$*oo%% RYs4:77@@%--00111\\*eD\ I IF-7FO)* 6<C OO++ 1222 Ms5B!D D:9D:cx|tj|d}tj|d}t t |dzt |k}||dddddfj}t tj| }||fS)ah Parameters ----------- edges : (n, 2) int List of vertex indices edges_sorted : (n, 2) int Pass vertex indices sorted on axis 1 as a speedup Returns --------- watertight : boolean Whether every edge is shared by an even number of faces winding : boolean Whether every shared edge is reversed Nrrrr)r/rrO) r6rrrr}r rFr2equalr)r%rgroups watertightopposingwindings r* is_watertightr#Ps$wu1---  Q ? ? ?Fs6{{Q3u::566JV}$$W--aaa1f57H28X&**,,--G w r,cddl}ddl}|5}tjj||j|d|jdg}dddn #1swxYwY|S)z Turn a networkx graph into an SVG string using graphviz `dot`. Parameters ---------- graph: networkx graph Returns --------- svg: string, pictoral layout in SVG format rNdotz-Tsvg) subprocesstempfileNamedTemporaryFilerfdrawing nx_agraph write_dotname check_output)rr&r'dot_filesvgs r* graph_to_svgr0qsOOO  $ $ & &G( &&uhm<<<%%uhmW&EFFGGGGGGGGGGGGGGG JsAA11A58A5c|Ft|t|zdz}|dfg}g}g}t|D]}|dd}||}t|dkr?||t|dkrn|}jd} |D]^} || D]A} | r|| | fd} ||dd| | fgzB_|S)a* For a networkx MultiDiGraph, find all paths from a source node to leaf nodes. This function returns edge instance numbers in addition to nodes, unlike networkx.all_simple_paths. Parameters --------------- G : networkx.MultiDiGraph Graph to evaluate source : hashable Node to start traversal at cutoff : int Number of nodes to visit If None will visit all nodes Returns ---------- traversals : (n,) list of [(node, edge instance index), ] paths Traversals of the multigraph Nrrr/TF)r r%ryrrrkeys) Gsourcecutoffcurrentqueuer_ current_nodechildrnodeinstances r*multigraph_pathsr=sn*~aggii..3qwwyy>>1Q6{mG EJ 6]]!H!Hr{1~ , u::??   g & & &5zzQiikkGGE H H %d 0 0 2 2 H HH H h'7888 %  WSbS\dH5E4F%FGGGG H H r,cg}tj|D]^\}}||d|d|d}|||C|||_|S)a\ Given a MultiDiGraph traversal, collect attributes along it. Parameters ------------- G: networkx.MultiDiGraph traversal: (n) list of (node, instance) tuples attrib: dict key, name to collect. If None, will return all Returns ------------- collected: (len(traversal) - 1) list of attributes rr)rpairwiser)r3rattrib collecteduvattribss r*multigraph_collectrEsI i((..1AaD'!A$-!% >   W % % % %   WV_ - - - - r,)NNF)NN)TNN)rNN)N)r)NF)Nr )6__doc__rrnumpyr6rrr constantsrrgeometryr typedr r r r rrrr scipy.sparserr scipy.spatialrrEExceptionWrapperrrfr+r=rMrdrkrvrrrrrrrrrr rr#r0r=rErr,r*rPs(((((((((($$$$$$UUUUUUUUUUUUUUUUUUUU000000000%%%%%%%000)j)!,,G)j)!,,G,,Q//JJJJJJ 0 (((( % $Q ' 'BBBBBB( KKKK\wu~2+++\...b   8,//x/?////d%%PT%%%%Pd5d5d5d5N2<<W <<<<~,,,uXwEV?W,,,,^7777t%%%%PD ) ) )MQVV&!V9A&9IVVVVrB.AAAAHs/A B 0BB BB2B--B2