h~?JSSKJr SSKrS/rS SjrSrSrSrS Sjr S r g) ) defaultdictNcombinatorial_embedding_to_posc^[UR55S:a0/SQn0n[UR55H upEX$X5'M U$[X5up0n0n0m0n [ X5n U SSU SSU SSpn STU 'SX'XU 'SX{'STU 'SX'SX'SX|'STU 'SX'XU 'SX}'[ S[U 55HnXunnUSnUSnUSnUS n[U5S:nTU==S- ss'TU==S- ss'[ U4S jUSS55nU U*U-U U-S-TU'U UU-U U-S-X'UTU- TU'U(aTU==TU-ss'XU'UX'U(a UX'SUU'MSX'M 0nSX4X;'U /nU(a7UR5n[UUUTX5 [UUUTX5 U(aM7U$) aAssigns every node a (x, y) position based on the given embedding The algorithm iteratively inserts nodes of the input graph in a certain order and rearranges previously inserted nodes so that the planar drawing stays valid. This is done efficiently by only maintaining relative positions during the node placements and calculating the absolute positions at the end. For more information see [1]_. Parameters ---------- embedding : nx.PlanarEmbedding This defines the order of the edges fully_triangulate : bool If set to True the algorithm adds edges to a copy of the input embedding and makes it chordal. Returns ------- pos : dict Maps each node to a tuple that defines the (x, y) position References ---------- .. [1] M. Chrobak and T.H. Payne: A Linear-time Algorithm for Drawing a Planar Graph on a Grid 1989 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.6677 ))rr)r)rrrrNc3.># UH nTUv M g7fN).0xdelta_xs T/var/www/html/env/lib/python3.13/site-packages/networkx/algorithms/planar_drawing.py 1combinatorial_embedding_to_pos..\sA0@1GAJ0@s) lennodes enumeratetriangulate_embeddingget_canonical_orderingrangesumpop set_position) embeddingfully_triangulatedefault_positionsposiv outer_face left_t_child right_t_child y_coordinate node_listv1v2v3kvk contour_nbrswpwp1wqwq1 adds_mult_tri delta_x_wp_wqremaining_nodes parent_noders @rrrs< 9?? !4ioo/0DA&)CF1 1)OI LMGL&y=I 1a)A,q/9Q<?BBGBKL"LGBKLMLGBKL"L 1c)n %$<L !_1o " 2L)A-     q A QR0@AA %R((=8<;KKPQQ (,}<|B?OOTUU #gbk1  CLGBK 'Lb  "L !%M# #L 9&> C,"#CGdO %))+      ,  / JcbXnXPSnUb!XsU-nXU4XV'URU5 gg)z:Helper method to calculate the absolute position of nodes.rN)append) parenttreer5rr'r!child parent_node_xchild_xs rrrsH LEKNM %.0E23 u% r7c|^^^^USmUSn[[5n[5m[U5n0mUn[S[ U55HnXTU'XnM TTU'0mTn[[ U5S- SS5HnXTU'XnM UU4SjnUUU4SjnUHVn UR U 5H>n U"U 5(dMU"X5(aM!X9==S- ss'UR U 5 M@ MX S/[ UR55-n T/4U S'U/4U S'UR T5 UR U5 [[ UR55S- SS5GHn UR5n TRU 5 Sn Sn[UR U 55n[U5n U T;aMU"U 5(aU T:XaTn OX:XaUnOTU U :XaU n OU nU bUbOMHU /nU n X:wa.X U SnURU5 UTU 'U TU'Un X:waM.[ U5S:XaKX===S-ss'X=S:XaURU 5 X>==S-ss'X>S:XaURU5 O[USS5nUHnURU5 UR U5Hen U"U 5(dMU"UU 5(aM"UU==S- ss'UR U5 U U;dMHX:==S- ss'UR U 5 Mg M U U4X'GM U $) aReturns a canonical ordering of the nodes The canonical ordering of nodes (v1, ..., vn) must fulfill the following conditions: (See Lemma 1 in [2]_) - For the subgraph G_k of the input graph induced by v1, ..., vk it holds: - 2-connected - internally triangulated - the edge (v1, v2) is part of the outer face - For a node v(k+1) the following holds: - The node v(k+1) is part of the outer face of G_k - It has at least two neighbors in G_k - All neighbors of v(k+1) in G_k lie consecutively on the outer face of G_k (excluding the edge (v1, v2)). The algorithm used here starts with G_n (containing all nodes). It first selects the nodes v1 and v2. And then tries to find the order of the other nodes by checking which node can be removed in order to fulfill the conditions mentioned above. This is done by calculating the number of chords of nodes on the outer face. For more information see [1]_. Parameters ---------- embedding : nx.PlanarEmbedding The embedding must be triangulated outer_face : list The nodes on the outer face of the graph Returns ------- ordering : list A list of tuples `(vk, wp_wq)`. Here `vk` is the node at this position in the canonical ordering. The element `wp_wq` is a list of nodes that make up the outer face of G_k. References ---------- .. [1] Steven Chaplick. Canonical Orders of Planar Graphs and (some of) Their Applications 2015 https://wuecampus2.uni-wuerzburg.de/moodle/pluginfile.php/545727/mod_resource/content/0/vg-ss15-vl03-canonical-orders-druckversion.pdf .. [2] M. Chrobak and T.H. Payne: A Linear-time Algorithm for Drawing a Planar Graph on a Grid 1989 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.6677 rrrr cj>UT;aTUU:H$UT;aTUU:H$TUU:H=(d TUU:H$r r)ryouter_face_ccw_nbrouter_face_cw_nbrs ris_outer_face_nbr1get_canonical_ordering..is_outer_face_nbrsU & &$Q'1, , % %%a(A- -!!$)F->q-AQ-FFr7c>>UT;=(a UT;=(d UT:H$r r)r marked_nodesrBr)s ris_on_outer_face0get_canonical_ordering..is_on_outer_faces" $M!/A*A*LQ"WMr7Nccw) rintsetrrneighbors_cw_orderdiscardrradditernextr9)rr$r*chords ready_to_pickprev_nbridxrDrHr#nbrcanonical_orderingr,r/r1 nbr_iteratorwp_wqnext_nbrnew_face_nodeswrGrBrCr)s @@@@rrrsz^ AB AB  F5L OMHQJ('18$?)$&x HS_q(!R0&0o(#?1GN//2C$$->q-F-F Q %%a(3#ioo&7"88HqHq"" 3y()A-q" 5     I88;< |$Cl"$$"9BYB(-2 !~".).i |C(/H LL "%- c "+. x (Ci u:? J!OJzQ!!"% J!OJzQ!!"%!q-N#!!!$$77:C',,5Fq#5N5Nq Q %--a0n4#K1,K)11#6;$"#E M6P r7cURX5up4URX$5up5XU4;agX:waZURX5(aX$UpBnO$URXUS9 URXAUS9 XUpBnURX$5up5X:waMYgg)zTriangulates the face given by half edge (v, w) Parameters ---------- embedding : nx.PlanarEmbedding v1 : node The half-edge (v1, v2) belongs to the face that gets triangulated v2 : node NrJcw)next_face_half_edgehas_edge add_half_edge)rr)r*_r+v4s rtriangulate_facerf3s  ) )" 1EA  ) )" 1EA "X~ (   b % %BBB  # #B # 3  # #Br # 2BB--b5 (r7c[UR5S::aU[UR54$[R"U5n[R "U5Vs/sHn[ [U55PM nn[[U5S- 5HnX4nX4S-nURXV5 M! /n/n[5n UR5H]n URU 5HEn [X X5n U (dMURU 5 [U 5[U5:dMCU nMG M_ UH"n XLd U(dM[X SU S5 M$ U(aUSnUSnXUSnXVU/nX4$s snf)aTriangulates the embedding. Traverses faces of the embedding and adds edges to a copy of the embedding to triangulate it. The method also ensures that the resulting graph is 2-connected by adding edges if the same vertex is contained twice on a path around a face. Parameters ---------- embedding : nx.PlanarEmbedding The input graph must contain at least 3 nodes. fully_triangulate : bool If set to False the face with the most nodes is chooses as outer face. This outer face does not get triangulated. Returns ------- (embedding, outer_face) : (nx.PlanarEmbedding, list) tuple The element `embedding` is a new embedding containing all edges from the input embedding and the additional edges to triangulate the graph. The element `outer_face` is a list of nodes that lie on the outer face. If the graph is fully triangulated these are three arbitrary connected nodes. rrrJ)rrlistnxPlanarEmbeddingconnected_componentsrQrPrconnect_componentsrLrMmake_bi_connectedr9rf)rrrcomponent_nodesr"r)r*r$ face_list edges_visitedr#r\new_facefacer+s rrrPsy6 9??q $y///""9-I/1.E.Ei.PQ.PtDG}.POQ3'!+ ,   U #$$R,- JIEM __ --a0A(qHHx  *x=3z?2!)J1  !%6%6 YQa 9  ] ] ]2 u %b\   ERsFcX4U;a/$URX45 UnUnU/n[U5nURXE5upXQ:wdX:waXE:Xa[R"S5eXW;aGUR XIUS9 UR XUS9 URXY45 URX45 UnO"URU5 UR U5 UnURXY5upYURXE45 XQ:waMX:waMU$)aTriangulate a face and make it 2-connected This method also adds all edges on the face to `edges_counted`. Parameters ---------- embedding: nx.PlanarEmbedding The embedding that defines the faces starting_node : node A node on the face outgoing_node : node A node such that the half edge (starting_node, outgoing_node) belongs to the face edges_counted: set Set of all half-edges that belong to a face that have been visited Returns ------- face_nodes: list A list of all nodes at the border of this face zInvalid half-edger^r_)rOrLrariNetworkXExceptionrcr9) r starting_node outgoing_node edges_countedr)r*roface_setrdr+s rrmrms!0 %6 }45 B BI9~H  ) )" 1EA !4 8&&':; ; >  # #B # 3  # #Br # 2   rh '   rh 'B LL    R ..r6 2(#) !4, r7)F)T) collectionsrnetworkxri__all__rrrrfrrmrr7rr|s7# + ,up &dN6:B!J;r7