Miy}pSSKrSSKJr SSKJr SSKJrJrJ r J r SSK J r SSK J r SSKJr SS KJr SS KJrJrJrJrJrJrJrJr S S KJr S S KJr SSK r!SSK&J'r' Sr(S\\S\\4Sjr)S\\\\44Sjr*S\\\44Sjr+Sr,S*Sjr-S+Sjr.S*S\S\/4Sjjr0Sr1S,S\S\\4Sjjr2S\S\\4S jr3S-S!jr4S"r5S*S#jr6S.S$jr7S/S%jr8S0S&\9S'\/4S(jjr:S1S\4S)jjr;g!\"ar#SSK$J%r% \%"\#5r!Sr#C#NSr#C#ff=f!\"ar#SSK$J%r% \%"\#5r'Sr#C#NSr#C#ff=f)2N)ops)Polygon)boundsgeometrygraphgrouping)log)tol_path)reduce_cascade)transform_points) ArrayLikeIterableNDArrayNumberOptionalUnionfloat64int64)fit_circle_check) resample_path)ExceptionWrapper)Indexc [R"5n[U5S:Xa%[R"/[R S9U4$[U5S:Xa7UR S5 [R"S/[R S9U4$[U5VVs0sHup#U[US/5_M snnR5VVs0sHupE[U5S:XdMXE_M nnnURUR"55 [U5S:aA[[UR"5UR"5S/[U5-55nUR"5H~up(WRU5Hdn X):XaM XR!X 5(aUR#X)5 M7X R!X5(dMSUR#X5 Mf M [%UR'55n [R"[)U R555n [R"[)U R555n XS-S:Hn [U 5S:aU R+5S:a/nU [R,"U Vs/sHoUPM sn5n U HSnXU US-:HnUR/UR1[R2"UU55R555 MU [R6"U[R"55nURU 5 X4$s snnfs snnfs snf)a6 Given a list of shapely polygons with only exteriors, find which curves represent the exterior shell or root curve and which represent holes which penetrate the exterior. This is done with an R-tree for rough overlap detection, and then exact polygon queries for a final result. Parameters ----------- polygons : (n,) shapely.geometry.Polygon Polygons which only have exteriors and may overlap Returns ----------- roots : (m,) int Index of polygons which are root contains : networkx.DiGraph Edges indicate a polygon is contained by another polygon rdtyperrNr)nxDiGraphlennparrayradd_node enumerategetattritemsadd_nodes_fromkeysrzipvalues intersectioncontainsadd_edgedict in_degreelistmaxargsortextendsubgraphappendedges from_edgelist)polygonsr-ipolygonkvrtreebjdegreeindexesdegreesrootsr7rrootchildrens o/var/www/eduai.edurigo.com/storigo/production/storigo_env/lib/python3.13/site-packages/trimesh/path/polygons.pyenclosure_treerIs0zz|H 8}xx"((+X55 X! !xx288,h66 AJ(@S @S*!Aww"- -@S %'DA q6Q;   FKKM* 6{Q S $#f+9MNO ""1%Av{##HK00!!!'%%hk22!!!'&($$& 'FhhtFKKM*+GhhtFMMO,-G q[Q& 'E 7|aGKKMA-bjjU!;U)U!;<=D&,*::;H LL**299Xt+DEKKM N##E2::<8& ?m \"rFr:s rHedges_to_polygonsrZ|s$ h + ++ +HE2 %ghm&<=Hx))/)3 8}!*KE   D .))151BC1BAA;''1BC      D s0AD D 9,D %D= D  DDD r9cS/[U5-nS/[U5-n[U5Hup4[U5uX#'X'M [R"U5[R"U54$)z7 Find the OBBs for a list of shapely.geometry.Polygons N)r!r% polygon_obbr"r#)r9 rectangles transformsr:ps rH polygons_obbr`sd#h-'J#h-'J(#'21~$ z}$ 88J *!5 55r;c[US5(a+[R"URR5nO-[ U[R 5(aUnO [S5e[R"U5up#[R(af[XS9n[R"U*S- URSS95(de[R"US- URSS95(deX#4$)a Find the oriented bounding box of a Shapely polygon. The OBB is always aligned with an edge of the convex hull of the polygon. Parameters ------------- polygons : shapely.geometry.Polygon Input geometry Returns ------------- transform : (3, 3) float Transformation matrix which will move input polygon from its original position to the first quadrant where the AABB is the OBB extents : (2,) float Extents of transformed polygon rXz"polygon or points must be providedpointsmatrix@raxis)rVr" asanyarrayrXcoordsrRrSrWroriented_bounds_2Dtolstrictr allcloseminr2)r;rd transformextentsmoveds rHr\r\s(w ##w//667 GRZZ ( (=>>226:I zz A{{G8c>599!9+<===={{7S=%)))*;<<<<  rac[R"U[RS9n[US5(a*[ X5VVs/sHup#[ X#5PM nnnU$[ [R"URR5U5SS2SS24nURVs/sH6n[ [R"UR5U5SS2SS24PM8 nn[XWS9nU$s snnfs snf)a& Transform a polygon by a a 2D homogeneous transform. Parameters ------------- polygon : shapely.geometry.Polygon 2D polygon to be transformed. matrix : (3, 3) float 2D homogeneous transformation. Returns -------------- result : shapely.geometry.Polygon Polygon transformed by matrix. rrNNrrO) r"rirrVr*transform_polygonr r#rXrj interiorsr)r;rer_tresultrPr:rQs rHrtrts ]]6 4Fw  69'6JK6Jda#A)6JK RXXg&6&6&=&=> G2A2 NEFMEVEV EV!((+V4QU;EV  5 .F ML  s C4*=C:crUbEURS:Xde[[R"URR 5US9nO*[R"URR 5n[R"UR SS9URSS9/5nURS:XdeU$)aO Get the transformed axis aligned bounding box of a shapely Polygon object. Parameters ------------ polygon : shapely.geometry.Polygon Polygon pre-transform matrix : (3, 3) float or None. Homogeneous transform moving polygon in space Returns ------------ bounds : (2, 2) float Axis aligned bounding box of transformed polygon. )ryrcrrgrr)shaper r"r#rXrjror2)r;rerdrs rHpolygon_boundsr|s"||v%%%!'2B2B2I2I)JSYZ'**112 XXvzzqz)6::1:+=> ?F <<6 !! ! Mrac ^^SSKJn UU4SjnTcUR5mTRSS5 URR S:Xa"UR Vs/sH oe"U5PM nO4[US5(aUVs/sH oe"U5PM nO UbU"U5 U(aUR5 T$s snfs snf)z Plot a shapely polygon using matplotlib. Parameters ------------ polygon : shapely.geometry.Polygon Polygon to be plotted show : bool If True will display immediately **kwargs Passed to plt.plot rNc>TR"URR0TD6 URHnTR"UR0TD6 M! gN)plotrXxyru)singleinterioraxeskwargss rH plot_singleplot..plot_single+sC 6??%%00((H IIx{{ -f -)raequaldatalim MultiPolygon__iter__) matplotlib.pyplotpyplotr set_aspect __class____name__rNrVshow)r;rrrpltrr:s `` rHrrs$.  |xxzOOGY'!!^3!(/AQ/ * % %!()AQ)  G   K 0)s B>C resolutionc^^UU4SjnTcSS/mU"UR5/S.nURHnUSRU"U55 M U$)a Return a version of a polygon with boundaries re-sampled to a specified resolution. Parameters ------------- polygon : shapely.geometry.Polygon Source geometry resolution : float Desired distance between points on boundary clip : (2,) int Upper and lower bounds to clip number of samples to avoid exploding count Returns ------------ kwargs : dict Keyword args for a Polygon constructor `Polygon(**kwargs)` c>URT- n[[R"U/TQ765n[ UR US9$)N)count)lengthintr"cliprrj)boundaryrrrs rHresample_boundary.resample_boundaries..resample_boundaryWs<*,BGGE)D)*X__E::rarOrQ)rXrur6)r;rrrrrs `` rHresample_boundariesrBs\*; |3x()9)9:R HF%%w0:;& Mrac[US5S:XaUS$[R"US[R"US545$)z Stack the boundaries of a polygon into a single (n, 2) list of vertices. Parameters ------------ boundaries : dict With keys 'shell', 'holes' Returns ------------ stacked : (n, 2) float Stacked vertices rQrrP)r!r"vstack) boundariess rHstack_boundariesrhsH :g 1$'"" 99j)299Z5H+IJ KKrac~[UR5S:Xa[R"[R"UR S5SS9R 5n[URRUS9nUb[R"USS- S[R5n[R"USSU/-USSU/- /[RS 9n[R"SS //[RS 9nXv4$SS KJn SS KJn UcE[R"[R"UR S5SS9R 5S - n['XUS9n [)U 5n U"U 5n U R*"U/U R,R.Q76n [R0"U S5n [R2"U R4[RS 9n XU R7S S9n[R8"U5n[R:"[U R,5[RS 9n[R<"[U55X'U R,UnXn[>R@(a/[R"UUU R,U- 5S:deUU4$)a Given a shapely polygon, find the approximate medial axis using a voronoi diagram of evenly spaced points on the boundary of the polygon. Parameters ---------- polygon : shapely.geometry.Polygon The source geometry resolution : float Distance between each sample on the polygon boundary clip : None, or (2,) int Clip sample count to min of clip[0] and max of clip[1] Returns ---------- edges : (n, 2) int Vertex indices representing line segments on the polygon's medial axis vertices : (m, 2) float Vertex positions in space rrzrg)scaleradiusih㈵>centerrr)Voronoi vectorizedd)r;rrF)!r!rur"ptpreshaperr2rrXrjrinfr#rr scipy.spatialrshapelyrrrr-rJTr6riridge_verticesalluniquezerosarangerlrm)r;rrrfitepsilonrJr7rrsamplesvoronoir-ridge containedmask edges_finals rH medial_axisr|s10 7  "rzz'..&9BFFHw//66eD ?ggc(mc14@GxxX!W-s8}7|/KLjjH HHq!fXRXX6E? "%"VVBJJw~~v>QGKKMPSS "'tTGw'GgG""7@W-=-=-?-?@Hyy5)H MM'00 AE 5/%%1%- .E % I 88C(() :DiiI/DO *H+K zzvvh{+g.>.>u.EEFMMM   rareturnc\[UR5URRURRURURUR R/n[ USS9up# nURU5 [R"U[RS9$)z Return a vector containing values representative of a particular polygon. Parameters --------- polygon : shapely.geometry.Polygon Input geometry Returns --------- identifier : (8,) float Values which should be unique for this polygon. T)return_centeredr) r!ru convex_hullarearrXsecond_momentsr4r"r#r)r;rw_ principals rH identifierrs G    ""  F(FA!Q MM) 88F"** --ract[R"[R"[RRU5[R-S-5[RS--5n[RRU5U-n[R "[R "U5[R"U545URS5-n[R"XDS45n[U5RS5n[US5(aURS$U$)a` Generate a random polygon with a maximum number of sides and approximate radius. Parameters --------- segments : int The maximum number of sides the random polygon will have radius : float The approximate radius of the polygon desired Returns --------- polygon : shapely.geometry.Polygon Geometry object with random exterior and no interiors. r)rrrN)r"sortcumsumrandompi column_stackcossinrrrbufferrVrN)segmentsranglesradiirdr;s rHrandom_polygonrs WWRYYryy//9BEEAAEF"%%RS)T UF II  X & /E __bffVnbffVn= >wAW WF YYq * +Ffo$$S)Gw  }}Q Nrac[R"[R"URS5SS9nUS-R 5S-nU$)z For a Polygon object return the diagonal length of the AABB. Parameters ------------ polygon : shapely.geometry.Polygon Source geometry Returns ------------ scale : float Length of AABB diagonal rzrrgr?)r"rrrsum)r;rqrs rH polygon_scalers?ffRZZ7a@G aZ   # %E Lrac^S/[U5-n[U5HFup4[U5S:aM[U5nUR(aXRU'M9[ XQ5X#'MH [R"U5nU$![ a Mo[ a [R"SSS9 Mf=f)a" Given a sequence of connected points turn them into valid shapely Polygon objects. Parameters ----------- paths : (n,) sequence Of (m, 2) float closed paths scale : float Approximate scale of drawing for precision Returns ----------- polys : (p,) list Filled with Polygon or None Nrzunrecoverable polygonT)exc_info) r!r%ris_validrUrW BaseExceptionr errorr"r#)pathsrr9r:pathr;s rHpaths_to_polygonsrs$vE "HU# t9q=  >dmG% ,W< $"xx!H O   > II- = >s A= A== B, B,+B,cSSKJn [R"URS5n[R "USS9n[ X-5nUSU[RRUS45--nUR"U/URQ76n X/n [U S5n X:aU SSU$[U5Hun [RRUS45U-US-nUR"U/URQ76n U RX5 U [U S5- n X:dMu O [R"U 5SUn U $)aO Use rejection sampling to generate random points inside a polygon. Note that this function may return fewer or no points, in particular if the polygon as very little area compared to the area of the axis-aligned bounding box. Parameters ----------- polygon : shapely.geometry.Polygon Polygon that will contain points count : int Number of points to return factor : float How many points to test per loop max_iter : int Maximum number of intersection checks is: > count * factor * max_iter Returns ----------- hit : (n, 2) float Random points inside polygon where n <= count rrrzrgrNr)rrr"rrrrrr-rr!ranger6r) r;rfactormax_iterrrrqper_looprdrhit hit_countrs rHsamplerBs;4#ZZ /FffV!$G5>"HAY299#3#3XqM#BB BF   w 2 2D <.CCF I1vfu~8_))""Ha=1G;vayH""76VXX6 6< SR\!    ))C.% C Jrac[US5(aUR(aU$UR[R5n[US5(aGUR [ R"UR Vs/sHoDRPM sn5nUR(a1[ R"URURUS9(aU$UcFS[ R"[ R"URS5SS9R5-nOSU-n[UR 5S:XGaHUR"RU5R n[U5S:Xa][%USS 9RU5nUR(a1[ R"URURUS9(aU$[ R&"UR"R(5n[ R*"S [ R,"USS9S -R/SS9S -S :5n [%XS 9n U R(a1[ R"U RURUS9(aU $URU5RU*5n [U S5(aW[ R&"U R V s/sHoRPM sn 5n U R U R5$U R(aG[ R"U RURUS9(a[0R2"S5 U $[5S5es snfs sn f)a Given a shapely.geometry.Polygon, attempt to return a valid version of the polygon through buffering tricks. Parameters ----------- polygon : shapely.geometry.Polygon Source geometry rtol : float How close does a perimeter have to be scale : float or None For numerical precision reference Returns ---------- repaired : shapely.geometry.Polygon Repaired polygon Raises ---------- ValueError If polygon can't be repaired rrN)rtolgMb`?rzrrgr)rPTrrg:0yE>z2Recovered invalid polygon through double bufferingzunable to recover polygon!)rVrrrlzerorNr"argmaxriscloserrrrmeanr!rurXrr#rjr6diffrr debugrW)r;rrbasicr:distanceringsreconrdrdedupebufferedr?areass rHrUrUs{0w ##(8(8 NN388 $Eug BIIu{{&C{!vv{&CDE ~~"**U\\7>>M  }266"**W^^V"D1MRRTT5= 7  "  ''1;; u:?%(+228>PT"U '**1124"''&q"9Q">!C!C!C!Ks!RUY!YZv~. ??rzz&--dSM~~h'..y9Hx!!(..9.Q&&.9:~~elln--RZZdS FG 1 22a'DP:s >M: M?precise precise_epsc 4[R"U[RS9nU[RR U5-n[R "XR R5n U(ayX:n X*:n [R"U R5U R5/5n U R5S:XaU R5n OU R5n X/U nOX:nXRRSS9nURUn[R"X!S9n[!UR"U5SS2SS24nU(GaUR$Un['[R("[R*"U55S-5n[R,"UU5nU[R."UUSS2SS2445nUSS2/SQ4USS2/S Q4:HRSS9R1SS9)n[2R4"UUVs/sHn[7U5PM sn5R9U5R9U*5$[:R<"U[R>"U5SS 9nUR@RCS 5n/nUHHnUURCS 5n[DRF"USS 9nURI[KUUUS95 MJ SnUbU[MU5- nUb5[RN"USS9RQ5nU[MU5U-- nO$[SU5S:XaUS$[SU5S:Xag[USU5n U b!U R9U5R9U*5$gs snf)a Project a mesh onto a plane and then extract the polygon that outlines the mesh projection on that plane. Note that this will ignore back-faces, which is only relevant if the source mesh isn't watertight. Also padding: this generates a result by unioning the polygons of multiple connected regions, which requires the polygons be padded by a distance so that a polygon union produces a single coherent result. This distance is calculated as: `apad + (rpad * scale)` Parameters ---------- mesh : trimesh.Trimesh Source geometry normal : (3,) float Normal to extract flat pattern along origin : None or (3,) float Origin of plane to project mesh onto ignore_sign : bool Allow a projection from the normal vector in either direction: this provides a substantial speedup on watertight meshes where the direction is irrelevant but if you have a triangle soup and want to discard backfaces you should set this to False. rpad : float Proportion to pad polygons by before unioning and then de-padding result by to avoid zero-width gaps. apad : float Absolute padding to pad polygons by before unioning and then de-padding result by to avoid zero-width gaps. tol_dot : float Tolerance for discarding on-edge triangles. precise : bool Use the precise projection computation using shapely. precise_eps : float Tolerance for precise triangle checks. Returns ---------- projected : shapely.geometry.Polygon or None Outline of source mesh Raises --------- ValueError If max_regions is exceeded rrrrg)originnormalNr)rrr)rrr)nodes)r)rr) require_count)r7rJrc$URU5$r)union)ar?s rHprojected..ws !''!*ra)+r"r#rlinalgnormdot face_normalsrrrorargminface_adjacencyrrplane_transformr rJfacesrabslog10roundranyr unary_unionrrrconnected_componentsnonzero edges_sortedrr group_rowsr4rZfloatrr2r!r )!meshrr ignore_signrpadapadtol_dotrrdot_facefrontbackrpicksideadjacency_check adjacencyto_2D vertices_2Drdigitsrounded trianglesvalidf face_groupsr7r9edgegrouppaddingrreduceds! rH projectedr3sI|XXfBJJ /F biinnV$$Fvvf//112H"(" %))+txxz23 99;! <<>D<<>D}T"!../333;O##O4I  $ $F BE"4==%8BQB?K 4 RVVBHH[12Q67((;/BOOUE!RaR%L,ABC AyL)Yq)|-DDIIqIQUUV   OO51AB1AAWQZ1AB C VK V[L ! ,,Ybjj>Nq>QRK    % %g .EHU|##G,##D:)U kRS G 5; {+//15;&& X! { X! 4h?G~~g&--wh77QCs"Nc[R"S5nU(a=[R"URR5*USS2S4'[ X5n[R"UR R5n[R"USUSS45RupEURupgXG-Xe-- n[R"XU-XW--Xw---5S- n [R"XU-XF--Xf---5S- n [R"XU-SU-U--SU-U--Xe---5S- n URHn [R"U R5n[R"USUSS45RupEURupgXG-Xe-- nU [R"XU-XW--Xw---5S- -n U [R"XU-XF--Xf---5S- -n U [R"XU-SU-U--SU-U--Xe---5S- -n M XU /n U(dU $[R"X- S- S-U S--5nX-S- U-nX-S- U- nUU/n[R"U SS S 9(aS nOP[R"X5(aS [R-nO!S [R"SU -X- - 5-n[R"U5n[R "U5nUUS'UUS'U*US'UUS'U UUU4$)a Calculate the second moments of area of a polygon from the boundary. Parameters ------------ polygon : shapely.geometry.Polygon Closed polygon. return_centered : bool Get second moments for a frame with origin at the centroid and perform a principal axis transformation. Returns ---------- moments : (3,) float The values of `[Ixx, Iyy, Ixy]` principal_moments : (2,) float Principal second moments of inertia: `[Imax, Imin]` Only returned if `centered`. alpha : float Angle by which the polygon needs to be rotated, so the principal axis align with the X and Y axis. Only returned if `centered`. transform : (3, 3) float Transformation matrix which rotates the polygon by alpha. Only returned if `centered`. ryNrrg(@g8@rfrg-q=)atolrg?r)rr)rr)rr)rr)r"eyer#centroidrjrtrXrrrrusqrtrrarctanrr)r;rrprjx1y1x2y2r=IxxIyyIxyrmomentsrFImaxIminprincipal_momentsalpha cos_alpha sin_alphas rHrr~s.:q IHHW%5%5%<%<== "1"a%#G7XXg&&-- .F YYr F3BK0 1 3 3FB XXFB "'A &&2g'"'12 3d :C &&2g'"'12 3d :C &&2gB +a"frk9BGCD E LC%%(//*F2Js 4577 Gbg  rvva7RW,rw6784?? rvva7RW,rw6784?? rvva7QVb[01r6B;>HIJTQQ&oG  77SY#%!+c1f4 5D I t #D I t #Dt  zz#s' C  ruu biic SY 788u Iu IIdOIdO jIdOIdO %ui 77rar)NTN)NN)rg?)g? )Nr)NTrN绽|=FrI)F)<numpyr"rrshapely.geometryrrrrr constantsr r rl iterationr transformationsr typedrrrrrrrrsimplifyr traversalrnetworkxrrE exceptionsr rtree.indexrrIrZr`r\rtr|rrrrrrrrrrrUboolr3rrarHrYs$00'&.YYY&$ !Zz1WU^1ww7G1h65'!2I!=>6"w/0"J@8#L##e#LL(L!L!hv.>L!^..GG$4.>6(&RAHP3l  b8b8b8JV8GV8]. ! B  - Q E  s0C6D6D<DDD5D00D5