Tiy}ddlZddlmZddlmZddlmZmZm Z m Z ddl m Z ddl m ZddlmZdd lmZdd lmZmZmZmZmZmZmZmZd d lmZd d lmZ ddl Z!n##e"$rZ#ddl$m%Z%e%e#Z!YdZ#[#ndZ#[#wwxYw ddl&m'Z'n##e"$rZ#ddl$m%Z%e%e#Z'YdZ#[#ndZ#[#wwxYwdZ(deedeefdZ)deeeeffdZ*deeeffdZ+dZ,d3dZ-d4dZ.d3dede/fdZ0dZ1d5dedeefdZ2ded eefd!Z3d6d$Z4d%Z5d3d&Z6d7d)Z7d8d+Z8 d9d/e9d0e/fd1Z:d:defd2Z;dS);N)opsPolygon)boundsgeometrygraphgrouping)log)tol_path)reduce_cascade)transform_points) ArrayLikeIterableNDArrayNumberOptionalUnionfloat64int64)fit_circle_check) resample_path)ExceptionWrapper)Indexc  tj}t|dkr"tjgtj|fSt|dkr8|dtjdgtj|fSddt|DD}| |j t|dkrItt|j |j dgt|z}|jD]\}}||D]x}||kr ||||r|||A||||r|||yt#| tjt' }tjt' }||dzdk} t|dkr|dkrg} | tj fd| D} | D]d} || | dzk} | |tj| | etj| tj}| | | |fS) az 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 rdtyperc@i|]\}}t|dk||S))len).0kvs O/DATA/AppData/hermes/venv/lib/python3.11/site-packages/trimesh/path/polygons.py z"enclosure_tree..As9 Aq q66Q;; 1 ;;c8i|]\}}|t|dgS)r)getattr)r"ipolygons r%r&z"enclosure_tree..Cs7   2z"enclosure_tree..os!;!;!;&)!;!;!;r')nxDiGraphr!nparrayradd_node enumerateitemsadd_nodes_fromkeysrzipvalues intersectioncontainsadd_edgedict in_degreelistmaxargsortextendsubgraphappendedges from_edgelist)polygonsr=rtreer*bjindexesdegreesrootsrGrootchildrenr/s @r%enclosure_treerRs?0z||H 8}}x"(+++X55 X!  !x28,,,h66  @I(@S@S   %'' F KFKMM*** 6{{Q S  $#f++9MNNOO  ( (1""1%% ( (AAvv{##HQK00 (!!!Q''''!%%hqk22 (!!!Q''' (($$&& ' 'FhtFKKMM**++GhtFMMOO,,--G Wq[Q& 'E 7||aGKKMMA--bj!;!;!;!;U!;!;!;<<= O ODw&,*::;H LL**29Xt+D+DEEKKMM N N N N#E2:<<88&&& (?r'rGverticesct|tjsJgtj|dD]u} t t ||}t|dr|j n |f#t$rYrwxYwtdkrSt\}fd|DS)aw Given an edge list of indices and associated vertices representing lines, generate a list of polygons. Parameters ----------- edges : (n, 2) Indexes of vertices which represent lines vertices : (m, 2) Vertices in 2D space. Returns ---------- polygons : (p,) shapely.geometry.Polygon Polygon objects with interiors dfs)modegeomsrcg|]B}t|jfd|DCS)c*g|]}|jSr-)exterior)r"r*rIs r%r0z0edges_to_polygons...s CCCA8A;'CCCr'shellholes)rrZr9)r"rPrIrJs r%r0z%edges_to_polygons..si     4.)CCCCd1B1BCCC      r') isinstancer3ndarrayr traversalsrepair_invalidrhasattrrDrWrF ValueErrorr!rR)rGrSrUrepairedrOrIrJs @@r%edges_to_polygonsre|s$ h + +++ +HE222   %ghsm&<&<==Hx)) *////)))    H  8}}!**KE4          sA"B B*)B*rIcdgt|z}dgt|z}t|D]\}}t|\||<||<tj|tj|fS)z? Find the OBBs for a list of shapely.geometry.Polygons N)r!r6 polygon_obbr3r4)rI rectangles transformsr*ps r% polygons_obbrks|#h--'J#h--'J(##661'21~~$ 1 z!}} 8J  *!5!5 55r'r+ct|drtj|jj}n,t |tjr|}ntdtj |\}}tj rnt||}tj | dz |dsJtj |dz |dsJ||fS)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 rZz"polygon or points must be providedpointsmatrix@raxis)rbr3 asanyarrayrZcoordsr^r_rcroriented_bounds_2DtolstrictrallcloseminrB)r+rn transformextentsmoveds r%rgrgs(w ##?w/677 GRZ ( (?=>>>26::Iw z= yAAA{G8c>599!9+<+<====={7S=%)))*;*;<<<<< g r'cXtjtjt|drdt |D}|St tj|jjddddf}fd|j D}t||}|S)aV 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. rrWc4g|]\}}t||Sr-)transform_polygon)r"rjts r%r0z%transform_polygon..s'KKKda#Aq))KKKr'Nrcvg|]5}ttj|jddddf6S)Nr)rr3r4rt)r"r*ros r%r0z%transform_polygon..sN   @A!(++V44QQQU;   r'r[) r3rsrrbr:rr4rZrt interiorsr)r+roresultr\r]s ` r%rrs ]6 4 4 4Fw  KKc'66J6JKKK RXg&6&=>> G G2A2 NE    ELEV   E5 . . .F Mr'cR|;|jdksJttj|jj|}ntj|jj}tj|d|dg}|jdksJ|S)a 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. N)rrmrrqrr)shaperr3r4rZrtryrB)r+rornrs r%polygon_boundsrs"|v%%%%!'2B2I)J)JSYZZZ'*122 Xvzzqz))6::1:+=+=> ? ?F <6 ! ! ! ! Mr'Tc Hddlm}fd|dd|jjdkrfd|jDn,t|drfd |Dn | ||r|S) 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 rNcnj|jji|jD]}j|jidSN)plotrZxyr)singleinterioraxeskwargss r% plot_singlezplot..plot_single+sW 6?%0000( . .H DIx{ -f - - - - . .r'equaldatalim MultiPolygonc&g|] }|Sr-r-r"r*rs r%r0zplot..6s!///AQ///r'__iter__c&g|] }|Sr-r-rs r%r0zplot..8s!)))AQ)))r') matplotlib.pyplotpyplotr set_aspect __class____name__rWrbshow)r+rrrpltrs `` @r%rrs$#####......  |xxzzOOGY'''!^33///////// * % %)))))))))   G   Kr' resolutioncfd}ddg||jgd}|jD]&}|d||'|S)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|jz }ttj|gR}t |j|S)N)count)lengthintr3cliprrt)boundaryrrrs r%resample_boundaryz.resample_boundaries..resample_boundaryWsE*,BGE)D)))**X_E::::r'Nr[r])rZrrF)r+rrrrrs `` r%resample_boundariesrBs*;;;;;; |3x(()9::R H HF%<<w00::;;;; Mr'ct|ddkr|dStj|dtj|dfS)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 r]rr\)r!r3vstack) boundariess r%stack_boundariesrhsP :g 1$$'"" 9j)29Z5H+I+IJ K KKr'cXt|jdkrtjtj|jdd}t|jj |}|tj |ddz dtj }tj |d d|gz|d d|gz gtj }tj dd ggtj }||fSdd lm}dd lm} |Ctjtj|jdddz }t'|||} t)| } || } | j|g| jjR} tj| d} tj| jtj } | | | d }tj|}tjt| jtj }tjt|||<| j|}||}t>j r.tj||| j|z dksJ||fS)ai 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 rrrq)scaleNradiusih㈵>centerrr)Voronoi vectorizedd)r+rrF)!r!rr3ptpreshaperrBrrZrtrinfr4rr scipy.spatialrshapelyrrrr=rSTrFrsridge_verticesalluniquezerosarangervrw)r+rrrfitepsilonrSrGrrsamplesvoronoir=ridge containedmask edges_finals r% medial_axisr|s0 7 ""rz'.&99BBBFFHHw/6eDDD ?gc(mc14@@GxX!W-s8}7|/KLjH Hq!fXRX666E(? "%%%%%%""""""VBJw~v>>QGGGKKMMPSS "'jtTTTGw''GggG"z"7@W-=-?@@@Hy5))H M'0 A A AE (5/%%1%-- .E %  I 8C()) : : :DiI//DO *Hu+K zNvh{+g.>u.EEFFMMMM   r'returnct|j|jj|jj|j|j|jjg}t |d\}}}}||tj |tj S)a 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!r convex_hullarearrZsecond_momentsrDr3r4r)r+r_ principals r% identifierrs G  "  F(FFFAy!Q MM) 8F"* - - --r'r?cftjtjtj|tjzdztjdzz}tj||z}tjtj|tj|f|dz}tj ||df}t| d}t|dr |j dS|S)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)rrrW)r3sortcumsumrandompi column_stackcossinrrrbufferrbrW)segmentsranglesradiirnr+s r%random_polygonrs WRYry//99BEAAEFF"%RS)T U UF I  X & & /E _bfVnnbfVnn= > >wAWAW WF Yq * + +Ffoo$$S))Gw   }Q Nr'ctjtj|jdd}|dzdz}|S)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 rrrqr?)r3rrrsum)r+r{rs r% polygon_scalersEfRZ77a@@@G aZ    # %E Lr'chdgt|z}t|D]z\}}t|dkr t|}|jr|||<nt ||||<J#t $rYVt $rtjddYwwxYwtj |}|S)aV Given a sequence of connected points turn them into valid shapely Polygon objects. Parameters ----------- paths : (n,) sequence Of (m, 2) float closed paths scale : float Approximate scale of drawing for precision Returns ----------- polys : (p,) list Filled with Polygon or None Nr zunrecoverable polygonT)exc_info) r!r6ris_validrarc BaseExceptionr errorr3r4)pathsrrIr*pathr+s r%paths_to_polygonsrs$vE "HU##>>4 t99q==  >dmmG =% ,We<<     H > > > I- = = = = = = >x!!H Os/A-- B9BB? cddlm}tj|jd}tj|d}t ||z}|d|tj|dfzz}|j|g|j R} || g} t| d} | |kr| dd|St|D]}} tj|df|z|dz}|j|g|j R} | || | t| dz } | |krn~tj | d|} | S)a 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 rrrrqrNr)rrr3rrrrrr=rr!rangerFr) r+rfactormax_iterrrr{per_looprnrhit hit_countrs r%samplerBs4#"""""Z / /FfV!$$$G56>""HAY29#3#3XqM#B#BB BF : w 2 2 2 2D $<.CCF IE1vfuf~8__  )""Ha=11G;vayH"z"76VX666 6$<   SR\\! u   E  )C..% C Jr'rct|dr |jr|S|tj}t|dr.|jt jd|jD}|jr#t j|j |j |r|S|Ddt j t j |j dd  z}nd|z}t|jdkr*|j|j}t|d krSt#|d |}|jr#t j|j |j |r|St j|jj}t jd t j|d d zd dzdk}t#|| } | jr#t j| j |j |r| S||| } t| drBt jd| jD} | j| S| jr7t j| j |j |rt/jd| St3d)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 rrWcg|] }|j Sr-r)r"r*s r%r0z"repair_invalid..s&C&C&C!qv&C&C&Cr')rtolNgMb`?rrrqr)r\Trrg:0yE>cg|] }|j Sr-r)r"rKs r%r0z"repair_invalid..s999Q!&999r'z2Recovered invalid polygon through double bufferingzunable to recover polygon!)rbrrrvzerorWr3argmaxiscloserrrrmeanr!rrZrr4rtrFdiffrr debugrc) r+rrbasicdistanceringsreconrnrdedupebufferedareass r%raras0w ##(8 NN38 $ $EugF BI&C&Cu{&C&C&CDDE ~"*U\7>MMM  }26"*W^V"D"D1MMMRRTTT5= 7 "" ''11; u::??%(+++228<PT"U"U"U  '*1224"'&q"9"9"9Q">!C!C!C!K!Ks!RUY!YZZvf~... ? rz&-dSSS M~~h''..y99Hx!!.99(.999::~ellnn--RZdSSS FGGG 1 2 22r'r绽|=Fprecise precise_epsc tj|tj}|tj|z}tj||jj} |r| |k} | | k} tj| | g} | dkr| } n| } | | g| }n| |k}||j  d}|j |}tj||}t!|j|ddddf}|r|j|}t'tjtj|dz}tj||}|tj||ddddff}|ddgdf|ddgd fk dd}t3jd ||D|| St9j|tj|d }|j d }g}|D]]}|| d }tCj"|d}|#tI|||^d}||tK|z }|>tj&|d'}|tK||zz }n0tQ|dkr|dStQ|dkrdStSd|}|)||| SdS)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 rrrrq)originnormalNr)rrr)rrrc,g|]}t|Sr-r)r"fs r%r0zprojected..RsBBBAWQZZBBBr')nodes)r)rr) require_count)rGrSrc,||Sr)union)arKs r%zprojected..ws!''!**r')*r3r4rlinalgnormdot face_normalsrrryrargminface_adjacencyrrplane_transformrrSfacesrabslog10roundranyr unary_unionrr connected_componentsnonzero edges_sortedrr group_rowsrDrefloatrrBr!r ) meshrr ignore_signrpadapadtol_dotrrdot_facefrontbackrpicksideadjacency_check adjacencyto_2D vertices_2Dr%digitsrounded trianglesvalid face_groupsrGrIedgegrouppaddingrreduceds r% projectedrGs|XfBJ / / /F binnV$$$Fvfd/122H"7"7(" %))++txxzz233 99;;!  <<>>DD<<>>Dt}T"'!4./333;;O#O4I  $F6 B B BE"4=%88BQB?K  4 RVBH[1122Q677(;//BOUE!!!RaR%L,ABBC AAAyyyL)Yqqq)))|-DDIIqIQQUUV    OBB51ABBB C C VK V[L ! ! ,Ybj>N>Nq>QRRRK   % %g . .EHTTU|##G,,#D:::)U kRRRSSSSG 5;; {+++//115;;&& X!  { X!  t44h??G~~g&&--wh777r'ctjd}|r6tj|jj |dddf<t ||}tj|jj}tj|d|ddfj\}}|j\}}||z||zz }tj |||z||zz||zzzdz } tj |||z||zz||zzzdz } tj |||zd|z|zzd|z|zz||zzzdz } |j D]} tj| j}tj|d|ddfj\}}|j\}}||z||zz }| tj |||z||zz||zzzdz z} | tj |||z||zz||zzzdz z} | tj |||zd|z|zzd|z|zz||zzzdz z} | | | g} |s| Stj | | z dz dz| dzz}| | zdz |z}| | zdz |z }||g}tj | dd rd }nEtj | | rd tj z}n d tjd| z| | z z z}tj|}tj|}||d<||d<| |d<||d<| |||fS)a> Calculate the second moments of area of a polygon from the boundary. Parameters ------------ polygon : shapely.geometry.Polygon Closed polygon. return_centered : bool Get second moments for a frame with origin at the centroid and perform a principal axis transformation. Returns ---------- moments : (3,) float The values of `[Ixx, Iyy, Ixy]` principal_moments : (2,) float Principal second moments of inertia: `[Imax, Imin]` Only returned if `centered`. alpha : float Angle by which the polygon needs to be rotated, so the principal axis align with the X and Y axis. Only returned if `centered`. transform : (3, 3) float Transformation matrix which rotates the polygon by alpha. Only returned if `centered`. rNrrg(@g8@rprg-q=)atolrg?r)rr)rr)rr)rr)r3eyer4centroidrtrrZrrrrsqrtrrarctanrr)r+rrzrtx1y1x2y2r$IxxIyyIxyrmomentsrPImaxIminprincipal_momentsalpha cos_alpha sin_alphas r%rr~s:q I8HW%5%<=== "1"a%#GY77Xg&- . .F Yr F3B3K0 1 1 3FB XFB R"r'A &b2gR'"r'12 3 3d :C &b2gR'"r'12 3 3d :C &b2gB +a"frk9BGCD E E LC% R R(/**F2Jss 4557BB Gb2g  rva27R"W,rBw67884?? rva27R"W,rBw67884?? rva27QVb[01r6B;>bHIJJTQQCoG  7S3Y#%!+c1f4 5 5D #I t #D #I t #Dt  z#s'''9 C  9ru bic S3Y 7888u Iu IIdOIdO jIdOIdO %ui 77r'r)NTN)NN)rr)rr)Nr)NTrNrFr)F)<numpyr3rrshapely.geometryrrrr r constantsr r rv iterationr transformationsrtypedrrrrrrrrsimplifyr traversalrnetworkxr1rE exceptionsr rtree.indexrrRrerkrgrrrr/rrrrrrrrraboolrGrr-r'r%rjs $$$$$$000000000000''''''&&&&&&......YYYYYYYYYYYYYYYYYYYY&&&&&&$$$$$$.-----  !  BBBBBB   !!!!!!!   ------  Q  EEEEEE  ZZZz1WU^1ww7G1111h65'!2I!=>6666"w/0""""J@8####L###e####LLLL(L!L!L!hv.>L!L!L!L!^..GG$4....>6(&&&&RAAAAHP3P3P3P3l  b8b8b8b8b8b8b8JV8V8GV8V8V8V8V8V8s0AA; A66A;?BB& B!!B&