:vjTddlZddlmZddlmZddlmZmZm Z m Z ddl m Z ddl m ZddlmZdd lmZdd lmZmZmZmZmZmZmZdd lmZd d lmZd dlm Z  ddl!Z" ddl'm(Z(dZ)deedeefdZ*deeezfdZ+deezfdZ,dZ-d,dZ.d-dZ/d,dede0fdZ1dZ2d.dededzfdZ3ded eefd!Z4d/d"efd#Z5d$Z6d,d%Z7d0d"efd&Z8d1d'Z9 d2d(e:d)e0fd*Z;d3defd+ZrFr:s rHedges_to_polygonsrZs$ h ++ +HE2 %ghsm&<=Hx)/)3 8}!*KE4   D 4.))15d1BC1BA8A;''1BC      D s*AD/-DD2 D D  D Dr9cdgt|z}dgt|z}t|D]\}}t|\||<||<tj|tj|fS)z? Find the OBBs for a list of shapely.geometry.Polygons N)r!r% polygon_obbr"r#)r9 rectangles transformsr:ps rH polygons_obbr`sj#h-'J#h-'J(#1'21~$ 1 z!}$ 88J *!5 55r;ct|dr*tj|jj}n(t |tj r|}n tdtj|\}}tjrdt||}tj| dz |jdsJtj|dz |jdsJ||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 rXz"polygon or points must be providedpointsmatrix@raxis)rVr" asanyarrayrXcoordsrRrSrWroriented_bounds_2Dtolstrictr allcloseminr2)r;rd transformextentsmoveds rHr\r\s(w #w//667 GRZZ (=>>226:Iw zz yA{{G8c>599!9+<==={{7S=%)))*;<<< g ractj|tj}t|dr*t ||Dcgc]\}}t ||}}}|St tj|jj|ddddf}|jDcgc]4}t tj|j|ddddf6}}t||}|Scc}}wcc}w)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. rrNNrrO) r"rirrVr*transform_polygonr r#rXrj interiorsr)r;rer_tresultrPr:rQs rHrtrts ]]6 4Fw 69'66JK6Jda#Aq)6JK RXXg&6&6&=&=> G2A2 NEFMEVEV EV!((+V4QU;EV  5 .F ML  s C0&9C6cx|F|jdk(sJttj|jj |}n)tj|jj }tj|j d|jdg}|jdk(sJ|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. )ryrcrrgrr)shaper r"r#rXrjror2)r;rerdrs rHpolygon_boundsr|s"||v%%%!'2B2B2I2I)JSYZ'**112 XXvzzqz)6::1:+=> ?F <<6 !! ! Mrac pddlm}fd}|jjdd|jj dk(r!|j Dcgc] }|| c}n-t|dr|Dcgc] }|| c}n ||||r|jScc}wcc}w)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 rNcj|jji|jD]}j|ji yN)plotrXxyru)singleinterioraxeskwargss rH plot_singlezplot..plot_single1sG 6??%%00((H DIIx{{ -f -)raequaldatalim MultiPolygon__iter__) matplotlib.pyplotpyplotr set_aspect __class____name__rNrVshow)r;rrrpltrr:s `` rHrr"s$.  |xxzOOGY'!!^3!(/AQ/ * %!()AQ)  G   K 0)s B.=B3 resolutioncfd}ddg||jgd}|jD]}|dj|||S)a Return a version of a polygon with boundaries re-sampled to a specified resolution. Parameters ------------- polygon : shapely.geometry.Polygon Source geometry resolution : float Desired distance between points on boundary clip : (2,) int Upper and lower bounds to clip number of samples to avoid exploding count Returns ------------ kwargs : dict Keyword args for a Polygon constructor `Polygon(**kwargs)` c|jz }ttj|g}t |j |S)N)count)lengthintr"cliprrj)boundaryrrrs rHresample_boundaryz.resample_boundaries..resample_boundary]s<*,BGGE)D)*X__E::rarOrQ)rXrur6)r;rrrrrs `` rHresample_boundariesrHs\*; |3x()9)9:R HF%%w0:;& Mract|ddk(r|dStj|dtj|dfS)z Stack the boundaries of a polygon into a single (n, 2) list of vertices. Parameters ------------ boundaries : dict With keys 'shell', 'holes' Returns ------------ stacked : (n, 2) float Stacked vertices rQrrP)r!r"vstack) boundariess rHstack_boundariesrnsH :g 1$'"" 99j)299Z5H+IJ KKract|jdk(rtjtj|j ddj }t|jj|}|tj|ddz dtj}tj|dd|gz|dd|gz gtj }tjdd ggtj }||fSdd lm}dd lm} |Ftjtj|j ddj d z }t'|||} t)| } || } | j*|g| j,j.} tj0| d} tj2| j4tj } | | | j7d }tj8|}tj:t| j,tj }tj<t|||<| 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 rrzrg)scaleradiusih㈵>centerrr)Voronoi vectorizedd)r;rrF)!r!rur"ptpreshaperr2rrXrjrinfr#rr scipy.spatialrshapelyrrrr-rJTr6riridge_verticesalluniquezerosarangerlrm)r;rrrfitepsilonrJr7rrsamplesvoronoir-ridge containedmask edges_finals rH medial_axisrs=0 7  "rzz'..&9BFFHw//66eD ?ggc(mc14@GxxX!W-s8}7|/KLjjH HHq!fXRXX6E(? "%"VVBJJw~~v>QGKKMPSS "'jtTGw'GgG"z""7@W-=-=-?-?@Hyy5)H MM'00 AE (5/%%1%- .E % I 88C(() :DiiI/DO *Hu+K zzvvh{+g.>.>u.EEFMMM   rareturncht|j|jj|jj|j|j|j jg}t |d\}}}}|j|tj|tjS)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!ru convex_hullarearrXsecond_momentsr4r"r#r)r;rw_ principals rH identifierrs G    ""  F(FAy!Q MM) 88F"** --raseedc>t|}tjtj|j |tj zdztj dzz}|j ||z}tj tj|tj|f|jdz}tj||df}t|jd}t|dr|jdS|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 seed : None or int Seed for deterministic results, otherwise OS entropy. Returns --------- polygon : shapely.geometry.Polygon Geometry object with random exterior and no interiors. r)rrrN)rr"sortcumsumrandompi column_stackcossinrrrbufferrVrN)segmentsrrranglesradiirdr;s rHrandom_polygonrs$d #F WWRYYv}}X6>BCruuqyQ RF MM( #f ,E __bffVnbffVn= >wAW WF YYq * +Ffo$$S)Gw }}Q Nractjtj|jdd}|dzj dz}|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 rzrrgr?)r"rrrsum)r;rqrs rH polygon_scalers?ffRZZ7a@G aZ   # %E LracLdgt|z}t|D]A\}}t|dkr t|}|jr|||<nt ||||<Ctj|}|S#t $rYft $rtjddYwxYw)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 Nrzunrecoverable polygonT)exc_info) r!r%ris_validrUrW BaseExceptionr errorr"r#)pathsrr9r:pathr;s rHpaths_to_polygonsr"s$vE "HU#4 t9q=  >dmG% ,We< $"xx!H O   > II- = >s,A66 B#B#"B#cddlm}tj|jd}tj |d}t ||z}t|} |d|| j|dfzz} |j|g| j} | | g} t| d} | |k\r| dd|St|D]g}| j|df|z|dz} |j|g| j} | j| | | t| dz } | |kDsgntj| 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 seed : None or int Seed for deterministic results, otherwise OS entropy. Returns ----------- hit : (n, 2) float Random points inside polygon where n <= count rrrzrgrNr)rrr"rrrrrrr-rr!ranger6r)r;rfactormax_iterrrrrqper_looprrdrhit hit_countrs rHsamplerKsG8#ZZ /FffV!$G56>"Hd #F AY6==(A#?? ?F :  w 2 2D $<.CCF IE1vfu~8_--1 .8F1IE"z""76VXX6 6$< SR\! u   ))C.% C Jract|dr|jr|S|jtj}t|drD|j t j|j Dcgc]}|jc}}|jr.t j|j|j|r|S|Gdt jt j|jddjz}nd|z}t|j dk(rA|j"j|j }t|dk(rXt%|d j|}|jr.t j|j|j|r|St j&|j"j(}t j*d t j,|dd zj/dd zd kD} t%||  } | jr.t j| j|j|r| S|j|j| } t| drTt j&| j D cgc]} | jc} } | j | jS| jrCt j| j|j|rt1j2d| St5dcc}wcc} w)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 rHrUrUsx0w #(8(8 NN388 $Eug BIIu{{&C{!qvv{&CDE ~~"**U\\7>>M  }266"**W^^V"D1MRRTT5= 7  "  ''1;; u:?%(+228>PT"U '**1124"''&q"9Q">!C!C!C!Ks!RUY!YZvf~. ??rzz&--dSM~~h'..y9Hx!(..9.Q!&&.9:~~elln--RZZdS FG 1 22a'DP:s .M 6M precise precise_epsc 4tj|tj}|tjj |z}tj ||j j} |rz| |kD} | | k} tj| j| jg} | jdk(r| j} n| j} | | g| }n| |kD}||jjd}|j|}tj||}t!|j"|ddddf}|r|j$|}t'tj(tj*|dz}tj,||}|tj.||ddddff}|ddgdf|ddgd fk(jdj1d}t3j4||Dcgc] }t7|c}j9|j9| St;j<|tj>|d }|j@jCd }g}|D]L}||jCd }tEjF|d }|jItK|||Nd}||tM|z }|7tjN|djQ}|tM||zz }n"tS|dk(r|dStS|dk(rytUd|} | !| j9|j9| Sycc}w)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$|j|Sr)union)ar?s rHzprojected..s !''!*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 projectedr1sW|XXfBJJ /F biinnV$$Fvvfd//112H7"7(" %))+txxz23 99;! <<>D<<>Dt}T"'!4../333;O##O4I  $ $F6 BE"4==%8BQB?K 4 RVVBHH[12Q67((;/BOOUE!RaR%L,ABC AyL)Yq)|-DDIIqIQUUV   OO51AB1AAWQZ1AB C VK V[L ! ,,Ybjj>Nq>QRK    % %g .EHU|##G,##D:)U kRS G 5; {+//15;&& X! { X! 4h?G~~g&--wh77QCs$Nctjd}|r=tj|jj |dddf<t ||}tj|j j}tj|d|ddfj\}}|j\}}||z||zz }tj|||z||zz||zzzdz } tj|||z||zz||zzzdz } tj|||zd|z|zzd|z|zz||zzzdz } |jD]} 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 }nKtj| | rd tjz}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`. ryNrrg(@g8@rfrg-q=)atolrg?r)rr)rr)rr)rr)r"eyer#centroidrjrtrXrrrrusqrtrrarctanrr)r;rrprjx1y1x2y2r=IxxIyyIxyrmomentsrFImaxIminprincipal_momentsalpha cos_alpha sin_alphas rHrrsi:q IHHW%5%5%<%<== "1"a%#GY7XXg&&-- .F YYr F3BK0 1 3 3FB XXFB R"r'A &&b2gR'"r'12 3d :C &&b2gR'"r'12 3d :C &&b2gB +a"frk9BGCD E LC%%(//*F2Js 4577BB Gb2g  rvva27R"W,rBw6784?? rvva27R"W,rBw6784?? rvva27QVb[01r6B;>bHIJTQQ&CoG  77S3Y#%!+c1f4 5D #I t #D #I t #Dt  zz#s' C ruu biic S3Y 788u Iu IIdOIdO jIdOIdO %ui 77rar)NTN)NN)rg?N)g? N)Nr)NTrN绽|=FrG)F)=numpyr"rrshapely.geometryrrrrr constantsr r rl iterationr transformationsr typedrrrrrrrutilrsimplifyr traversalrnetworkxrrE exceptionsr rtree.indexrrIrZr`r\rtr|rrrrrrrrrrrUboolr1rrarHrXs$00'&.NNN#&$ !_D1WU^1ww7G1h68G,y86"7*"J@8#L##e#LL(L!L!ftmL!^..GG$4.><(&RD$DNP3l  b8b8b8JV8GV8s. ! B  - Q E  s0C*D *D/DD D'D""D'