'jUiddlmZddlmZmZmZmZddlmZddl Z ddl Z ddl m Z mZmZmZmZmZmZgdZe jdz Zd^d_d Z d`dadZ dbdcdZdddZdedZdfdZdgd#Z dhdid*Z djdkd2ZdZ Gd3d4eZ!Gd5d6Z"de d7dld<Z#dde d=dmd>Z$de d?dndBZ%dodGZ&GdHdIZ'dpdLZ(dqdNZ)drdRZ*dsdVZ+efdtdWZ,dedXZ-e dYdud[Z.e dYdvd\Z/dwd]Z0dS)x) annotations)SequenceIterableOptionalIterator)IntEnumN)Vec3Vec2Matrix44X_AXISY_AXISZ_AXISUVec)is_planar_facesubdivide_facesubdivide_ngonsPlanePlaneLocationStatenormal_vector_3psafe_normal_vectordistance_point_line_3dintersection_line_line_3dintersection_ray_polygon_3dintersection_line_polygon_3dbasic_transformationbest_fit_normalBarycentricCoordinateslinear_vertex_spacinghas_matrix_3d_stretchingspherical_envelopeinscribe_circle_tangent_length bending_anglesplit_polygon_by_plane is_face_normal_pointing_outwardsis_vertex_order_ccw_3d@& .>faceSequence[Vec3]returnboolct|dkrdSt|dkrdSd}tt|dz D]q}|||dz\}}} ||z ||z }n#t$rYNwxYw||}W|||sdSr|dSdS)zReturns ``True`` if sequence of vectors is a planar face. Args: face: sequence of :class:`~ezdxf.math.Vec3` objects abs_tol: tolerance for normals check FTNabs_tol)lenrangecross normalizeZeroDivisionErrorisclose)r(r0 first_normalindexabcnormals P/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/math/construct3d.pyrr/s 4yy1}}u 4yyA~~tLs4yy1}%%  uuqy()1a !e]]1q5))3355FF     H   !LL%%fg%>> 55 t 5s -B BBTquadsIterator[Sequence[Vec3]]c#nKtdkrtdttjz }fdt D}t D]<\}}|r||||||dz fV||dz ||fV||||fV=dS)zSubdivides faces by subdividing edges and adding a center vertex. Args: face: a sequence of :class:`Vec3` quads: create quad faces if ``True`` else create triangles r-z3 or more vertices required.c^g|])}||dzz*S))lerp).0ir(len_faces r= z"subdivide_face..ZsD###34Q T1q5H,-..###rBN)r1 ValueErrorr sumr2 enumerate)r(r>mid_possubdiv_locationr8vertexrFs` @r=rrKs 4yy1}}7888IIHhtnnx'G#####8=h###O#4:: v  :/%0'?5ST9;UU U U U U!%!),fg= = = =/%0'9 9 9 9 9 ::rHfacesIterable[Sequence[Vec3]]c#K|D]u}t||krtj|V,tj|t|z }t |D]\}}||dz ||fVvdS)zSubdivides faces into triangles by adding a center vertex. Args: faces: iterable of faces as sequence of :class:`Vec3` max_vertex_count: subdivide only ngons with more vertices rBN)r1r tuplerJrK)rPmax_vertex_countr(rLr8rNs r=rrfs77 t99( ( (*T"" " " " "htnns4yy0G!*4 7 7 v519ovw66666 7 77rHr9r r:r;c\||z ||z S)zlReturns normal vector for 3 points, which is the normalized cross product for: :code:`a->b x a->c`. )r3r4)r9r:r;s r=rrzs* E==Q   ) ) + ++rHverticesct|dkrtd|^}}}} ||z ||z S#t$rt |cYSwxYw)zjSafe function to detect the normal vector for a face or polygon defined by 3 or more `vertices`. r-3 or more vertices required)r1rIr3r4r5r)rVr9r:r;_s r=rrs  8}}q6777KAq!a)A}}QU##--/// )))x((((()s,AA32A3Iterable[UVec]ctj|}t|dkrtd|d}||ds|||j\}}}d}d}d}|ddD]=} | j\} } } ||| z|| z zz }||| z|| z zz }||| z|| z zz }| }| }| }>t|||S)zReturns the "best fit" normal for a plane defined by three or more vertices. This function tolerates imperfect plane vertices. Safe function to detect the extrusion vector of flat arbitrary polygons. r-rXrrBN)r listr1rIr6appendxyzr4) rV _verticesfirstprev_xprev_yprev_znxnynzvxyzs r=rrs (##I 9~~6777 aLE ==2 ' ' "YFFF B B B qrr]%1a vzfqj)) vzfqj)) vzfqj)) B   % % ' ''rHpointstartendfloatc||rtd||z }||z |}|j|jz }|dkrdSt j|S)zReturns the normal distance from a `point` to a 3D line. Args: point: point to test start: start point of the 3D line end: end point of the 3D line z Not a line.r])r6r5projectmagnitude_squaremathsqrt)rmrnrov1v2diffs r=rrst }}S/ ... B +  r " "B !4 4D s{{syrH绽|=line1line2virtualr0Optional[Vec3]cddlm}m}||||}t|dkrdS|d}|r|S|||r |||r|SdS)a Returns the intersection point of two 3D lines, returns ``None`` if lines do not intersect. Args: line1: first line as tuple of two points as :class:`Vec3` objects line2: second line as tuple of two points as :class:`Vec3` objects virtual: ``True`` returns any intersection point, ``False`` returns only real intersection points abs_tol: absolute tolerance for comparisons r)intersection_ray_ray_3d BoundingBoxrBN) ezdxf.mathrrr1inside)rzr{r|r0rrresrms r=rrs$@??????? ! !% 8 8C 3xx1}}t FE {5  ''KK,>,>,E,Ee,L,L 4rHrrrrBrBrBmoverscale z_rotationr ct|\}}}tj|||}|r|tj|z}t|}|js(|tj|j|j|jz}|S)aReturns a combined transformation matrix for translation, scaling and rotation about the z-axis. Args: move: translation vector scale: x-, y- and z-axis scaling as float triplet, e.g. (2, 2, 1) z_rotation: rotation angle about the z-axis in radians ) r r rz_rotateis_null translaterjrkrl)rrrsxsyszmrs r=rrseJBBr2r""A+ X z * **T I  G X  Y[)+ F FF HrHceZdZdZdZdZdZdS)rrrBr.r-N)__name__ __module__ __qualname__COPLANARFRONTBACKSPANNINGrHr=rrs"H E DHHHrHrceZdZdZdZd.dZed/d Zed0d Zed/d Z e d1dZ e d2dZ d3dZ e ZdZd4dZd5dZd5dZd6d7dZd6d8d Zd!ed"d9d&Zd:d)Zefd;d,Zd-S)&&& %-"""rHr*c|jS)zNormal vector of the plane.)rrs r=r<z Plane.normals |rHc|jS)z@The (perpendicular) distance of the plane from origin (0, 0, 0).)rrs r=distance_from_originzPlane.distance_from_origins ))rHc |j|jzS)zReturns the location vector.rrs r=vectorz Plane.vectors|d888rHr9r:r;'Plane'c ||z ||z }n#t$rtdwxYwt |||S)z+Returns a new plane from 3 points in space.z"undefined plane: colinear vertices)r3r4r5rIrdot)clsr9r:r;ns r=from_3pz Plane.from_3p#sw CQ a!e$$..00AA  C C CABB B CQa!!!s -0A rrct|} t||jS#t$rt dwxYw)z3Returns a new plane from the given location vector.zinvalid NULL vector)r rr4 magnituder5rI)rrris r= from_vectorzPlane.from_vector,sX LL 4 44 4  4 4 4233 3 4s &8AcB||j|jS)zReturns a copy of the plane.) __class__rrrs r=__copy__zPlane.__copy__5s~~dlD,FGGGrHcBdt|jd|jdS)NzPlane(z, ))reprrrrs r=__repr__zPlane.__repr__;s(KT\**KKd.HKKKKrHotherobjectr+cZt|tstS|j|jkSN) isinstancerNotImplementedr)rrs r=__eq__z Plane.__eq__>s)%'' "! !{el**rHricF|j||jz S)a Returns signed distance of vertex `v` to plane, if distance is > 0, `v` is in 'front' of plane, in direction of the normal vector, if distance is < 0, `v` is at the 'back' of the plane, in the opposite direction of the normal vector. )rrrrris r=signed_distance_tozPlane.signed_distance_toCs"|""T%???rHcPtj||S)zP>PPzz#v&&&rHorigin directionc|j} |j||z ||z }n#t$rYdSwxYw|||zzS)zReturns the intersection point of the infinite 3D ray defined by `origin` and the `direction` vector and this plane or ``None`` if there is no intersection. A coplanar ray does not intersect the plane! N)r<rrr5)rrrrrs r= intersect_rayzPlane.intersect_rayusl K /!%%--?155CSCSSFF    44 V+,,s3= A  A rNrc|j||jz }|| kr tjS||kr tjStjS)zjReturns the :class:`PlaneLocationState` of the given `vertex` in relative to this plane. )rrrrrrr)rrNr0rs r=rzPlane.vertex_location_statesT<##F++d.HH wh  %* *   %+ +%. .rHN)r<r rrp)r*r r*rp)r9r r:r r;r r*r)rrr*r)r*r)rrr*r+)rir r*rpr')rir r*r+)rrr*r+)rnr ror r*r})rr rr r*r})rNr r*r)rrr__doc__ __slots__rpropertyr<rr classmethodrrrcopyrrrrrr PLANE_EPSILONrrrrrHr=rrs 5I.... X***X*999X9"""["444[4HHHH DLLL++++ @@@@5555-----      37 '''''', - - - -%2 / / / / / / /rHrrpolygonIterable[Vec3]plane%tuple[Sequence[Vec3], Sequence[Vec3]]c~tj}g}g}g}t|}|j} |j} |D]2} || |} || z}|| 3|tjkr2|r.t|} | | dkr|}n~|}nz|tj kr|}nf|tj kr|}nR|tj krAt|}t|D]}|dz|z}||} ||}||} ||}| tj kr|| | tj kr|| | |ztj krq| | | z | || z z }| ||}||||t|dkrg}t|dkrg}t|t|fS)a7Split a convex `polygon` by the given `plane`. Returns a tuple of front- and back vertices (front, back). Returns also coplanar polygons if the argument `coplanar` is ``True``, the coplanar vertices goes into either front or back depending on their orientation with respect to this plane. rrBr-)rrr^rr<rr_rrrrrr1r2rCrS)rrrr0 polygon_type vertex_typesfront_vertices back_verticesrVwr<rN vertex_typepolygon_normal len_verticesr8 next_indexnext_vertex_type next_vertexinterpolation_weightplane_intersection_points r=r#r#s~&.L-/L!#N "MG}}H "A \F))11&'BB  # K(((()222  ),X66Nzz.))A--!) ( +1 1 1! +0 0 0 +4 4 48}} <(( ? ?E!)|3J&u-K+J7 e_F":.K0555%%f---0666$$V,,,..3E3NNN()FJJv,>,>(>&**&(CC($,2;;!5,,(%%&>???$$%=>>> ~   " "N }   ! !M  % "6"6 66rH)rboundaryr0cZt|}t|dkrtd t|}n#t$rYdSwxYwt |||d}|||||} | dSt| ||||S)aReturns the intersection point of the 3D line form `start` to `end` and the given `polygon`. Args: start: start point of 3D line as :class:`Vec3` end: end point of 3D line as :class:`Vec3` polygon: 3D polygon as iterable of :class:`Vec3` coplanar: if ``True`` a coplanar start- or end point as intersection point is valid boundary: if ``True`` an intersection point at the polygon boundary line is valid abs_tol: absolute tolerance for comparisons r-rXNrr) r^r1rIrr5rrr(_is_intersection_point_inside_3d_polygon) rnrorrrr0rVr<rips r=rrs.G}}H 8}}q6777#H-- tt &&**Xa[11 2 2E   eS8W  M MB zt 3 Hfh  A AArr0rrcTt|}t|dkrtd t|}n#t$rYdSwxYwt |||d}|||}|dSt|||||S)aReturns the intersection point of the infinite 3D ray defined by `origin` and the `direction` vector and the given `polygon`. Args: origin: origin point of the 3D ray as :class:`Vec3` direction: direction vector of the 3D ray as :class:`Vec3` polygon: 3D polygon as iterable of :class:`Vec3` boundary: if ``True`` intersection points at the polygon boundary line are valid abs_tol: absolute tolerance for comparisons r-rXNr) r^r1rIrr5rrrr) rrrrr0rVr<rrs r=rrs*G}}H 8}}q6777#H-- tt &&**Xa[11 2 2E   VY / /B zt 3 Hfh  rr list[Vec3]r<rcddlm}m}||}tj||}|t||||} | dks|r| dkr|SdS)Nr)is_point_in_polygon_2dOCSr/)rrrr r^points_from_wcsfrom_wcs) rrVr<rr0rrocs ocs_verticesstates r=rr$s76666666 #f++C9S00::;;L " " S\\"   g   E qyyXy%1** 4rHc*eZdZdZd dZdd Zdd Zd S)rahBarycentric coordinate calculation. The arguments `a`, `b` and `c` are the cartesian coordinates of an arbitrary triangle in 3D space. The barycentric coordinates (b1, b2, b3) define the linear combination of `a`, `b` and `c` to represent the point `p`:: p = a * b1 + b * b2 + c * b3 This implementation returns the barycentric coordinates of the normal projection of `p` onto the plane defined by (a, b, c). These barycentric coordinates have some useful properties: - if all barycentric coordinates (b1, b2, b3) are in the range [0, 1], then the point `p` is inside the triangle (a, b, c) - if one of the coordinates is negative, the point `p` is outside the triangle - the sum of b1, b2 and b3 is always 1 - the center of "mass" has the barycentric coordinates (1/3, 1/3, 1/3) = (a + b + c)/3 r9rr:r;ct||_t||_t||_|j|jz |_|j|jz |_|j|jz |_|j|j}||_ | |j |_ t|j dkrtddS)Nr'zinvalid triangle)r r9r:r;_e1_e2_e3r3r4_nr_denomabsrI)rr9r:r;e1xe2s r=rzBarycentricCoordinates.__init__Msaaa6DF?6DF?6DF?tx((//##ii(( t{  d " "/00 0 # "rHrr*r ct|}|j}|j}||jz }||jz }||jz }|j|||z }|j |||z }|j |||z } t||| Sr) r rrr9r:r;rr3rrr) rrrdenomd1d2d3b1b2b3s r=from_cartesianz%BarycentricCoordinates.from_cartesianZs GG G  Z Z Z X^^B   # #A & & . X^^B   # #A & & . X^^B   # #A & & .BBrHcrt|j\}}}|j|z|j|zz|j|zzSr)r r`r9r:r;)rr:rrrs r= to_cartesianz#BarycentricCoordinates.to_cartesianfs7!WW[ Bv{TVb[(46B;66rHN)r9rr:rr;r)rrr*r )r:rr*r )rrrrrrrrrHr=rr3sZ2 1 1 1 1     777777rHrcountintc|dkr||gS||z }|jr|g|zS|g}||j|dz z }td|dz D]}||z }|||||S)z=Returns `count` evenly spaced vertices from `start` to `end`.r.rB)rr4rr2r_)rnrorrrVsteprYs r=rrks zzs|U{HwwH   h0EAI> ? ?D 1eai    OOC OrHrc|tj}|t}|t}t j||j pt j||j S)a4Returns ``True`` if matrix `m` performs a non-uniform xyz-scaling. Uniform scaling is not stretching in this context. Does not check if the target system is a cartesian coordinate system, use the :class:`~ezdxf.math.Matrix44` property :attr:`~ezdxf.math.Matrix44.is_cartesian` for that. )transform_directionr rsr rrtr6)r ux_mag_sqruyuzs r=rr|s}&&v..?J  v & &B  v & &B|J(;<< < DLB'EEArHpointsSequence[UVec]tuple[Vec3, float]ctj|t|z tfd|D}|fS)zCalculate the spherical envelope for the given points. Returns the centroid (a.k.a. geometric center) and the radius of the enclosing sphere. .. note:: The result does not represent the minimal bounding sphere! c3BK|]}|VdSr)r)rDrcentroids r= z%spherical_envelope..s166!""1%%666666rH)r rJr1max)rradiusr$s @r=r r sLx#f++-H 6666v666 6 6F V rHdir1dir2r'c||}t|dz z }tjt |trdSt tj||zS)aReturns the tangent length of an inscribe-circle of the given `radius`. The direction `dir1` and `dir2` define two intersection tangents, The tangent length is the distance from the intersection point of the tangents to the touching point on the inscribe-circle. r&r]) angle_betweenPI2rtr6r tan)r(r)r'alphabetas r=r!r!s_   t $ $E %#+ D |CIIs##s tx~~& ' ''rHc||}||}||s|jr|S|| r| St d)zReturns the bending angle from `dir1` to `dir2` in radians. The normal vector is required to detect the bending orientation, an angle > 0 bends to the "left" an angle < 0 bends to the "right". zinvalid normal vector)r+r3r6rrI)r(r)r<anglenns r=r"r"sv   t $ $E D  B zz&RZ VG  v , - --rHclddlm}||}tjt |dz S)z6Returns a vertex from the "inside" of the given face.r)mapbox_earcut_3dg@)ezdxf.math.triangulationr4r rJnext)rVr4its r=any_vertex_inside_facer8sA:99999  ( # #B 8DHH   ##rHr/Sequence[Sequence[Vec3]]c d fd t|}t|}t||| fd|D}t }|D]Z}t |||d}||kr(||d [t|S) zReturns the count of intersections of the normal-vector of the given `face` with the `faces` in front of this `face`. A counter-clockwise vertex order is assumed! rVr)r*r+cft|dkrdStfd|DS)Nr-Fc3JK|]}|kVdSr)r)rDrir0detector_planes r=r%zZfront_faces_intersect_face_normal..is_face_in_front_of_detector..s6TTa>44Q77'ATTTTTTrH)r1any)rVr0r=s r=is_face_in_front_of_detectorzGfront_faces_intersect_face_normal..is_face_in_front_of_detectors? x==1  5TTTTT8TTTTTTrHc32K|]}| |VdSrr)rDfr?s r=r%z4front_faces_intersect_face_normal..s4GG'C'CA'F'FG1GGGGGGrHTrN)rVr)r*r+) rr8rrsetrraddroundr1) rPr(r0 face_normalr front_facesintersection_pointsrr=r?s ` @@r=!front_faces_intersect_face_normalrIsUUUUUUU %T**K #D ) )F; (?(?@@NHGGGeGGGK &)UU 1 1 ( Kg    :   , ,R 0 07 : : # #BHHQKK 0 0 0 " # ##rHc4t|||dzdkS)aPReturns ``True`` if the face-normal for the given `face` of a closed surface is pointing outwards. A counter-clockwise vertex order is assumed, for faces with clockwise vertex order the result is inverted, therefore ``False`` is pointing outwards. This function does not check if the `faces` are a closed surface. r/r.r)rI)rPr(r0s r=r$r$s$ -UD' J J JQ NRS SSrHcZtdkrtddfd }t|jt|jt|jf}|t||dk}|}|r|dkn|dkS)aReturns ``True`` when the given 3D vertices have a counter-clockwise order around the given normal vector. Works for convex and concave shapes. Does not check or care if all vertices are located in a flat plane or if the normal vector is really perpendicular to the shape, but the result may be incorrect in that cases. Args: vertices (list): corner vertices of a flat shape (polygon) normal (Vec3): normal vector of the shape Raises: ValueError: input has less than 3 vertices r-rXr*rpcztj}dkr|dddf|dddf}}n7dkr|dddf|dddf}}n|dddf|dddf}}tj|tj|dtj|tj|dz S)NrrBr.r\)nparrayrroll)rrjrkdomrVs r= signed_areaz+is_vertex_order_ccw_3d..signed_areas(8$$ !88111a4='!!!Q$-qAA AXX111a4='!!!Q$-qAA111a4='!!!Q$-qAvaB((26!RWQ^^+D+DDDrHrr)r1rIr rjrkrlr8r&)rVr<rQabs_axisccwdom_axisrPs` @r=r%r%s  8}}q6777 E E E E E E E68}}c&(mmS]]:H ..X ' 'C +--! Cc{H 08a<r+r*r?)rO)rPrQr*r?)r9r r:r r;r r*r )rVr)r*r )rVrZr*r )rmr rnr ror r*rp)Try) rzr)r{r)r|r+r0rpr*r})rrr)rrrrrrpr*r )rrrrr*r)rnr ror rrr*r})rr rr rrr*r}) rr rVrr<r rr+r0rp)rnr ror rrr*r)rr r*r+)rr r*r!)r(r r)r r'rpr*rp)r(r r)r r*rp)rPr9r(r)r*r)rPr9r(r)r*r+)rVrr<r r*r+)1 __future__rtypingrrrrenumrrtnumpyrMrr r r r r rr__all__pir,rrrrrrrrrrrrr#rrrrrrr r!r"r8rIr$r%rrHr=r[s#"""""999999999999    0 gm:)-::::::77777(,,,, ) ) ) )((((86 B     0 J/J/J/J/J/J/J/J/b  C7C7C7C7C7C7V  $$$$$$X  """"""J    5757575757575757p"         ( ( ( (28 . . . . . $$$$  ($($($($($($^  TTTTTT"'1'1'1'1'1'1rH