hUiSSKJr SSKJrJrJrJr SSKJr SSK r SSK r SSK J r JrJrJrJrJrJr /SQr\ R*S- rS*S+S jjrS,S-S jjrS.S/S jjrS0S jrS1SjrS2SjrS3SjrS4S5SjjrS6S7SjjrSr "SS\5r!"SS5r"S \ S.S8Sjjr#S S \ S.S9Sjjr$S \ S.S:Sjjr%S;Sjr&"SS5r'SS"jr*S?S#jr+\4S@S$jjr,S1S%jr-\ S&.SAS'jjr.\ S&.SBS(jjr/SCS)jr0g)D) 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@& .>cD[U5S:ag[U5S:XagSn[[U5S- 5HNnXUS-upEnXT- RXe- 5R5nUcUnM8UR XqS9(aMN g Ubgg![a Mdf=f)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)facer, first_normalindexabcnormals H/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/construct3d.pyrr/s 4y1} 4yA~Ls4y1}%uqy)a e]]15)335F  !L%%f%>>& !   s#B BBTc#z# [U5S:a [S5e[U5n[R"U5U- n[ U5Vs/sHo@UR XS-U-5PM nn[ U5H1upgU(aXuUX5US- 4v MXVS- Xs4v XuUU4v M3 gs snf7f)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.N)r- ValueErrorr sumr.lerp enumerate)r3quadslen_facemid_posisubdiv_locationr5vertexs r:rrKs 4y1}788IHhhtnx'G8=h#8G1Q Tq5H,-.##4  %0'5ST9;UU U!!),f= =%0'9 9 ) #sA B;%B63AB;c## UHmn[U5U::a[R"U5v M,[R"U5[U5- n[ U5HupEX$S- XS4v M Mo g7f)zSubdivides faces into triangles by adding a center vertex. Args: faces: iterable of faces as sequence of :class:`Vec3` max_vertex_count: subdivide only ngons with more vertices r<N)r-r tupler>r@)facesmax_vertex_countr3rCr5rFs r:rrfsd t9( (**T" "hhtns4y0G!*4 19ov66"1 sA5A7cHX- RX - 5R5$)zdReturns normal vector for 3 points, which is the normalized cross product for: :code:`a->b x a->c`. )r/r0)r6r7r8s r:rrzs  E==  ) ) ++c[U5S:a [S5eUtpp4X!- RX1- 5R5$![a [ U5s$f=f)zbSafe function to detect the normal vector for a face or polygon defined by 3 or more `vertices`. r)3 or more vertices required)r-r=r/r0r1r)verticesr6r7r8_s r:rrs`  8}q677KA!)}}QU#--// )x(()s"AAAc[R"U5n[U5S:a [S5eUSnUR US5(dUR U5 UR up4nSnSnSnUSSH<n U R upn XeU -XK- -- nXsU -X\- -- nXU -X:- -- nU nU nU nM> [XgU5R5$)zReturns the "best fit" normal for a plane defined by three or more vertices. This function tolerates imperfect plane vertices. Safe function to detect the extrusion vector of flat arbitrary polygons. r)rNrr<N)r listr-r=r2appendxyzr0) rO _verticesfirstprev_xprev_yprev_znxnynzvxyzs r:rrs (#I 9~677 aLE ==2 ' '"YYFF B B B qr]%%a zfj)) zfj)) zfj))   % % ''rLcURU5(a [S5eX- nX!- RU5nURUR- nUS::ag[R "U5$)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.rS)r2r1projectmagnitude_squaremathsqrt)pointstartendv1v2diffs r:rrsg }}S .. B +  r "B  !4!4 4D s{yyrLcSSKJnJn U"XU5n[U5S:wagUSnU(aU$U"U5R U5(aU"U5R U5(aU$g)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 BoundingBoxr<N) ezdxf.mathrorpr-inside)line1line2virtualr,rorpresrhs r:rrsf$@ !% 8C 3x1} FE 5  ''K,>,E,Ee,L,L rLc:[U5up4n[R"X4U5nU(aU[R"U5-n[U5nUR(d9U[R "UR URUR5-nU$)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 scalez_rotateis_null translater`rarb)moverx z_rotationsxsyszmr{s r:rrsueJBBrr"A X  z **T I    X   Y[[)++ FF HrLc$\rSrSrSrSrSrSrSrg)rrr<r*r)N) __name__ __module__ __qualname____firstlineno__COPLANARFRONTBACKSPANNING__static_attributes__rrLr:rrsH E DHrLrc\rSrSrSrSrSSjr\SSj5r\SSj5r \SSj5r \ SSj5r \ SS j5r SS jr\rS rSS jrSS jrSSjrS S!SjjrS S"SjjrS\S.S#SjjrS$Sjr\4S%SjjrSrg)&rizConstruction tool for 3D planes. Represents a plane in 3D space as a normal vector and the perpendicular distance from the origin. _normal_distance_from_origincHURSLdS5eXlX lg)NFzinvalid plane normal)rzrr)selfr9distances r:__init__Plane.__init__s%~~&>(>>& %-"rLcUR$)zNormal vector of the plane.)rrs r:r9 Plane.normals||rLcUR$)z@The (perpendicular) distance of the plane from origin (0, 0, 0).)rrs r:distance_from_originPlane.distance_from_origins)))rLc4URUR-$)zReturns the location vector.rrs r:vector Plane.vectors||d8888rLcX!- RX1- 5R5n[ XDR U55$![a [S5ef=f)z+Returns a new plane from 3 points in space.z"undefined plane: colinear vertices)r/r0r1r=rdot)clsr6r7r8ns r:from_3p Plane.from_3p#sW C ae$..0AQa!!! CAB B Cs #?Ac[U5n[UR5UR5$![a [ S5ef=f)z3Returns a new plane from the given location vector.zinvalid NULL vector)r rr0 magnituder1r=)rrr_s r: from_vectorPlane.from_vector,sD L 4 4 4  423 3 4s #1AcNURURUR5$)zReturns a copy of the plane.) __class__rrrs r:__copy__Plane.__copy__5s~~dllD,F,FGGrLcNS[UR5SURS3$)NzPlane(z, ))reprrrrs r:__repr__Plane.__repr__;s(T\\*+2d.H.H-IKKrLcj[U[5(d[$URUR:H$N) isinstancerNotImplementedr)rothers r:__eq__ Plane.__eq__>s(%''! !{{ell**rLcRURRU5UR- $)zReturns signed distance of vertex `v` to plane, if distance is > 0, `v` is in 'front' of plane, in direction of the normal vector, if distance is < 0, `v` is at the 'back' of the plane, in the opposite direction of the normal vector. )rrrrr_s r:signed_distance_toPlane.signed_distance_toCs$||"T%?%???rLcL[R"URU55$)zPPzz#&&rLcURnURURU5- URU5- nXU--$![a gf=f)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)r9rrr1)rorigin directionrrs r: intersect_rayPlane.intersect_rayus\ KK //!%%-?155CSSFV+,,!  s0A AAcURRU5UR- nX2*:a[R$X2:a[R $[R $)zZReturns the :class:`PlaneLocationState` of the given `vertex` in relative to this plane. )rrrrrrr)rrFr,rs r:rPlane.vertex_location_statesU<<##F+d.H.HH h %** *  %++ +%.. .rL)rrN)r9r rfloat)returnr rr)r6r r7r r8r r'Plane')rrrr)rr)robjectrbool)r_r rrr')r_r rr)rrrr)rir rjr rOptional[Vec3])rr rr rr)rFr rr)rrrr__doc__ __slots__rpropertyr9rr classmethodrrrcopyrrrrrr PLANE_EPSILONrrrrrrLr:rrs 5I. **99""44H DL+ @5-  37 '' $' ', -%2 / /  / /rLrrc>[Rn/n/n/n[U5nURn URn UH)n UR X5n XL-nUR U 5 M+ U[R:Xa/U(a&[U5n U RU 5S:aUnGOaUnGO]U[R:XaUnGOEU[R:XaUnGO-U[R:XGa[U5n[U5HnUS-U-nX_n UUnXn UUnU [R:waUR U 5 U [R:waUR U 5 U U-[R:XdMXRU 5- U RUU - 5- nU RUU5nUR U5 UR U5 M [U5S:a/n[U5S:a/n[U5[U54$)a#Split 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. rr<r))rrrTrr9rrUrrrrrr-r.r?rH)polygonplanerr, polygon_type vertex_typesfront_vertices back_verticesrOwr9rF vertex_typepolygon_normal len_verticesr5 next_indexnext_vertex_type next_vertexinterpolation_weightplane_intersection_points r:r#r#s&..L-/L!#N "MG}H ""A \\F11&B # K( )222 ,X6Nzz.)A-!) ( +11 1! +00 0 +44 48} <(E!)|3J&-K+J7 _F":.K0555%%f-0666$$V,..3E3N3NN()JJv,>(>&**&(C($,2;;!5,(%%&>?$$%=>%)& ~  "N }  !M  % "6 66rL)rboundaryr,c[U5n[U5S:a [S5e[U5n[ XwR US55nURXX5S9n U cg[XXtU5$![a gf=f)aReturns the intersection point of the 3D line form `start` to `end` and the given `polygon`. Args: start: start point of 3D line as :class:`Vec3` end: end point of 3D line as :class:`Vec3` polygon: 3D polygon as iterable of :class:`Vec3` coplanar: if ``True`` a coplanar start- or end point as intersection point is valid boundary: if ``True`` an intersection point at the polygon boundary line is valid abs_tol: absolute tolerance for comparisons r)rNNrr) rTr-r=rr1rrr(_is_intersection_point_inside_3d_polygon) rirjrrrr,rOr9rips r:rrs.G}H 8}q677#H- &**Xa[1 2E   e8  MB z 3 f  s A00 A=<A=rr,c[U5n[U5S:a [S5e[U5n[ XfR US55nURX5nUcg[XXcU5$![a gf=f)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)rNNr) rTr-r=rr1rrrr) rrrrr,rOr9rrs r:rrs*G}H 8}q677#H- &**Xa[1 2E   V /B z 3 f  s A11 A>=A>cSSKJnJn U"U5n[R"UR U55nU"[UR U55XS9n U S:d U(aU S:XaU$g)Nr)is_point_in_polygon_2dOCSr+)rqrrr rTpoints_from_wcsfrom_wcs) rrOr9rr,rrocs ocs_verticesstates r:rr$s_7 f+C99S00:;L " S\\"   E qyX%1* rLc6\rSrSrSrSSjrS SjrS SjrSrg) ri3a,Barycentric 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 c[U5Ul[U5Ul[U5UlURUR- UlURUR- UlURUR- UlURRUR 5nUR5Ul URUR5Ul [UR5S:a [S5eg)Nr'zinvalid triangle)r r6r7r8_e1_e2_e3r/r0_nr_denomabsr=)rr6r7r8e1xe2s r:rBarycentricCoordinates.__init__Msaaa66DFF?66DFF?66DFF?txx(//#ii( t{{ d "/0 0 #rLc[U5nURnURnXR- nXR- nXR - nUR RU5RU5U- nURRU5RU5U- nURRU5RU5U- n [XxU 5$r) r r r r6r7r8rr/rr r ) rrrdenomd1d2d3b1b2b3s r:from_cartesian%BarycentricCoordinates.from_cartesianZs G GG  Z Z Z XX^^B  # #A & . XX^^B  # #A & . XX^^B  # #A & .BBrLc[U5Rup#nURU-URU--URU--$r)r rVr6r7r8)rr7rrrs r: to_cartesian#BarycentricCoordinates.to_cartesianfs;!W[[ vv{TVVb[(466B;66rL)r rr r r r6r7r8N)r6rr7rr8r)rrrr )r7rrr ) rrrrrrrrrrrLr:rr3s2 1  7rLrcUS::aX/$X- nUR(aU/U-$U/nURURUS- - 5n[SUS- 5HnX- nUR U5 M UR U5 U$)z=Returns `count` evenly spaced vertices from `start` to `end`.r*r<)rzr0rr.rU)rirjcountrrOsteprPs r:rrks z|{HwwH   h00EAI> ?D 1eai  ! OOC OrLc6UR[5RnUR[5nUR[5n[ R "XR5(+=(d% [ R "XR5(+$)a Returns ``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 rer rrfr2)r ux_mag_sqruyuzs r:rr|st&&v.??J  v &B  v &B||J(;(;< < DLL''EArLcz^[R"U5[U5- m[U4SjU55nTU4$)zCalculate the spherical envelope for the given points. Returns the centroid (a.k.a. geometric center) and the radius of the enclosing sphere. .. note:: The result does not represent the minimal bounding sphere! c3F># UHnTRU5v M g7fr)r).0rcentroids r: %spherical_envelope..s6v!""1%%vs!)r r>r-max)pointsradiusr(s @r:r r s7xx#f+-H 6v6 6F V rLcURU5n[US- - n[R"[ U5[5(ag[ [R "U5U-5$)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&rS) angle_betweenPI2rfr2r tan)dir1dir2r-alphabetas r:r!r!sR   t $E %#+ D ||CIs## txx~& ''rLcURU5nURU5nURU5(dUR(aU$URU*5(aU*$[ S5e)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/r/r2rzr=)r2r3r9anglenns r:r"r"s`   t $E D B zz&RZZ VG  v , --rLcbSSKJn U"U5n[R"[ U55S- $)z6Returns a vertex from the "inside" of the given face.r)mapbox_earcut_3dg@)ezdxf.math.triangulationr:r r>next)rOr:its r:any_vertex_inside_facer>s): ( #B 88DH  ##rLr+c ^^^^ SUU4Sjjm [U5n[U5n[X3RU55mU 4SjU5n[ 5nUHKn[ XCUSTS9nUcMTR U5T:dM+URURS55 MM [U5$)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! cP>[U5S:ag[UU4SjU55$)Nr)Fc3L># UHnTRU5T:v M g7fr)r)r'r_r,detector_planes r:r)Zfront_faces_intersect_face_normal..is_face_in_front_of_detector..s!T8a>44Q7'A8s!$)r-any)rOr,rBs r:is_face_in_front_of_detectorGfront_faces_intersect_face_normal..is_face_in_front_of_detectors# x=1 T8TTTrLc3F># UHnT"U5(dMUv M g7frr)r'frEs r:r)4front_faces_intersect_face_normal..sGe'CA'F11es! !Tr)rOSequence[Vec3]rr) rr>rrsetrraddroundr-) rIr3r, face_normalr front_facesintersection_pointsrrBrEs ` @@r:!front_faces_intersect_face_normalrRsUU %T*K #D )F;(?@NHeGK &)U ( g  :   , ,R 07 : # #BHHQK 0 " ##rLc"[XUS9S-S:H$)a<Returns ``True`` if the face-normal for the given `face` of a closed surface is pointing outwards. A counter-clockwise vertex order is assumed, for faces with clockwise vertex order the result is inverted, therefore ``False`` is pointing outwards. This function does not check if the `faces` are a closed surface. r+r*r)rR)rIr3r,s r:r$r$s -U' JQ NRS SSrLc<^^[T5S:a [S5eSUU4Sjjn[UR5[UR5[UR 54nUR [U55mU"5S:nUTnU(aUS:$US:$)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)rNcd>[R"T5nTS:XaUSS2S4USS2S4p!O)TS:XaUSS2S4USS2S4p!OUSS2S4USS2S4p![R"U[R"US55[R"U[R"US55- $)Nrr<r*rR)nparrayrroll)rr`radomrOs r: signed_area+is_vertex_order_ccw_3d..signed_areas((8$ !81a4='!Q$-q AX1a4='!Q$-q1a4='!Q$-qvvaB(266!RWWQ^+DDDrLrr)r-r=r r`rarbr5r+)rOr9rZabs_axisccwdom_axisrYs` @r:r%r%s  8}q677 E E688}c&((mS]:H ..X 'C -! Cc{H8a<0HqL0rLr)r3rKrr)T)r3rKrArrIterator[Sequence[Vec3]]))rIzIterable[Sequence[Vec3]]rr_)r6r r7r r8r rr )rOrKrr )rOzIterable[UVec]rr )rhr rir rjr rr)Tg|=) rsrKrtrKrurr,rrr))rrr)r<r<r<r)r|rrxrr}rrr )rIterable[Vec3]rrrz%tuple[Sequence[Vec3], Sequence[Vec3]])rir rjr rrarr)rr rr rrarr) rr rO list[Vec3]r9r rrr,r)rir rjr rintrrb)rr rr)r,zSequence[UVec]rztuple[Vec3, float])r2r r3r r-rrr)r2r r3r rr)rISequence[Sequence[Vec3]]r3rKrrc)rIrdr3rKrr)rOrbr9r rr)1 __future__rtypingrrrrenumrrfnumpyrVrqr r r r r rr__all__pir0rrrrrrrrrrrrr#rrrrrrr r!r"r>rRr$r%rrLr:rkse#99  0 ggm:)-: :!%:::7 #77(, )(86      B      0 J/J/b  C7 C7 C7 + C7V  $ $ $$$X  " """"J   " ,0 <@ KP 5757p"   (28 . $  ($ #($ ($  ($^  T #T T  T"'1rL