ha(SSKJr SSKJrJrJrJrJrJr SSK J r SSK r SSK r \(aSSK JrJr Sr\ "\ R"\S9rSS /r"S S5r\"S SS5r\"SS S5r\"SSS 5r\"SSS5rSS jrSSS jjr"SS 5rg)) annotations)TupleIterableSequence TYPE_CHECKINGIteratorOptional)partialN)UVecAnyVec-q=)abs_tolVec3Vec2c\rSrSrSr/SQrSr\SBSj5r\SBSj5r \SBSj5r \SCSj5r \SDS j5r \SES j5r SFSGS jjrSHSCS jjr\SISj5r\SJSj5r\SKSj5r\SLSMSjj5r\SLSMSjj5r\SNSj5r\SOSPSjj5rSQSjrSQSjrSRSjrSRSjrSCSjr\rSSSjrSTSjr SUSjr!SBSjr"\SBSj5r#\SBSj5r$\SBS j5r%\SVS!j5r&S"S#S$.SWS%jjr'\SBS&j5r(\SBS'j5r)\SBS(j5r*\SBS)j5r+SXSYS*jjr,SZS[S+jjr-S[S,jr.SLSPS-jjr/SCS.jr0\0r1SVS/jr2S"S#S$.S\S0jjr3S]S1jr4S]S2jr5S[S3jr6S[S4jr7S[S5jr8S[S6jr9S^S7jr:S^S8jr;S^S9jr<\S_S:j5r=S`S;jr>S[S<jr?S`S=jr@S`S>jrASaS?jrBSbS@jrCSbSAjrDSrEg )craImmutable 3D vector class. This class is optimized for universality not for speed. Immutable means you can't change (x, y, z) components after initialization:: v1 = Vec3(1, 2, 3) v2 = v1 v2.z = 7 # this is not possible, raises AttributeError v2 = Vec3(v2.x, v2.y, 7) # this creates a new Vec3() object assert v1.z == 3 # and v1 remains unchanged :class:`Vec3` initialization: - ``Vec3()``, returns ``Vec3(0, 0, 0)`` - ``Vec3((x, y))``, returns ``Vec3(x, y, 0)`` - ``Vec3((x, y, z))``, returns ``Vec3(x, y, z)`` - ``Vec3(x, y)``, returns ``Vec3(x, y, 0)`` - ``Vec3(x, y, z)``, returns ``Vec3(x, y, z)`` Addition, subtraction, scalar multiplication and scalar division left and right-handed are supported:: v = Vec3(1, 2, 3) v + (1, 2, 3) == Vec3(2, 4, 6) (1, 2, 3) + v == Vec3(2, 4, 6) v - (1, 2, 3) == Vec3(0, 0, 0) (1, 2, 3) - v == Vec3(0, 0, 0) v * 3 == Vec3(3, 6, 9) 3 * v == Vec3(3, 6, 9) Vec3(3, 6, 9) / 3 == Vec3(1, 2, 3) -Vec3(1, 2, 3) == (-1, -2, -3) Comparison between vectors and vectors or tuples is supported:: Vec3(1, 2, 3) < Vec3 (2, 2, 2) (1, 2, 3) < tuple(Vec3(2, 2, 2)) # conversion necessary Vec3(1, 2, 3) == (1, 2, 3) bool(Vec3(1, 2, 3)) is True bool(Vec3(0, 0, 0)) is False _x_y_zcHUR"U6uUlUlUlgN decomposerrr)selfargss D/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/_vector.py__init__ Vec3.__init__Hs$(NND$9!$'cUR$)z x-axis value)rrs rxVec3.xK wwr cUR$)z y-axis value)rr"s ryVec3.yPr%r cUR$)z z-axis value)rr"s rzVec3.zUr%r cNURURUR5$)z1Vec3 as ``(x, y, 0)``, projected on the xy-plane.) __class__rrr"s rxyVec3.xyZs~~dggtww//r cHURURUR4$)zVec3 as ``(x, y, z)`` tuple.rr"s rxyzVec3.xyz_sww((r cD[URUR45$)z'Real 2D vector as :class:`Vec2` object.)rrrr"s rvec2 Vec3.vec2dsTWWdgg&''r NcUc URnUc URnUc URnURXU5$)z# UH nT"U5v M g7fr.0itemrEs r Vec3.generate..,edD erPrDs` rrC Vec3.generates-e,,r crU"[R"U5U-[R"U5U-S5$)zXReturns a :class:`Vec3` object from `angle` in radians in the xy-plane, z-axis = ``0``. mathcossinrEanglelengths r from_angleVec3.from_angles- 488E?V+TXXe_v-EsKKr cNUR[R"U5U5$)zXReturns a :class:`Vec3` object from `angle` in degrees in the xy-plane, z-axis = ``0``. rbr\radiansr_s rfrom_deg_angleVec3.from_deg_angles ~~dll516::r c[U5nUS:XagUS:XaUSn[U[5(a#URURUR 4$[U5nUS:XaUup4SnOUS:XaUup4nO[ e[U5[U5[U54$US:XaUup4[U5[U5S4$US:Xa%Uup4n[U5[U5[U54$[ e)aConverts input into a (x, y, z) tuple. Valid arguments are: - no args: ``decompose()`` returns (0, 0, 0) - 1 arg: ``decompose(arg)``, `arg` is tuple or list, tuple has to be (x, y[, z]): ``decompose((x, y))`` returns (x, y, 0.) - 2 args: ``decompose(x, y)`` returns (x, y, 0) - 3 args: ``decompose(x, y, z)`` returns (x, y, z) Returns: (x, y, z) tuple (internal API) r)rZrZrZrZ)len isinstancerrrr TypeErrorfloat)rradatar#r'r*s rrVec3.decomposes$T Q; q[7D$%%ww00TQ;DAAq["GA!#OQxq5833 q[DA8U1Xs* * q[GA!8U1XuQx/ /r c[R"SS5n[R"SS5n[R"SS5n[X#U5RU5$)zReturns a random vector.rj)randomuniformr normalize)rErar#r'r*s rru Vec3.randomsK NN2q ! NN2q ! NN2q !A!}&&v..r c$SRU5$)z!Return ``'(x, y, z)'`` as string.z({0.x}, {0.y}, {0.z})formatr"s r__str__ Vec3.__str__s&--d33r c(SUR5-$)z%Return ``'Vec3(x, y, z)'`` as string.rr|r"s r__repr__ Vec3.__repr__s &&r cg)zReturns always ``3``.rlrPr"s r__len__ Vec3.__len__sr c,[UR5$)zZReturns hash value of vector, enables the usage of vector as key in ``set`` and ``dict``. )hashr1r"s r__hash__ Vec3.__hash__sDHH~r cU$)z1Returns a copy of vector as :class:`Vec3` object.rPr"s rcopy Vec3.copy r cU$)z:func:`copy.deepcopy` support.rP)rmemodicts r __deepcopy__Vec3.__deepcopy__rr c[U[5(a [S5eUS:Xa UR$US:Xa UR$US:Xa UR $[ SU35e)zBSupport for indexing: - v[0] is v.x - v[1] is v.y - v[2] is v.z slicing not supportedrrjrkinvalid index )rnslicerorrr IndexErrorrindexs r __getitem__Vec3.__getitem__s_ eU # #34 4 A:77N aZ77N aZ77N~eW56 6r c#`# URv URv URv g7f)z&Returns iterable of x-, y- and z-axis.Nrr"s r__iter__ Vec3.__iter__s gg gg gg s,.cUR$)z%Returns length (magnitude) of vector. magnituder"s r__abs__ Vec3.__abs__s ~~r c URS-$)zLength of vector.?)magnitude_squarer"s rrVec3.magnitude s$$c))r cX[R"URUR5$)z!Length of vector in the xy-plane.)r\hypotrrr"s r magnitude_xyVec3.magnitude_xyzz$''477++r cdURURURp2nX-X"--X3--$)zSquare length of vector.rr7s rrVec3.magnitude_squares0''477DGGauqu}qu$$r c[UR5[:*=(a? [UR5[:*=(a [UR5[:*$)zr``True`` if all components are close to zero: ``Vec3(0, 0, 0)``. Has a fixed absolute testing tolerance of 1e-12! )absrABS_TOLrrr"s ris_null Vec3.is_nullsC LG # (DGG ' (DGG ' r & .>r rel_tolrcUR5nUR5nURXRUS9=(d URU*X#S9$)z?Returns ``True`` if `self` and `other` are parallel to vectors.r)rwisclose)rotherrrv1v2s r is_parallelVec3.is_parallel'sP^^  __ zz"wz? 2:: CDND  r cp[R"[RUR 555$)z3Spatial angle between vector and x-axis in radians.)r\acosX_AXISdotrwr"s r spatial_angleVec3.spatial_angle1s#yyDNN$4566r cB[R"UR5$)z3Spatial angle between vector and x-axis in degrees.)r\degreesrr"s rspatial_angle_degVec3.spatial_angle_deg6s||D..//r cX[R"URUR5$)z;Angle between vector and x-axis in the xy-plane in radians.)r\atan2rrr"s rr` Vec3.angle;rr cB[R"UR5$)z>Returns angle of vector and x-axis in the xy-plane in degrees.r\rr`r"s r angle_degVec3.angle_deg@||DJJ''r cU(a2URUR*URUR5$URURUR*UR5$)zqReturns orthogonal 2D vector, z-axis is unchanged. Args: ccw: counter-clockwise if ``True`` else clockwise )r-rrrrccws r orthogonalVec3.orthogonalEsQ NNDGG8TWWdgg 6 $''477; r cdURU5U- [U5-nURU5$)zReturns linear interpolation between `self` and `other`. Args: other: end point as :class:`Vec3` compatible object factor: interpolation factor (0 = self, 1 = other, 0.5 = mid point) )r-rp__add__)rrfactords rlerp Vec3.lerpRs.^^E "T )U6] :||Ar cHUR5nX"RU5-$)z0Returns projected vector of `other` onto `self`.rwrrruvs rproject Vec3.project^ ^^ FF5M!!r c<URXR- 5$)z7Returns normalized vector, optional scaled by `length`.__mul__rrras rrwVec3.normalizecs||F^^344r cjURUR*UR*UR*5$)z!Returns negated vector (-`self`).)r-rrrr"s rreversed Vec3.reversedgs'~~twwh477(;;r c$UR(+$)z,Returns ``True`` if vector is not (0, 0, 0).rr"s r__bool__ Vec3.__bool__ms<<r cURU5upEn[R"URXBUS9=(aG [R"URXRUS9=(a [R"UR XbUS9$)zReturns ``True`` if `self` is close to `other`. Uses :func:`math.isclose` to compare all axis. Learn more about the :func:`math.isclose` function in `PEP 485 `_. r)rr\rrrr)rrrrr#r'r*s rr Vec3.iscloseqsc..'a LL!g F K TWWa'J K TWWa'J r c[U[5(d [U5nURUR:H=(a9 URUR:H=(a URUR:H$)zBEqual operator. Args: other: :class:`Vec3` compatible object )rnrr#r'r*rrs r__eq__ Vec3.__eq__sQ %&&KEvv LTVVuww%6L466UWW;LLr cURU5up#nURU:Xa.URU:XaURU:$URU:$URU:$)zHLower than operator. Args: other: :class:`Vec3` compatible object rrrr#r'r*s r__lt__ Vec3.__lt__sV..'a 77a<ww!|ww{"ww{"77Q; r cURU5up#nURURU-URU-URU-5$)z-Add :class:`Vec3` operator: `self` + `other`.rr-rrrrs rr Vec3.__add__s?..'a~~dggk477Q;! DDr c$URU5$)z.RAdd :class:`Vec3` operator: `other` + `self`.)rrs r__radd__ Vec3.__radd__||E""r cURU5up#nURURU- URU- URU- 5$)z-Sub :class:`Vec3` operator: `self` - `other`.rrs r__sub__ Vec3.__sub__sA..'a~~dggk477Q;! DDr cURU5up#nURX R- X0R- X@R- 5$)z.RSub :class:`Vec3` operator: `other` - `self`.rrs r__rsub__ Vec3.__rsub__s9..'a~~a''k1ww;GG DDr c[U5nURURU-URU-URU-5$)z&Scalar Mul operator: `self` * `other`.rpr-rrrrrscalars rr Vec3.__mul__9u~~dgg.&0@$''FBRSSr c$URU5$)z'Scalar RMul operator: `other` * `self`.)rrs r__rmul__ Vec3.__rmul__rr c[U5nURURU- URU- URU- 5$)z&Scalar Div operator: `self` / `other`.rrs r __truediv__Vec3.__truediv__rr c,[nUHnX- nM U$)Add all vectors in `items`.)NULLVECrFsvs rsumVec3.sums A FAr cURU5up#nURU-URU--URU--$)zQDot operator: `self` . `other` Args: other: :class:`Vec3` compatible object rrs rrVec3.dots> ..'aww{TWWq[(477Q;66r cURU5up#nURURU-URU-- URU-URU-- URU-URU-- 5$)zSCross operator: `self` x `other` Args: other: :class:`Vec3` compatible object )rr-rrrrs rcross Vec3.crossso ..'a~~ GGaK$''A+ % GGaK$''A+ % GGaK$''A+ %  r cZURU5nURU5R$)z3Returns distance between `self` and `other` vector.)r-rr)rrrs rdistance Vec3.distances$ NN5 !yy(((r cUR5RURU5R55nUS:aSnOUS:aSn[R"U5$)zReturns angle between `self` and `other` in radians. +angle is counter clockwise orientation. Args: other: :class:`Vec3` compatible object ?)rwrr-r\rrr cos_thetas r angle_betweenVec3.angle_betweensUNN$(()>)H)H)JK t I _Iyy##r cXRU5- R5nURU5R5nURU5nURU5n[R "Xe5[R -$)zReturns counter-clockwise angle in radians about `self` from `base` to `target` when projected onto the plane defined by `self` as the normal vector. Args: base: base vector, defines angle 0 target: target vector )rrwrrr\rtau)rbasetargetx_axisy_axistarget_projected_xtarget_projected_ys r angle_aboutVec3.angle_aboutsld++668F#--/#ZZ/#ZZ/zz,ADHHLLr c URURURS5n[R UR U-UR 5nURURURUR5$)z\Returns vector rotated about `angle` around the z-axis. Args: angle: angle in radians rZ)r-r#r'rrbr`rr*)rr`rs rrotate Vec3.rotatesY NN4664663 / OOAGGeOQ[[ 9~~acc133//r cLUR[R"U55$)z\Returns vector rotated about `angle` around the z-axis. Args: angle: angle in degrees )r1r\rfrr`s r rotate_degVec3.rotate_deg s{{4<<.//r returnrpr8r)r8ztuple[float, float, float]r8r)NNN)r#Optional[float]r'r;r*r;r8rr)rFIterable[UVec]r8z list[Vec3])rFr<r8zSequence[Vec3])rFr<r8zIterator[Vec3]r!)r`rprarpr8r)r8zTuple[float, float, float])rj)rarpr8rr8strr8int)rdictr8rrrAr8rpr8zIterator[float]r8bool)rrrrprrpr8rFT)rrFr8rr)rr r8r)rr rrprrpr8rFrr r8rF)rrpr8r)rFr<r8r)rr r8rp)r(r r)r r8rp)r`rpr8r)F__name__ __module__ __qualname____firstlineno____doc__ __slots__rpropertyr#r'r*r.r1r4r8r< classmethodrBrKrCrbrg staticmethodrrur|rrrr__copy__rrrrrrrrrrrr`rrrrrwr__neg__rrrrrrrrrr r rrrrr$r.r1r5__static_attributes__rPr rrrs*X#I:00))(( "!! '  '  '  '  '  ))**--LL ;; ((T//4' H7& **,,%%   04e  ', >C  7700,,((   " 5<G 04e  ', >C  "M E #E E T #T 7  ) $ M 00r rjc6[U5RU5$)zReturns distance between points `p1` and `p2`. Args: p1: first point as :class:`Vec3` compatible object p2: second point as :class:`Vec3` compatible object )rr)p1p2s rrrs 8  R  r c6[U5RX5$)aReturns linear interpolation between points `p1` and `p2` as :class:`Vec3`. Args: p1: first point as :class:`Vec3` compatible object p2: second point as :class:`Vec3` compatible object factor: interpolation factor (``0`` = `p1`, ``1`` = `p2`, ``0.5`` = mid point) )rr)rWrXrs rrr's 8== $$r cx\rSrSrSrSS/rS5S6Sjjr\S7Sj5rS8S9Sjjr \ S:S j5r \ S;S j5r \ SS jj5r\ S=S>S jj5rS?SjrS?SjrS@SjrS@SjrS9Sjr\rSASjrSBSjrSCSjrSDSjr\SDSj5r\SESj5r\SDSj5r\SDSj5rSFSGSjjrSHSISjjrSJSjr S=SKSjjr!S9Sjr"\"r#SES jr$S!S"S#.SLS$jjr%SMS%jr&SMS&jr'SJS'jr(SJS(jr)SJS)jr*SNS*jr+SNS+jr,SNS,jr-SOS-jr.SOS.jr/SOS/jr0SOS0jr1SPS1jr2SPS2jr3\4SQS3j5r5S4r6g)Rri3a3Immutable 2D vector class. Args: v: vector object with :attr:`x` and :attr:`y` attributes/properties or a sequence of float ``[x, y, ...]`` or x-axis as float if argument `y` is not ``None`` y: second float for :code:`Vec2(x, y)` :class:`Vec2` implements a subset of :class:`Vec3`. r#r'NcURUlURUlg![aN Uc([US5Ul[US5Ulg[U5Ul[U5Ulgf=f)Nrrj)r#r'AttributeErrorrp)rrr's rr Vec2.__init__Bse "SSDFSSDF "yqtqtqq  "s"%3A= A=<A=cD[URURS5$)zReturns a 3D vector.r)rr#r'r"s rvec3 Vec2.vec3NsDFFDFFA&&r cvUR[URU5[URU55$r;)r-r<r#r'r=s rr< Vec2.roundSs+ ~~eDFFG4eDFFG6LMMr c6[URU55$rrArDs rrB Vec2.listZsCLL'((r c6[URU55$rIrJrDs rrK Vec2.tuple^rMr c^U4SjU5$)Nc34># UH nT"U5v M g7frrPrQs rrT Vec2.generate..erVrWrPrDs` rrC Vec2.generatecs,e,,r cpU"[R"U5U-[R"U5U-5$rr[r_s rrbVec2.from_anglegs)488E?V+TXXe_v-EFFr cNUR[R"U5U5$rrer_s rrgVec2.from_deg_angleks~~dll516::r c$SRU5$)Nz({0.x}, {0.y})rzr"s rr| Vec2.__str__os&&t,,r c(SUR5-$)Nrrr"s rr Vec2.__repr__rs &&r cg)NrkrPr"s rr Vec2.__len__usr cD[URUR45$r)rr#r'r"s rr Vec2.__hash__xsTVVTVV$%%r cPURURUR45$rr-r#r'r"s rr Vec2.copy{s~~tvvtvv.//r c~U[U5$![a" UR5nX![U5'Us$f=fr)idKeyErrorr)rrrs rrVec2.__deepcopy__sA BtH% %  A!"RX H s )<<c[U[5(a [S5eUS:Xa UR$US:Xa UR$[ SU35e)Nrrrjr)rnrror#r'rrs rrVec2.__getitem__sM eU # #34 4 A:66M aZ66M~eW56 6r c#D# URv URv g7frr#r'r"s rr Vec2.__iter__sff ff s cUR$rrr"s rr Vec2.__abs__s ~~r cX[R"URUR5$)zReturns length of vector.r\rr#r'r"s rrVec2.magnitudezz$&&$&&))r c[UR5[:*=(a [UR5[:*$r)rr#rr'r"s rr Vec2.is_nulls'466{g%@#dff+*@@r cX[R"URUR5$)zAngle of vector in radians.)r\rr'r#r"s rr` Vec2.anglerr cB[R"UR5$)zAngle of vector in degrees.rr"s rrVec2.angle_degrr cU(a'URUR*UR5$URURUR*5$)zPOrthogonal vector Args: ccw: counter-clockwise if ``True`` else clockwise )r-r'r#rs rrVec2.orthogonals= >>466'4662 2>>$&&466'2 2r cURURUR- U--nURURUR- U--nURX45$)zLinear interpolation between `self` and `other`. Args: other: target vector/point factor: interpolation factor (0=self, 1=other, 0.5=mid point) Returns: interpolated vector )r#r'r-)rrrr#r's rr Vec2.lerpsS FFegg&&0 0 FFegg&&0 0~~a##r cHUR5nX"RU5-$)z#Project vector `other` onto `self`.rrs rr Vec2.projectrr c<URXR- 5$rrrs rrwVec2.normalizes||F^^344r cRURUR*UR*5$rrxr"s rr Vec2.reverseds~~tvvgw//r c$UR(+$rrr"s rr Vec2.__bool__s<<r rr rc[U[5(d [U5n[R"URURX#S9=(a* [R"UR UR X#S9$)Nr)rnrr\rr#r')rrrrs rr Vec2.isclosesY%&&KE|| FFEGGW Nll466577GM Nr c[U[5(d [U5nURUR:H=(a URUR:H$r)rnrr#r'rs rr Vec2.__eq__s=%&&KEvv 6TVVuww%66r cfUtp#nURU:XaURU:$URU:$rr)rrr#r'_s rr Vec2.__lt__s2q 66Q;66A: 66A: r cURURUR-URUR-5$![a [ S5ef=fNzinvalid argumentr-r#r'r\rors rr Vec2.__add__M 0>>$&&577"2DFFUWW4DE E 0./ / 0 ?AAcURURUR- URUR- 5$![a [ S5ef=frrrs rr Vec2.__sub__rrcURURUR- URUR- 5$![a [ S5ef=frrrs rr Vec2.__rsub__sM 0>>%''DFF"2EGGdff4DE E 0./ / 0rcZURURU-URU-5$rrxrs rr Vec2.__mul__#~~dffundffun==r cZURURU-URU-5$rrxrs rr  Vec2.__rmul__rr cZURURU- URU- 5$rrxrs rr Vec2.__truediv__rr chURUR-URUR--$rrrs rrVec2.dot'vv$&&577"222r chURUR-URUR-- $rrrs rdetVec2.det rr c[R"URUR- URUR- 5$rrrs rr Vec2.distance s-zz$&&577*DFFUWW,<==r cUR5RUR55nUS:aSnOUS:aSn[R"U5$)zaCalculate angle between `self` and `other` in radians. +angle is counter-clockwise orientation. r r!)rwrr\rr"s rr$Vec2.angle_betweensJ NN$(():; t I _Iyy##r chURRURU-UR5$)zARotate vector around origin. Args: angle: angle in radians )r-rbr`rr4s rr1 Vec2.rotates(~~((e);T^^LLr cURRUR[R"U5-UR 5$)zZRotate vector around origin. Args: angle: angle in degrees Returns: rotated vector )r-rbr`r\rfrr4s rr5Vec2.rotate_deg&s6~~(( JJe, ,dnn  r c8[SS5nUHnX- nM U$)rr)rrs rrVec2.sum3s% AJA FAr r))rZrZN)r8Noner9rr:)rFr<r8z list[Vec2])rFr<r8zSequence[Vec2])rFr<r8zIterator[Vec2]r=)r`rprarpr8rr>r@)rrBr8rrCrDr7rErG)rrFr8rrH)rr rrpr8r)rr r8r)rarpr8r)rr rrprrpr8rFrI)rrpr8r)rr r8rp)r`rpr8r)rFzIterable[Vec2]r8r)7rJrKrLrMrNrOrrPr_r<rQrBrKrCrbrgr|rrrrrSrrrrrrr`rrrrrwrrTrrrrrrrrr r rrrr$r1r5rRrrUrPr rrr3s c I "''N))**--GG;;-'&0H7**AA**(( 3 $" 50G 26NN).N@EN N7 0 0 0 >>>33> $M  r )rWr rXr r8rprH)rWr rXr rrpr8r) __future__rtypingrrrrrr functoolsr r\ru ezdxf.mathr r rr__all__rrY_AXISZ_AXISrrrrrPr rrs# '  $,, 0 6 z0z0z aA aA aA q!Q-! %FFr