'ja@ddlmZddlmZmZmZmZmZmZddl m Z ddl Z ddl Z erddl mZmZdZe e jeZdd gZGd dZed ddZedd dZeddd ZedddZddZdddZGdd ZdS)) annotations)TupleIterableSequence TYPE_CHECKINGIteratorOptional)partialN)UVecAnyVec-q=)abs_tolVec3Vec2cveZdZdZgdZdZedcdZedcdZedcdZ eddd Z eded Z edfd Z dgdhdZ didddZedjdZedkdZedldZedmdnd Zedmdnd!Zedod#Zedpdqd%Zdrd'Zdrd(Zdsd*Zdsd+Zddd,ZeZdtd/Zdud1Zdvd3Z dcd4Z!edcd5Z"edcd6Z#edcd7Z$edwd9Z%d:d;d<dxd@Z&edcdAZ'edcdBZ(edcdCZ)edcdDZ*dydzdGZ+d{d|dJZ,d|dKZ-dmdqdLZ.dddMZ/e/Z0dwdNZ1d:d;d<d}dOZ2d~dPZ3d~dQZ4d|dRZ5d|dSZ6d|dTZ7d|dUZ8ddVZ9ddWZ:ddXZ;eddYZdd\Z?dd]Z@dd`ZAddaZBddbZCdS)raImmutable 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_zc@|j|\|_|_|_dSN decomposerrr)selfargss L/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/math/_vector.py__init__z Vec3.__init__Hs!$2DND$9!$'''returnfloatc|jS)z x-axis value)rrs rxzVec3.xK wrc|jS)z y-axis value)rr"s ryzVec3.yPr$rc|jS)z z-axis value)rr"s rzzVec3.zUr$rcB||j|jS)z1Vec3 as ``(x, y, 0)``, projected on the xy-plane.) __class__rrr"s rxyzVec3.xyZs~~dgtw///rtuple[float, float, float]c*|j|j|jfS)zVec3 as ``(x, y, z)`` tuple.rr"s rxyzzVec3.xyz_sw((rrc8t|j|jfS)z'Real 2D vector as :class:`Vec2` object.)rrrr"s rvec2z Vec3.vec2dsTWdg&'''rNr#Optional[float]r&r(cf||j}||j}||j}||||S)z 9A 9A 9A~~aA&&&rc|t|j|t|j|t|j|SzReturns a new vector where all components are rounded to `ndigits`. Uses standard Python :func:`round` function for rounding. )r*roundrrrrndigitss rr7z Vec3.roundxsG ~~ $'7 # # $'7 # # $'7 # #   ritemsIterable[UVec] list[Vec3]cFt||S)z(Returns a list of :class:`Vec3` objects.listgenerateclsr:s rr?z Vec3.listsCLL''(((rSequence[Vec3]cFt||Sz)Returns a tuple of :class:`Vec3` objects.tupler@rAs rrGz Vec3.tupleS\\%(()))rIterator[Vec3]c fd|DS)z-Returns an iterable of :class:`Vec3` objects.c3.K|]}|VdSr.0itemrBs r z Vec3.generate..+,,dD ,,,,,,rrLrAs` rr@z Vec3.generates-,,,e,,,,r?anglelengthcp|tj||ztj||zdS)zhReturns a :class:`Vec3` object from `angle` in radians in the xy-plane, z-axis = ``0``. mathcossinrBrSrTs r from_anglezVec3.from_angles2 s48E??V+TXe__v-EsKKKrcR|tj||S)zhReturns a :class:`Vec3` object from `angle` in degrees in the xy-plane, z-axis = ``0``. r\rXradiansr[s rfrom_deg_anglezVec3.from_deg_angles" ~~dl5116:::rTuple[float, float, float]c*t|}|dkrdS|dkr|d}t|tr|j|j|jfSt|}|dkr|\}}d}n|dkr|\}}}nt t|t|t|fS|dkr$|\}}t|t|dfS|dkr2|\}}}t|t|t|fSt )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)rVrVrVrV)len isinstancerrrr TypeErrorr )rrTdatar#r&r(s rrzVec3.decomposes$T Q;; = q[[7D$%% 4w00TQ;;DAqAAq[["GAq!!#OQxxq58833 q[[DAq88U1XXs* * q[[GAq!88U1XXuQxx/ /rrcctjdd}tjdd}tjdd}t||||S)zReturns a random vector.rc)randomuniformr normalize)rBrTr#r&r(s rrlz Vec3.randomsU N2q ! ! N2q ! ! N2q ! !Aq!}}&&v...rstrc,d|S)z!Return ``'(x, y, z)'`` as string.z({0.x}, {0.y}, {0.z})formatr"s r__str__z Vec3.__str__s&--d333rc0d|zS)z%Return ``'Vec3(x, y, z)'`` as string.rrsr"s r__repr__z Vec3.__repr__s &&rintcdS)zReturns always ``3``.rerLr"s r__len__z Vec3.__len__sqrc*t|jS)zjReturns hash value of vector, enables the usage of vector as key in ``set`` and ``dict``. )hashr.r"s r__hash__z Vec3.__hash__sDH~~rc|S)z1Returns a copy of vector as :class:`Vec3` object.rLr"s rcopyz Vec3.copy rmemodictdictc|S)z:func:`copy.deepcopy` support.rL)rrs r __deepcopy__zVec3.__deepcopy__rrindexct|trtd|dkr|jS|dkr|jS|dkr|jSt d|)zbSupport for indexing: - v[0] is v.x - v[1] is v.y - v[2] is v.z slicing not supportedrrcrdinvalid index )rgslicerhrrr IndexErrorrrs r __getitem__zVec3.__getitem__sl eU # # 5344 4 A::7N aZZ7N aZZ7N5e5566 6rIterator[float]c#@K|jV|jV|jVdS)z&Returns iterable of x-, y- and z-axis.Nrr"s r__iter__z Vec3.__iter__s+g g g rc|jS)z%Returns length (magnitude) of vector. magnituder"s r__abs__z Vec3.__abs__s ~rc|jdzS)zLength of vector.?)magnitude_squarer"s rrzVec3.magnitude s$c))rc@tj|j|jS)z!Length of vector in the xy-plane.)rXhypotrrr"s r magnitude_xyzVec3.magnitude_xyz$'47+++rcN|j|j|j}}}||z||zz||zzS)zSquare length of vector.rr3s rrzVec3.magnitude_squares2'47DGa11uq1u}q1u$$rboolct|jtko9t|jtkot|jtkS)z``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_nullz Vec3.is_nullsC LLG # (DG ' (DG ' r& .>r rel_tolrotherrrc|}|}||||p|| ||S)z?Returns ``True`` if `self` and `other` are parallel to vectors.r)rnisclose)rrrrv1v2s r is_parallelzVec3.is_parallel'sc^^   __  zz"gwz?? 2:: C'DND D  rc~tjt|S)z3Spatial angle between vector and x-axis in radians.)rXacosX_AXISdotrnr"s r spatial_anglezVec3.spatial_angle1s*yDNN$4$455666rc4tj|jS)z3Spatial angle between vector and x-axis in degrees.)rXdegreesrr"s rspatial_angle_degzVec3.spatial_angle_deg6s|D.///rc@tj|j|jS)z;Angle between vector and x-axis in the xy-plane in radians.)rXatan2rrr"s rrSz Vec3.angle;rrc4tj|jS)z>Returns angle of vector and x-axis in the xy-plane in degrees.rXrrSr"s r angle_degzVec3.angle_deg@|DJ'''rTccwc|r'||j |j|jn&||j|j |jS)zReturns orthogonal 2D vector, z-axis is unchanged. Args: ccw: counter-clockwise if ``True`` else clockwise )r*rrrrrs r orthogonalzVec3.orthogonalEsI `_. r)rrXrrrr)rrrrr#r&r(s rrz Vec3.iscloseqst..''1a L!Wg F F F K TWa'JJJ K TWa'JJJ rct|tst|}|j|jko|j|jko|j|jkS)zZEqual operator. Args: other: :class:`Vec3` compatible object )rgrr#r&r(rrs r__eq__z Vec3.__eq__sL %&& KKEv LTVuw%6L46UW;LLrc||\}}}|j|kr!|j|kr |j|kS|j|kS|j|kS)z`Lower than operator. Args: other: :class:`Vec3` compatible object rrrr#r&r(s r__lt__z Vec3.__lt__sU..''1a 7a<<w!||w{"w{"7Q; rc||\}}}||j|z|j|z|j|zS)z-Add :class:`Vec3` operator: `self` + `other`.rr*rrrrs rrz Vec3.__add__sA..''1a~~dgk47Q;! DDDrc,||S)z.RAdd :class:`Vec3` operator: `other` + `self`.)rrs r__radd__z Vec3.__radd__||E"""rc||\}}}||j|z |j|z |j|z S)z-Sub :class:`Vec3` operator: `self` - `other`.rrs r__sub__z Vec3.__sub__sC..''1a~~dgk47Q;! DDDrc||\}}}|||jz ||jz ||jz S)z.RSub :class:`Vec3` operator: `other` - `self`.rrs r__rsub__z Vec3.__rsub__sA..''1a~~a$'k1tw;DG DDDrc~t|}||j|z|j|z|j|zS)z&Scalar Mul operator: `self` * `other`.r r*rrrrrscalars rrz Vec3.__mul__8u~~dg.&0@$'FBRSSSrc,||S)z'Scalar RMul operator: `other` * `self`.)rrs r__rmul__z Vec3.__rmul__rrc~t|}||j|z |j|z |j|z S)z&Scalar Div operator: `self` / `other`.rrs r __truediv__zVec3.__truediv__rrc(t}|D]}||z }|S)Add all vectors in `items`.)NULLVECr:svs rsumzVec3.sums(   A FAArct||\}}}|j|z|j|zz|j|zzS)ziDot operator: `self` . `other` Args: other: :class:`Vec3` compatible object rrs rrzVec3.dots= ..''1aw{TWq[(47Q;66rc||\}}}||j|z|j|zz |j|z|j|zz |j|z|j|zz S)zkCross operator: `self` x `other` Args: other: :class:`Vec3` compatible object )rr*rrrrs rcrossz Vec3.crosssm ..''1a~~ GaK$'A+ % GaK$'A+ % GaK$'A+ %   rc`||}||jS)z3Returns distance between `self` and `other` vector.)r*rr)rrrs rdistancez Vec3.distances& NN5 ! !yy((rc|||}|dkrd}n|dkrd}tj|S)zReturns angle between `self` and `other` in radians. +angle is counter clockwise orientation. Args: other: :class:`Vec3` compatible object rR)rnrr*rXrrr cos_thetas r angle_betweenzVec3.angle_betweensiNN$$(()>)>)H)H)J)JKK t  II __Iy###rbasetargetc<|||z }||}||}||}t j||tjzS)aReturns 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 )rrnrrrXrtau)rrrx_axisy_axistarget_projected_xtarget_projected_ys r angle_aboutzVec3.angle_aboutsd+++6688F##--//#ZZ//#ZZ//z,.@AADHLLrc||j|jd}t|j|z|j}||j|j|jS)ztReturns vector rotated about `angle` around the z-axis. Args: angle: angle in radians rV)r*r#r&rr\rSrr()rrSrs rrotatez Vec3.rotatesT NN46463 / / OOAGeOQ[ 9 9~~ac13///rcP|tj|S)ztReturns vector rotated about `angle` around the z-axis. Args: angle: angle in degrees )rrXr_rrSs r rotate_degzVec3.rotate_deg s {{4<..///rrr rr)rr,rr)NNN)r#r1r&r1r(r1rrr)r:r;rr<)r:r;rrC)r:r;rrIrR)rSr rTr rr)rra)rc)rTr rrrrorrw)rrrrrrwrr rrrr)rrrr rr rrT)rrrrr)rr rr)rr rr rr rrrr rr)rr rr)r:r;rr)rr rr )rr rr rr )rSr rr)D__name__ __module__ __qualname____doc__ __slots__rpropertyr#r&r(r+r.r0r4r7 classmethodr?rGr@r\r` staticmethodrrlrsrvryr|r~__copy__rrrrrrrrrrrrSrrrrrnr__neg__rrrrrrrrrrrrrrrrrrrrLrrrrs<**X#""I:::XXX000X0)))X)(((X( "!! ' ' ' ' '      )))[)***[*---[-LLLL[L ;;;;[; (((\(T////[/4444'''' H7777& ***X*,,,X,%%%X%    X 04e      777X7000X0,,,X,(((X(           """" 55555<<<<G    04e      "MMMM EEEE ####EEEE EEEE TTTT ####TTTT \7777     )))) $$$$ MMMM 0 0 0 0000000rrcp1r p2rr cFt||S)zReturns distance between points `p1` and `p2`. Args: p1: first point as :class:`Vec3` compatible object p2: second point as :class:`Vec3` compatible object )rr)rrs rrrs 88  R  rrrcHt|||S)a+Returns linear interpolation between points `p1` and `p2` as :class:`Vec3`. Args: p1: first point as :class:`Vec3` compatible object p2: second point as :class:`Vec3` compatible object factor: interpolation factor (``0`` = `p1`, ``1`` = `p2`, ``0.5`` = mid point) )rr)rrrs rrr's 88==V $ $$rc@eZdZdZddgZdQdRdZedSd ZdTdUd Ze dVdZ e dWdZ e dXdZ e dYdZdZ e dYdZdZd[dZd[dZd\dZd\dZdUd ZeZd]d#Zd^d%Zd_d'Zd`d(Zed`d)Zedad+Zed`d,Zed`d-Zdbdcd0Zddded5Zdfd6ZdYdgd7Z dUd8Z!e!Z"dad9Z#d:d;d<dhd?Z$didAZ%didBZ&dfdCZ'dfdDZ(dfdEZ)djdFZ*djdGZ+djdHZ,dkdIZ-dkdJZ.dkdKZ/dkdLZ0dldMZ1dldNZ2e3dmdPZ4dS)nraOImmutable 2D vector class. Args: v: vector object with :attr:`x` and :attr:`y` attributes/properties or a sequence of float ``[x, y, ...]`` or x-axis as float if argument `y` is not ``None`` y: second float for :code:`Vec2(x, y)` :class:`Vec2` implements a subset of :class:`Vec3`. r#r&rVrVNrNonec |j|_|j|_dS#t$re|7t|d|_t|d|_YdSt||_t||_YdSwxYw)Nrrc)r#r&AttributeErrorr )rrr&s rrz Vec2.__init__Bs "SDFSDFFF " " "yqtqtqq  "sAB (B  B rc8t|j|jdS)zReturns a 3D vector.r)rr#r&r"s rvec3z Vec2.vec3NsDFDFA&&&rcz|t|j|t|j|Sr6)r*r7r#r&r8s rr7z Vec2.roundSs0 ~~eDFG44eDFG6L6LMMMrr:r; list[Vec2]cFt||Srr>rAs rr?z Vec2.listZsCLL''(((rSequence[Vec2]cFt||SrErFrAs rrGz Vec2.tuple^rHrIterator[Vec2]c fd|DS)Nc3.K|]}|VdSrrLrMs rrPz Vec2.generate..erQrrLrAs` rr@z Vec2.generatecs,,,,e,,,,rrRrSr rTcn|tj||ztj||zSrrWr[s rr\zVec2.from_anglegs.s48E??V+TXe__v-EFFFrcR|tj||Srr^r[s rr`zVec2.from_deg_angleks ~~dl5116:::rroc,d|S)Nz({0.x}, {0.y})rqr"s rrsz Vec2.__str__os&&t,,,rc0d|zS)Nrrur"s rrvz Vec2.__repr__rs &&rrwcdS)NrdrLr"s rryz Vec2.__len__usqrc8t|j|jfSr)r{r#r&r"s rr|z Vec2.__hash__xsTVTV$%%%rcD||j|jfSrr*r#r&r"s rr~z Vec2.copy{s~~tvtv.///rrrc |t|S#t$r+|}||t|<|cYSwxYwr)idKeyErrorr~)rrrs rrzVec2.__deepcopy__sY BtHH% %    A!"HRXX HHH s2A  A rct|trtd|dkr|jS|dkr|jSt d|)Nrrrcr)rgrrhr#r&rrs rrzVec2.__getitem__sZ eU # # 5344 4 A::6M aZZ6M5e5566 6rrc#.K|jV|jVdSrr#r&r"s rrz Vec2.__iter__s f f rc|jSrrr"s rrz Vec2.__abs__s ~rc@tj|j|jS)zReturns length of vector.rXrr#r&r"s rrzVec2.magnitudez$&$&)))rrcvt|jtkot|jtkSr)rr#rr&r"s rrz Vec2.is_nulls'46{{g%@#df++*@@rc@tj|j|jS)zAngle of vector in radians.)rXrr&r#r"s rrSz Vec2.anglerArc4tj|jS)zAngle of vector in degrees.rr"s rrzVec2.angle_degrrTrc|r!||j |jS||j|j S)zhOrthogonal vector Args: ccw: counter-clockwise if ``True`` else clockwise )r*r&r#rs rrzVec2.orthogonals@  3>>46'4622 2>>$&46'22 2rrrr rc|j|j|jz |zz}|j|j|jz |zz}|||S)zLinear interpolation between `self` and `other`. Args: other: target vector/point factor: interpolation factor (0=self, 1=other, 0.5=mid point) Returns: interpolated vector )r#r&r*)rrrr#r&s rrz Vec2.lerpsL Feg&&0 0 Feg&&0 0~~a###rcZ|}|||zS)z#Project vector `other` onto `self`.rrs rrz Vec2.projectrrc<|||jz Srrrs rrnzVec2.normalizes||FT^3444rcF||j |j Srr7r"s rrz Vec2.reverseds~~tvgw///rc|j Srrr"s rrz Vec2.__bool__s <rrr rrrct|tst|}tj|j|j||o!tj|j|j||S)Nr)rgrrXrr#r&)rrrrs rrz Vec2.isclosesh%&& KKE| FEGWg   Nl4657GWMMM Nrr ct|tst|}|j|jko|j|jkSr)rgrr#r&rs rrz Vec2.__eq__s<%&& KKEv 6TVuw%66rcN|^}}}|j|kr |j|kS|j|kSrr=)rrr#r&_s rrz Vec2.__lt__s01q 6Q;;6A: 6A: rc ||j|jz|j|jzS#t$rt dwxYwNzinvalid argumentr*r#r&r%rhrs rrz Vec2.__add__W 0>>$&57"2DFUW4DEE E 0 0 0.// / 0 /2A c ||j|jz |j|jz S#t$rt dwxYwrPrQrs rrz Vec2.__sub__rRrSc ||j|jz |j|jz S#t$rt dwxYwrPrQrs rrz Vec2.__rsub__sW 0>>%'DF"2EGdf4DEE E 0 0 0.// / 0rScN||j|z|j|zSrr7rs rrz Vec2.__mul__"~~dfundfun===rcN||j|z|j|zSrr7rs rrz Vec2.__rmul__rWrcN||j|z |j|z Srr7rs rrzVec2.__truediv__rWrc@|j|jz|j|jzzSrr=rs rrzVec2.dotv$&57"222rc@|j|jz|j|jzz Srr=rs rdetzVec2.det r[rc`tj|j|jz |j|jz Srr@rs rrz Vec2.distance s&z$&57*DFUW,<===rc||}|dkrd}n|dkrd}tj|S)zqCalculate angle between `self` and `other` in radians. +angle is counter-clockwise orientation. rrR)rnrrXrrs rrzVec2.angle_betweens[ NN$$(():):;; t  II __Iy###rcR|j|j|z|jS)zYRotate vector around origin. Args: angle: angle in radians )r*r\rSrrs rrz Vec2.rotates%~((e);T^LLLrcv|j|jtj|z|jS)zzRotate vector around origin. Args: angle: angle in degrees Returns: rotated vector )r*r\rSrXr_rrs rrzVec2.rotate_deg&s6~(( Je,, ,dn   rIterable[Vec2]c:tdd}|D]}||z }|S)rr)rrs rrzVec2.sum3s0 AJJ  A FAAr)r"N)rr#rrr )r:r;rr))r:r;rr+)r:r;rr-r )rSr rTr rrr r )rrrrr rrrr)rrrrr)rr rr rr)rr rr)rTr rr)rr rr rr rrr)rr rr)rr rr )rSr rr)r:rbrr)5rrrrrrrr'r7rr?rGr@r\r`rsrvryr|r~rrrrrrrrSrrrrrnrrrrrrrrrrrrrr]rrrrrrrLrrrr3sc  c I " " " " "'''X'NNNNN)))[)***[*---[-GGGG[G;;;;[;----''''&&&&0000H7777***X*AAAXA***X*(((X( 3 3 3 3 3 $ $ $ $ $"""" 555550000G    26NNNNNN7777 0000 0000 0000 >>>>>>>>>>>>33333333>>>> $ $ $ $MMMM     \r)rr rr rr r)rr rr rr rr) __future__rtypingrrrrrr functoolsr rXrl ezdxf.mathr r rr__all__rrY_AXISZ_AXISrrrrrLrrrks#""""" (''''''''  '$, 0 0 0 6 z0z0z0z0z0z0z0z0z aA aA aA $q!Q--!!!! % % % % %FFFFFFFFFFr