heddlmZddlmZmZmZmZmZmZddl m Z ddl Z ddl Z erddl mZmZdZe e j"eZdd gZGd dZed ddZedd dZeddd ZedddZdd Zddd ZGdd Zy)) annotations)TupleIterableSequence TYPE_CHECKINGIteratorOptional)partialN)UVecAnyVec-q=)abs_tolVec3Vec2ceZdZdZgdZdZedAdZedAdZedAdZ edBdZ edCdZ edDd Z dE dFd Z dGdBd ZedHd ZedIdZedJdZedKdLdZedKdLdZedMdZedNdOdZdPdZdPdZdQdZdQdZdBdZeZdRdZdSdZdTdZ dAdZ!edAdZ"edAdZ#edAdZ$edUd Z%d!d"d# dVd$Z&edAd%Z'edAd&Z(edAd'Z)edAd(Z*dWdXd)Z+dYdZd*Z,dZd+Z-dKdOd,Z.dBd-Z/e/Z0dUd.Z1d!d"d# d[d/Z2d\d0Z3d\d1Z4dZd2Z5dZd3Z6dZd4Z7dZd5Z8d]d6Z9d]d7Z:d]d8Z;ed^d9Zd_d<Z?d_d=Z@d`d>ZAdad?ZBdad@ZCy )braImmutable 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_zcH|j|\|_|_|_yN decomposerrr)selfargss 2lib/python3.12/site-packages/ezdxf/math/_vector.py__init__z Vec3.__init__Hs$2DNND$9!$'c|jS)z x-axis value)rrs rxzVec3.xK wwrc|jS)z y-axis value)rr s ryzVec3.yPr"rc|jS)z z-axis value)rr s rzzVec3.zUr"rcN|j|j|jS)z1Vec3 as ``(x, y, 0)``, projected on the xy-plane.) __class__rrr s rxyzVec3.xyZs~~dggtww//rcH|j|j|jfS)zVec3 as ``(x, y, z)`` tuple.rr s rxyzzVec3.xyz_sww((rcDt|j|jfS)z'Real 2D vector as :class:`Vec2` object.)rrrr s rvec2z Vec3.vec2dsTWWdgg&''rNc|| |j}| |j}| |j}|j|||S)zz Vec3.generate..,edD erDr:s` rr9z Vec3.generates-e,,rcn|tj||ztj||zdS)zhReturns a :class:`Vec3` object from `angle` in radians in the xy-plane, z-axis = ``0``. mathcossinr;anglelengths r from_anglezVec3.from_angles- 488E?V+TXXe_v-EsKKrcL|jtj||S)zhReturns a :class:`Vec3` object from `angle` in degrees in the xy-plane, z-axis = ``0``. rTrNradiansrQs rfrom_deg_anglezVec3.from_deg_angles ~~dll516::rct|}|dk(ry|dk(r|d}t|tr#|j|j|j fSt|}|dk(r|\}}d}n|dk(r|\}}}nt t|t|t|fS|dk(r|\}}t|t|dfS|dk(r&|\}}}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)rLrLrLrL)len isinstancerrrr TypeErrorfloat)rrSdatar!r$r&s rrzVec3.decomposes$T Q; q[7D$%ww00TQ;DAqAq["GAq!#OQxq5833 q[DAq8U1Xs* * q[GAq!8U1XuQx/ /rctjdd}tjdd}tjdd}t|||j|S)zReturns a random vector.rZ)randomuniformr normalize)r;rSr!r$r&s rrdz Vec3.randomsM NN2q ! NN2q ! NN2q !Aq!}&&v..rc$dj|S)z!Return ``'(x, y, z)'`` as string.z({0.x}, {0.y}, {0.z})formatr s r__str__z Vec3.__str__s&--d33rc(d|jzS)z%Return ``'Vec3(x, y, z)'`` as string.rrjr s r__repr__z Vec3.__repr__s &&rcy)zReturns always ``3``.r\rDr s r__len__z Vec3.__len__src,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__sDHH~rc|S)z1Returns a copy of vector as :class:`Vec3` object.rDr s rcopyz Vec3.copy rc|S)z:func:`copy.deepcopy` support.rD)rmemodicts r __deepcopy__zVec3.__deepcopy__rurct|tr td|dk(r |jS|dk(r |jS|dk(r |j St d|)zbSupport for indexing: - v[0] is v.x - v[1] is v.y - v[2] is v.z slicing not supportedrrZr[invalid index )r^slicer_rrr IndexErrorrindexs r __getitem__zVec3.__getitem__s\ eU #34 4 A:77N aZ77N aZ77N~eW56 6rc#`K|j|j|jyw)z&Returns iterable of x-, y- and z-axis.Nrr s r__iter__z Vec3.__iter__s!gg gg gg s,.c|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$$c))rcVtj|j|jS)z!Length of vector in the xy-plane.)rNhypotrrr s r magnitude_xyzVec3.magnitude_xyzz$''477++rcl|j|j|j}}}||z||zz||zzS)zSquare length of vector.rr/s rrzVec3.magnitude_squares8''477DGGa11uq1u}q1u$$rct|jtkxr:t|jtkxrt|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 LG # (DGG ' (DGG ' r& .>r rel_tolrc|j}|j}|j|||xs|j| ||S)z?Returns ``True`` if `self` and `other` are parallel to vectors.r)rfisclose)rotherrrv1v2s r is_parallelzVec3.is_parallel'sT^^  __ zz"gwz? 2:: C'DND  rcntjtj|j S)z3Spatial angle between vector and x-axis in radians.)rNacosX_AXISdotrfr s r spatial_anglezVec3.spatial_angle1s#yyDNN$4566rc@tj|jS)z3Spatial angle between vector and x-axis in degrees.)rNdegreesrr s rspatial_angle_degzVec3.spatial_angle_deg6s||D..//rcVtj|j|jS)z;Angle between vector and x-axis in the xy-plane in radians.)rNatan2rrr s rrRz Vec3.angle;rrc@tj|jS)z>Returns angle of vector and x-axis in the xy-plane in degrees.rNrrRr s r angle_degzVec3.angle_deg@||DJJ''rc|r2|j|j |j|jS|j|j|j |jS)zReturns orthogonal 2D vector, z-axis is unchanged. Args: ccw: counter-clockwise if ``True`` else clockwise )r(rrrrccws r orthogonalzVec3.orthogonalEsQ NNDGG8TWWdgg 6 $''477; rcd|j||z t|z}|j|S)zReturns linear interpolation between `self` and `other`. Args: other: end point as :class:`Vec3` compatible object factor: interpolation factor (0 = self, 1 = other, 0.5 = mid point) )r(r`__add__)rrfactords rlerpz Vec3.lerpRs.^^E "T )U6] :||ArcJ|j}||j|zS)z0Returns projected vector of `other` onto `self`.rfrrruvs rprojectz Vec3.project^! ^^ BFF5M!!rc>|j||jz S)z7Returns normalized vector, optional scaled by `length`.__mul__rrrSs rrfzVec3.normalizecs||FT^^344rcj|j|j |j |j S)z!Returns negated vector (-`self`).)r(rrrr s rreversedz Vec3.reversedgs'~~twwh477(;;rc|j S)z,Returns ``True`` if vector is not (0, 0, 0).rr s r__bool__z Vec3.__bool__ms<<rc|j|\}}}tj|j|||xrHtj|j|||xr#tj|j |||S)zReturns ``True`` if `self` is close to `other`. Uses :func:`math.isclose` to compare all axis. Learn more about the :func:`math.isclose` function in `PEP 485 `_. r)rrNrrrr)rrrrr!r$r&s rrz Vec3.iscloseqsk..'1a LL!Wg F K TWWa'J K TWWa'J rct|ts t|}|j|jk(xr4|j|jk(xr|j|jk(S)zZEqual operator. Args: other: :class:`Vec3` compatible object )r^rr!r$r&rrs r__eq__z Vec3.__eq__sN %&KEvv LTVVuww%6L466UWW;LLrc|j|\}}}|j|k(r-|j|k(r|j|kS|j|kS|j|kS)z`Lower than operator. Args: other: :class:`Vec3` compatible object rrrr!r$r&s r__lt__z Vec3.__lt__sX..'1a 77a<ww!|ww{"ww{"77Q; rc|j|\}}}|j|j|z|j|z|j|zS)z-Add :class:`Vec3` operator: `self` + `other`.rr(rrrrs rrz Vec3.__add__sA..'1a~~dggk477Q;! DDrc$|j|S)z.RAdd :class:`Vec3` operator: `other` + `self`.)rrs r__radd__z Vec3.__radd__||E""rc|j|\}}}|j|j|z |j|z |j|z S)z-Sub :class:`Vec3` operator: `self` - `other`.rrs r__sub__z Vec3.__sub__sC..'1a~~dggk477Q;! DDrc|j|\}}}|j||jz ||jz ||jz S)z.RSub :class:`Vec3` operator: `other` - `self`.rrs r__rsub__z Vec3.__rsub__sA..'1a~~a$''k1tww;DGG DDrct|}|j|j|z|j|z|j|zS)z&Scalar Mul operator: `self` * `other`.r`r(rrrrrscalars rrz Vec3.__mul__9u~~dgg.&0@$''FBRSSrc$|j|S)z'Scalar RMul operator: `other` * `self`.)rrs r__rmul__z Vec3.__rmul__rrct|}|j|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 FArc|j|\}}}|j|z|j|zz|j|zzS)ziDot operator: `self` . `other` Args: other: :class:`Vec3` compatible object rrs rrzVec3.dots@ ..'1aww{TWWq[(477Q;66rc|j|\}}}|j|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.crosssq ..'1a~~ GGaK$''A+ % GGaK$''A+ % GGaK$''A+ %  rcZ|j|}|j|jS)z3Returns distance between `self` and `other` vector.)r(rr)rrrs rdistancez Vec3.distances$ NN5 !yy(((rc|jj|j|j}|dkrd}n|dkDrd}tj|S)zReturns angle between `self` and `other` in radians. +angle is counter clockwise orientation. Args: other: :class:`Vec3` compatible object ?)rfrr(rNrrr cos_thetas r angle_betweenzVec3.angle_betweensUNN$(()>)H)H)JK t I _Iyy##rc||j|z j}|j|j}|j|}|j|}t j ||tj zS)aReturns counter-clockwise angle in radians about `self` from `base` to `target` when projected onto the plane defined by `self` as the normal vector. Args: base: base vector, defines angle 0 target: target vector )rrfrrrNrtau)rbasetargetx_axisy_axistarget_projected_xtarget_projected_ys r angle_aboutzVec3.angle_aboutsqd++668F#--/#ZZ/#ZZ/zz,.@ADHHLLrc |j|j|jd}tj |j |z|j }|j|j|j|jS)ztReturns vector rotated about `angle` around the z-axis. Args: angle: angle in radians rL)r(r!r$rrTrRrr&)rrRrs rrotatez Vec3.rotatesY NN4664663 / OOAGGeOQ[[ 9~~acc133//rcJ|jtj|S)ztReturns vector rotated about `angle` around the z-axis. Args: angle: angle in degrees )rrNrWrrRs r rotate_degzVec3.rotate_deg s{{4<<.//rreturnr`rr)rztuple[float, float, float]rr)NNN)r!Optional[float]r$rr&rrrr)r<Iterable[UVec]rz list[Vec3])r<rrzSequence[Vec3])r<rrzIterator[Vec3]r)rRr`rSr`rr)rzTuple[float, float, float])rZ)rSr`rrrstrrint)rwdictrrrrrr`rzIterator[float]rbool)rrrr`rr`rr T)rr rrr)rr rr)rr rr`rr`rr rr rr )rr`rr)r<rrr)rr rr`)rr rr rr`)rRr`rr)D__name__ __module__ __qualname____doc__ __slots__rpropertyr!r$r&r)r+r-r0r3 classmethodr8r@r9rTrX staticmethodrrdrjrmrorrrt__copy__rxrrrrrrrrrrrRrrrrrfr__neg__rrrrrrrrrrrrrrrrrrrrDrrrrs*X#I:00))(( "!! '  '  '  '  '  ))**--LL ;; ((T//4' H7& **,,%%   04e  ', >C  7700,,((   " 5<G 04e  ', >C  "M E #E E T #T 7  ) $ M 00rrZc6t|j|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)p1p2s rrrs 8  R  rc8t|j||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 8==V $$rc eZdZdZddgZd3d4dZed5dZd6d7dZe d8dZ e d9d Z e d:d Z e d;ddZd>dZd7dZeZd?dZd@dZdAdZdBdZedBdZedCdZedBdZedBdZdDdEdZdFdGdZdHdZd;dIdZ d7dZ!e!Z"dCdZ#d d!d" dJd#Z$dKd$Z%dKd%Z&dHd&Z'dHd'Z(dHd(Z)dLd)Z*dLd*Z+dLd+Z,dMd,Z-dMd-Z.dMd.Z/dMd/Z0dNd0Z1dNd1Z2e3dOd2Z4y)PraOImmutable 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$Nc |j|_|j|_y#t$rM|(t|d|_t|d|_Yyt||_t||_YywxYw)NrrZ)r!r$AttributeErrorr`)rrr$s rrz Vec2.__init__Bse "SSDFSSDF "yqtqtqq  "s"%1A; A;:A;cDt|j|jdS)zReturns a 3D vector.r)rr!r$r s rvec3z Vec2.vec3NsDFFDFFA&&rcv|jt|j|t|j|Sr2)r(r3r!r$r4s rr3z Vec2.roundSs+ ~~eDFFG4eDFFG6LMMrc6t|j|Srr7r:s rr8z Vec2.listZsCLL'((rc6t|j|Sr>r?r:s rr@z Vec2.tuple^rArcfd|DS)Nc3.K|] }|ywrrDrEs rrHz Vec2.generate..erIrJrDr:s` rr9z Vec2.generatecs,e,,rcl|tj||ztj||zSrrMrQs rrTzVec2.from_anglegs)488E?V+TXXe_v-EFFrcL|jtj||SrrVrQs rrXzVec2.from_deg_angleks~~dll516::rc$dj|S)Nz({0.x}, {0.y})rhr s rrjz Vec2.__str__os&&t,,rc(d|jzS)Nrrlr s rrmz Vec2.__repr__rs &&rcy)Nr[rDr s rroz Vec2.__len__usrcDt|j|jfSr)rqr!r$r s rrrz Vec2.__hash__xsTVVTVV$%%rcP|j|j|jfSrr(r!r$r s rrtz Vec2.copy{s~~tvvtvv.//rc~ |t|S#t$r#|j}||t|<|cYSwxYwr)idKeyErrorrt)rrwrs rrxzVec2.__deepcopy__sC BtH% %  A!"HRX H s )<<ct|tr td|dk(r |jS|dk(r |jSt d|)NrzrrZr{)r^r|r_r!r$r}r~s rrzVec2.__getitem__sJ eU #34 4 A:66M aZ66M~eW56 6rc#DK|j|jywrr!r$r s rrz Vec2.__iter__sff ff s c|jSrrr s rrz Vec2.__abs__s ~~rcVtj|j|jS)zReturns length of vector.rNrr!r$r s rrzVec2.magnitudezz$&&$&&))rcvt|jtkxrt|jtkSr)rr!rr$r s rrz Vec2.is_nulls'466{g%@#dff+*@@rcVtj|j|jS)zAngle of vector in radians.)rNrr$r!r s rrRz Vec2.angler7rc@tj|jS)zAngle of vector in degrees.rr s rrzVec2.angle_degrrc|r'|j|j |jS|j|j|j S)zhOrthogonal vector Args: ccw: counter-clockwise if ``True`` else clockwise )r(r$r!rs rrzVec2.orthogonals= >>466'4662 2>>$&&466'2 2rc|j|j|jz |zz}|j|j|jz |zz}|j||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.lerpsU FFegg&&0 0 FFegg&&0 0~~a##rcJ|j}||j|zS)z#Project vector `other` onto `self`.rrs rrz Vec2.projectrrc>|j||jz Srrrs rrfzVec2.normalizes||FT^^344rcR|j|j |j Srr-r s rrz Vec2.reverseds~~tvvgw//rc|j Srrr s rrz Vec2.__bool__s<<rrr rct|ts t|}tj|j|j||xr-tj|j |j ||S)Nr)r^rrNrr!r$)rrrrs rrz Vec2.isclosesZ%&KE|| FFEGGWg Nll466577GWM Nrct|ts t|}|j|jk(xr|j|jk(Sr)r^rr!r$rs rrz Vec2.__eq__s:%&KEvv 6TVVuww%66rcf|^}}}|j|k(r|j|kS|j|kSrr3)rrr!r$_s rrz Vec2.__lt__s41q 66Q;66A: 66A: rc |j|j|jz|j|jzS#t$r t dwxYwNzinvalid argumentr(r!r$rr_rs rrz Vec2.__add__M 0>>$&&577"2DFFUWW4DE E 0./ / 0 ?AAc |j|j|jz |j|jz S#t$r t dwxYwrFrGrs rrz Vec2.__sub__rHrIc |j|j|jz |j|jz S#t$r t dwxYwrFrGrs rrz Vec2.__rsub__sM 0>>%''DFF"2EGGdff4DE E 0./ / 0rIcZ|j|j|z|j|zSrr-rs rrz Vec2.__mul__#~~dffundffun==rcZ|j|j|z|j|zSrr-rs rrz Vec2.__rmul__rMrcZ|j|j|z |j|z Srr-rs rrzVec2.__truediv__rMrch|j|jz|j|jzzSrr3rs rrzVec2.dot'vv$&&577"222rch|j|jz|j|jzz Srr3rs rdetzVec2.det rQrctj|j|jz |j|jz Srr6rs rrz Vec2.distance s-zz$&&577*DFFUWW,<==rc|jj|j}|dkrd}n|dkDrd}tj|S)zqCalculate angle between `self` and `other` in radians. +angle is counter-clockwise orientation. rr)rfrrNrrs rrzVec2.angle_betweensJ NN$(():; t I _Iyy##rch|jj|j|z|jS)zYRotate vector around origin. Args: angle: angle in radians )r(rTrRrrs rrz Vec2.rotates(~~((e);T^^LLrc|jj|jtj|z|j S)zzRotate vector around origin. Args: angle: angle in degrees Returns: rotated vector )r(rTrRrNrWrrs rrzVec2.rotate_deg&s6~~(( JJe, ,dnn  rc6tdd}|D]}||z } |S)rr)rrs rrzVec2.sum3s' AJA FAr))rLrLN)rNonerrr)r<rrz list[Vec2])r<rrzSequence[Vec2])r<rrzIterator[Vec2]r)rRr`rSr`rrrr)rwrrrrrrr r )rr rrr )rr rr`rr)rr rr)rSr`rr)rr rr`rr`rr r )rr`rr)rr rr`)rRr`rr)r<zIterable[Vec2]rr)5rrrrrrrr r3rr8r@r9rTrXrjrmrorrrtrrxrrrrrrRrrrrrfrrrrrrrrrrrrrrSrrrrrrrDrrrr3s c I "''N))**--GG;;-'&0H7**AA**(( 3 $" 50G 26NN).N@EN N7 0 0 0 >>>33> $M  r)rr rr rr`r )rr rr rr`rr) __future__rtypingrrrrrr functoolsr rNrd ezdxf.mathr r rr__all__rrY_AXISZ_AXISrrrrrDrrras# '  $,, 0 6 z0z0z aA aA aA q!Q-! %FFr