hRvSSKJr SSKJrJrJr SSKrSSKrSSK J r J r J r J r JrJrJrJrJrJr \(a SSKJr SSKJr /SQrS\R2S-\R2\R2S -/r\R2S - r"S S 5rSS jrSSjrSSjrSSjr SSjr!SSjr"SSjr#g)) annotations) TYPE_CHECKINGIterableAnyN) Vec3UVecNULLVECX_AXISZ_AXISOCSMatrix44arc_angle_span_raddistance_point_line_3denclosing_angles) BaseLayoutEllipse)ConstructionEllipseangle_to_paramparam_to_anglerytz_axis_construction?g?@cX\rSrSrSr\\\SS\RS4SSjjr \ \S\SSS4SSjj5r S r \SS j5r\SS j5rSS jrSS jrSSjr\S Sj5rS!SjrS"SjrS#S$SjjrS%SjrS"SjrS&SjrS'S(SjjrS)SjrSrg)*r#acConstruction tool for 3D ellipsis. Args: center: 3D center point major_axis: major axis as 3D vector extrusion: normal vector of ellipse plane ratio: ratio of minor axis to major axis start_param: start param in radians end_param: end param in radians ccw: is counter-clockwise flag - swaps start- and end param if ``False`` rTc4[U5Ul[U5UlURR[5(a [ S5e[U5UlURR[5(a [ S5e[U5Ul[U5Ul [U5Ul U(d#URURsUl Ul [URUR UR5Ul g)Nz!Invalid major axis (null vector).z'Invalid extrusion vector (null vector).) rcenter major_axisiscloser ValueError extrusionfloatratio start_param end_param minor_axis)selfrrr"r$r%r&ccws D/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/ellipse.py__init__ConstructionEllipse.__init__1s6l z* ?? " "7 + +@B Bi ?? " "7 + +FH H5\  -y)/3~~t?O?O ,D dn$T__dnndjjQihc v[U5n[R"U5(a[S[ U535eSn[ U5nUR U5nUR [USS55n [R"U5n [R"U5n U"UU UUU U [U55$)adReturns :class:`ConstructionEllipse` from arc or circle. Arc and Circle parameters defined in OCS. Args: center: center in OCS radius: arc or circle radius extrusion: OCS extrusion vector start_angle: start angle in degrees end_angle: end angle in degrees ccw: arc curve goes counter clockwise from start to end if ``True`` zInvalid extrusion: ?r) absr r r!strr to_wcsrmathradiansbool) clsrradiusr" start_angle end_angler)r$ocsrr%r&s r*from_arcConstructionEllipse.from_arcIs,V ??9 % %23y>2BCD D)nF#ZZVQ 23 ll;/ LL+        I  r-cURURURURURUR UR 5$N) __class__rrr"r$r%r&r(s r*__copy__ConstructionEllipse.__copy__ts?~~ KK OO NN JJ    NN   r-c[URURURURUR 5$)z'Returns start point of ellipse as Vec3.)vertexr%rr'rr$r@s r* start_pointConstructionEllipse.start_point~s6    OO OO KK JJ   r-c[URURURURUR 5$)z%Returns end point of ellipse as Vec3.)rDr&rr'rr$r@s r* end_pointConstructionEllipse.end_points4 NN OO OO KK JJ   r-cURS:a!UR5nUR5 OUnURURUR [ URS5URURS.$)zyReturns required DXF attributes to build an ELLIPSE entity. Entity ELLIPSE has always a ratio in range from 1e-6 to 1. rư>)rrr"r$r%r&) r$rA swap_axisrrr"maxr%r&)r(es r* dxfattribsConstructionEllipse.dxfattribssc ::> A KKMAhh,,$'==   r-c## URnURn[HOn[X1U5(dM[ UUR UR URUR5v MQ g7f)zJYields main axis points of ellipse in the range from start- to end param. N) r%r&QUARTER_PARAMSrrDrr'rr$)r(startendparams r*main_axis_points$ConstructionEllipse.main_axis_pointss^  nn#Ec22OOOOKKJJ $s 1A5>A5c ^^^URUR5nUR=p4UR=pV[ UR UR UR5nURUR U45upUR5RU R55n [U 5S:a0[X5upmURU 5R5n Sn OFU RUR- mURU 5R5n [ XT5n Sn U (Ga[R "XFSS9(GdUR5mU R5mXd- [R"-n S UUU4SjjnUR[%UUR UURUR55nUR[%UUR UURUR55nU"X- 5nU"UU- 5n[R "U [R&SS9(d3Xd- [R"-n[R "U USS9(dXdpdOtUR[%[)X55UR UURUR55n[%[)XF5UU UT5nUR!USS9(dXdpdTS:au[ XT5nST- m[ XT5n [R "US 5(a*[R "U[R"5(dU[*-nU[*-nU[R"-nU[R"-n[R "XF5(aS n[R"nX lXlXlXlTUlX@lX`lg ) z8Transform ellipse in place by transformation matrix `m`.rKTF& .>abs_tolc>TRU5T- nTRU5n[R"X5[R-$r>)dotr3atan2tau)vecdydx new_ratiox_axisy_axiss r*rU,ConstructionEllipse.transform..params:ZZ_y0ZZ_zz")DHH44r-rr/rN)r`z'Vec3'returnr#) transformrr%r&r'rr"r$transform_directions normalizer]r0rcross magnituder3r r_rDpi mid_paramHALF_PI)r(m new_centerold_start_paramr% old_end_paramr&old_minor_axisnew_major_axisnew_minor_axis dot_product new_extrusion adjust_paramsold_param_spanrUrErHnew_param_span old_chk_point new_chk_pointrcrdres @@@r*riConstructionEllipse.transformsP[[- (,(8(88$(NN2 #DOOT^^TZZP)*)?)? __n -* &%..044^5M5M5OP { d "8N9 5NI+00@JJLM M'00>3K3KKI*00@JJLM'yQN!M kd!S!S#--/F#--/F(5AN 5 5 ++OO"KKJJ K OO"KKJJ I 89Ki*45I<<F #,"9TXX!E||NNDQ-6!" !/A&  ! !'k5"" ! %,,]D,I-6 q='yQNiI'yQNLLa00T\\)TXX5V5Vw& W$ "DHH, ( << / /KI ((& &"r-cB[URUR5$)zReturns the counter-clockwise params span from start- to end param, see also :func:`ezdxf.math.ellipse_param_span` for more information. )rr%r&r@s r* param_spanConstructionEllipse.param_span-s "$"2"2DNNCCr-c#b# [URURU5ShvN gN7f)uReturns `num` params from start- to end param in counter-clockwise order. All params are normalized in the range from [0, 2π). N) get_paramsr%r&)r(nums r*paramsConstructionEllipse.params5s#d..DDDs %/-/c#l# URnURnURR5nURR5nURR nXc-nUHDn[ R"U5U-U-n [ R"U5U-U-n X)-U -v MF g7f)uYields vertices on ellipse for iterable `params` in WCS. Args: params: param values in the range from [0, 2π) in radians, param goes counter-clockwise around the extrusion vector, major_axis = local x-axis = 0 rad. N) rr$rrkr'rmr3cossin) r(rrr$rdreradius_xradius_yrUxys r*verticesConstructionEllipse.vertices>s **,**,??,,#E(*V3A(*V3A*q. sB2B4c#>^^^ ^ ^ ^ ^ ^# SU U UU U4Sjjm SUU U 4Sjjm TRR5m TRR5mTRRm T TR-m TR U- nUS:XagTR [R-n[R"TR[R5(a[RnOTR[R-n[R"XE5(agXE:aU[R- nT "U5nUv XE:aFXC-n[R"Xu5(aUnT "U5nT "XhXG5ShvN UnUnXE:aMEggN7f)aAdaptive recursive flattening. The argument `segments` is the minimum count of approximation segments, if the distance from the center of the approximation segment to the curve is bigger than `distance` the segment will be subdivided. Returns a closed polygon for a full ellipse: start vertex == end vertex. Args: distance: maximum distance from the projected curve point onto the segment chord. segments: minimum segment count c>[R"U5T-T-n[R"U5T-T-nTRU-U-$r>)r3rrr)prrrrr(rdres r*vertex_/ConstructionEllipse.flattening..vertex_asD h&/A h&/A;;?Q& &r-c3># X#-S-nT "U5n[XPU5nUT:aUv gT"XX$5ShvN T"XQXC5ShvN gNN7f)Nr)r) srNs_parame_paramm_paramrqddistancesubdivrs r*r.ConstructionEllipse.flattening..subdivfs](C/G A&qQ/A8|!!999!!999:9s!3AA AAAArgN)rr#rhr)rrrNrrr#rr#) rrkr'rmr$rr%r3r_r r&)r(rsegmentsdeltarUr&rEnext_end_paramrHrrrrrdres`` @@@@@@r* flatteningConstructionEllipse.flatteningSsE ' '  : :**,**,??,,djj((* C<   488+ << 1 1I1I << ) )     !Ien "]N||N66!*/IkeL L L"E#K MsE?F F FFc#|# URR5nURR5nURnURn[ R "U5HRnXe-n[R"URU5U- URU55[R-v MT g7f)uYields ellipse params for all given `vertices`. The vertex don't have to be exact on the ellipse curve or in the range from start- to end param or even in the ellipse plane. Param is calculated from the intersection point of the ray projected on the ellipse plane from the center of the ellipse through the vertex. .. warning:: An input for start- and end vertex at param 0 and 2π return unpredictable results because of floating point inaccuracy, sometimes 0 and sometimes 2π. N) rrkr'r$rrgenerater3r^r]r_)r(rrdrer$rvs r*params_from_vertices(ConstructionEllipse.params_from_verticess**,**, x(A KA**VZZ]U2FJJqMBTXXM M)sB:B<c#2# URnURR5nURR5nUHMn[R "U5*U-n[R "U5U-U-nXg-R5v MO g7f)uYields tangents on ellipse for iterable `params` in WCS as direction vectors. Args: params: param values in the range from [0, 2π] in radians, param goes counter-clockwise around the extrusion vector, major_axis = local x-axis = 0 rad. N)r$rrkr'r3rr)r(rr$rdrerUrrs r*tangentsConstructionEllipse.tangentss{ **,**,E% 6)A%'&0A5##% %sBBcURUlSUR- n[US5Ul[URURUR5UlUR nUR n[R"US5(a+[R"U[R5(agU[- [R-UlU[- [R-Ulg)z.Swap axis and adjust start- and end parameter.r/rKrN) r'rr$rMr"r%r&r3r r_rp)r(r$r%r&s r*rLConstructionEllipse.swap_axiss//djj % $T__dnndjjQ&& NN << Q ' 'DLLDHH,M,M ''1TXX=#g-9r-NcSSKJn [U=(d 05nURUR 55 UR "X!R S9nURU5 U$)zAdd ellipse as DXF :class:`~ezdxf.entities.Ellipse` entity to a layout. Args: layout: destination layout as :class:`~ezdxf.layouts.BaseLayout` object dxfattribs: additional DXF attributes for the ELLIPSE entity rr)rOdoc)ezdxf.entitiesrdictupdaterOnewr add_entity)r(layoutrOrrNs r* add_to_layout!ConstructionEllipse.add_to_layoutsP +**+ $//+, KK::: >!r-c [UR5nURURUR5URUR 5R SS9URURURS9$)zaReturns ellipse parameters as OCS representation. OCS elevation is stored in :attr:`center.z`. rg)z)rrr$r%r&) r r"r?from_wcsrrreplacer$r%r&)r(r:s r*to_ocsConstructionEllipse.to_ocssm $..!~~<< ,||DOO4<)rrrhr)rhr)__name__ __module__ __qualname____firstlineno____doc__r r r r3r_r+ classmethodr;rApropertyrErHrOrVrirrrrrrrLrr__static_attributes__r-r*rr#s_ ! 88RRR R  R  RRR0 ( ( (  (  (  ( (  ( ( T      ( s#jDDE!*:$xN.&& :$  r-rc@X:aU[R- nX-S- $)Nr)r3r_)rSrTs r*roros! { txx K3 r-c\URU5RURU-5$r>)rlrkrm)rr"r$s r*r'r's' ??: & 0 01E1E1M NNr-cUR5nUR5nURnXt-n[R"U5U-U-n [R"U5U-U-n X9-U -$r>)rkrmr3rr) rUrr'rr$rdrerrrrs r*rDrDsm ! ! #F  ! ! #F##HH ("V+A ("V+A :>r-c## US:a [S5eX::aU[R- n[R"XU5HnU[R-v M g7f)uReturns `num` params from start- to end param in counter-clockwise order. All params are normalized in the range from [0, 2π). znum >= 2N)r!r3r_nplinspace)rSrTrrUs r*rrsO  Qw$$ | txxU-dhh.sAA c[R"[R"U5U- [R"U55[R-$)u+Returns ellipse parameter for argument `angle`. Args: ratio: minor axis to major axis ratio as stored in the ELLIPSE entity (always <= 1). angle: angle between major axis and line from center to point on the ellipse Returns: the ellipse parameter in the range [0, 2π) )r3r^rrr_)r$angles r*rrs3 ::dhhuo-txx ?$(( JJr-c[R"[R"U5U-[R"U55$)u6Returns circle angle from ellipse parameter for argument `angle`. Args: ratio: minor axis to major axis ratio as stored in the ELLIPSE entity (always <= 1). param: ellipse parameter between major axis and point on the ellipse curve Returns: the circle angle in the range [0, 2π) )r3r^rr)r$rUs r*rrs* ::dhhuo-txx ??r-cT[U5n[R"URSSS9(a>[R"URSSS9(a[U5R SS9nO;UR U5nUR U5R UR5nURU5nURnX#- R U5nXW- nXW-n UR[5(dU R[5(a [S5eX- Rn X- Rn [R"U S5(d[R"U S5(a [S5eX- n U R U 5n UR U 5nXU 4$)uThe Rytz’s axis construction is a basic method of descriptive Geometry to find the axes, the semi-major axis and semi-minor axis, starting from two conjugated half-diameters. Source: `Wikipedia `_ Given conjugated diameter `d1` is the vector from center C to point P and the given conjugated diameter `d2` is the vector from center C to point Q. Center of ellipse is always ``(0, 0, 0)``. This algorithm works for 2D/3D vectors. Args: d1: conjugated semi-major axis as :class:`Vec3` d2: conjugated semi-minor axis as :class:`Vec3` Returns: Tuple of (major axis, minor axis, ratio) rrYrZF)r)z.Conjugated axis required, invalid source data.rg) rr3r r orthogonalrlrkrmlerpr ArithmeticError)d1d2QP1r"Dr7 radius_vectorABmajor_axis_lengthminor_axis_lengthr$rr's r*rr,sR( RA ||BDD!T*t||BDD!T/R "X U +HHRL __R * *2<< 8  A [[FV&&v.M A AyyQYYw//NOO)))) ||%s++t||rs#//    (&  TWWs]DGGTWWs]; ''C-C C L O   " 04 >B KP     K @+)r-