hT^ddlmZddlmZmZmZddlZddlZddl m Z m Z m Z m Z mZmZmZmZmZmZer ddlmZddlmZgdZdej2dzej2ej2d zgZej2d z ZGd d Zdd ZddZ ddZddZ ddZ!ddZ"ddZ#y)) annotations) TYPE_CHECKINGIterableAnyN) Vec3UVecNULLVECX_AXISZ_AXISOCSMatrix44arc_angle_span_raddistance_point_line_3denclosing_angles) BaseLayoutEllipse)ConstructionEllipseangle_to_paramparam_to_anglerytz_axis_construction?g?@c(eZdZdZeeeddejdf ddZ e ededddf ddZ dZ e dd Ze dd Zdd Zdd Zdd Ze ddZddZd dZd!d"dZd#dZd dZd$dZd%d&dZd'dZy)(raConstruction tool for 3D ellipsis. Args: center: 3D center point major_axis: major axis as 3D vector extrusion: normal vector of ellipse plane ratio: ratio of minor axis to major axis start_param: start param in radians end_param: end param in radians ccw: is counter-clockwise flag - swaps start- and end param if ``False`` rTct||_t||_|jjtr t dt||_|jjtr t dt||_t||_ t||_ |s#|j|jc|_ |_ t|j|j |j|_ y)Nz!Invalid major axis (null vector).z'Invalid extrusion vector (null vector).) rcenter major_axisiscloser ValueError extrusionfloatratio start_param end_param minor_axis)selfrrr!r#r$r%ccws 2lib/python3.12/site-packages/ezdxf/math/ellipse.py__init__zConstructionEllipse.__init__1s6l z* ?? " "7 +@B Bi ?? " "7 +FH H5\  -y)/3~~t?O?O ,D dn$T__dnndjjQihc ft|}tj|rtdt |d}t |}|j |}|j t|dd} tj|} tj|} ||| ||| | t|S)aReturns :class:`ConstructionEllipse` from arc or circle. Arc and Circle parameters defined in OCS. Args: center: center in OCS radius: arc or circle radius extrusion: OCS extrusion vector start_angle: start angle in degrees end_angle: end angle in degrees ccw: arc curve goes counter clockwise from start to end if ``True`` zInvalid extrusion: ?r) absr rr strr to_wcsrmathradiansbool) clsrradiusr! start_angle end_angler(r#ocsrr$r%s r)from_arczConstructionEllipse.from_arcIs,V ??9 %23y>2BCD D)nF#ZZVQ 23 ll;/ LL+        I  r+c|j|j|j|j|j|j |j SN) __class__rrr!r#r$r%r's r)__copy__zConstructionEllipse.__copy__ts?~~ KK OO NN JJ    NN   r+ct|j|j|j|j|j S)z'Returns start point of ellipse as Vec3.)vertexr$rr&rr#r=s r) start_pointzConstructionEllipse.start_point~s6    OO OO KK JJ   r+ct|j|j|j|j|j S)z%Returns end point of ellipse as Vec3.)r@r%rr&rr#r=s r) end_pointzConstructionEllipse.end_points4 NN OO OO KK JJ   r+c|jdkDr!|j}|jn|}|j|j|j t |jd|j|jdS)zReturns 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$r%) r#r> swap_axisrrr!maxr$r%)r'es r) dxfattribszConstructionEllipse.dxfattribssc ::> A KKMAhh,,$'==   r+c#K|j}|j}tD]I}t|||st ||j |j |j|jKyw)zZYields main axis points of ellipse in the range from start- to end param. N) r$r%QUARTER_PARAMSrr@rr&rr#)r'startendparams r)main_axis_pointsz$ConstructionEllipse.main_axis_pointss^  nn#Euc2OOOOKKJJ $s /A.abs_tolcj|z }j|}tj||tjzSr;)dotr1atan2tau)vecdydx new_ratiox_axisy_axiss r)rNz,ConstructionEllipse.transform..params<ZZ_y0ZZ_zz"b)DHH44r+rr-rN)rXz'Vec3'returnr") transformrr$r%r&rr!r#transform_directions normalizerUr.rcross magnituder1rrWr@pi 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_spanrNrArCnew_param_span old_chk_point new_chk_pointr[r\r]s @@@r)r`zConstructionEllipse.transformsp[[- (,(8(88+$(NN2 #DOOT^^TZZP)*)?)? __n -* &%..044^5M5M5OP { d "8N9 5NNI+00@JJLM M'00>3K3KKI*00@JJLM' yQN!M k9d!S#--/F#--/F(+5AN 5 ++OO"KKJJ K OO"KKJJ I j 89Ki*45I<<F #,k"9TXX!E||NNDQ-6 K!" !/=A&  ! !'k95"" ! %,,]D,I-6 K q=' yQNiI' yQNLLa0T\\)TXX5Vw& W$ "DHH, ( << Y /KI  ((& &"r+cBt|j|jS)zReturns the counter-clockwise params span from start- to end param, see also :func:`ezdxf.math.ellipse_param_span` for more information. )rr$r%r=s r) param_spanzConstructionEllipse.param_span-s "$"2"2DNNCCr+c#bKt|j|j|Ed{y7w)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$r%)r'nums r)paramszConstructionEllipse.params5s$d..DDDs %/-/c#hK|j}|j}|jj}|jj}|jj }||z}|D]B}t j||z|z} t j||z|z} || z| zDyw)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#rrbr&rdr1cossin) r'r{rr#r\r]radius_xradius_yrNxys r)verticeszConstructionEllipse.vertices>s **,**,??,,e#E(*V3A(*V3A1*q. sB0B2c# Kd fd d fd jj jjjj jz j |z }|dk(ryj tjz}tjjtjrtj}njtjz}tj||ry||kDr|tjz } |}|||krC||z}tj||r|} |} ||||Ed{|}|}||krByy7w)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 ctj|zz}tj|zz}j|z|zSr;)r1r}r~r)prrrrr'r\r]s r)vertex_z/ConstructionEllipse.flattening..vertex_asD h&/A h&/A;;?Q& &r+c3K||zdz} |}t|||}|kr|y||||Ed{||||Ed{y77w)Nr)r) srHs_parame_paramm_paramrhddistancesubdivrs r)rz.ConstructionEllipse.flattening..subdivfsk(C/G A&q!Q/A8|!!Q999!!Q999:9s!6AAA A AAr^N)rr"r_r)rrrHrrr"rr") rrbr&rdr#rwr$r1rWrr%)r'rsegmentsdeltarNr%rAnext_end_paramrCrrrrr\r]s`` @@@@@@r) flatteningzConstructionEllipse.flatteningSsH ' '  :**,**,??,,djj((* C<   488+ << 1I1I <<y )  Y   !Ien i"U]N||NI6!*/Ik9e^L L L"E#Ki MsE-F 7F8 F F c#vK|jj}|jj}|j}|j}t j |D]Q}||z}tj|j||z |j|tjzSyw)u8Yields ellipse params for all given `vertices`. The vertex don't have to be exact on the ellipse curve or in the range from start- to end param or even in the ellipse plane. Param is calculated from the intersection point of the ray projected on the ellipse plane from the center of the ellipse through the vertex. .. warning:: An input for start- and end vertex at param 0 and 2π return unpredictable results because of floating point inaccuracy, sometimes 0 and sometimes 2π. N) rrbr&r#rrgenerater1rVrUrW)r'rr\r]r#rvs r)params_from_verticesz(ConstructionEllipse.params_from_verticess**,**, x(A KA**VZZ]U2FJJqMBTXXM M)sB7B9c#,K|j}|jj}|jj}|D]K}t j | |z}t j ||z|z}||zjMyw)u3Yields tangents on ellipse for iterable `params` in WCS as direction vectors. Args: params: param values in the range from [0, 2π] in radians, param goes counter-clockwise around the extrusion vector, major_axis = local x-axis = 0 rad. N)r#rrbr&r1r~r})r'r{r#r\r]rNrrs r)tangentszConstructionEllipse.tangentss~ **,**,E% 6)A%'&0Aq5##% %sBBc|j|_d|jz }t|d|_t|j|j|j|_|j }|j }tj|dr%tj|tjry|tz tjz|_|tz tjz|_y)z.Swap axis and adjust start- and end parameter.r-rErN) r&rr#rGr!r$r%r1rrWrg)r'r#r$r%s r)rFzConstructionEllipse.swap_axiss//djj % $T__dnndjjQ&& NN << Q 'DLLDHH,M ''1TXX=#g-9r+Ncddlm}t|xsi}|j|j |j ||j }|j||S)aAdd 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)rIdoc)ezdxf.entitiesrdictupdaterInewr add_entity)r'layoutrIrrHs r) add_to_layoutz!ConstructionEllipse.add_to_layoutsT +**+ $//+, GKK:6:: >!r+ct|j}|j|j|j|j|j j d|j|j|jS)zqReturns ellipse parameters as OCS representation. OCS elevation is stored in :attr:`center.z`. r^)z)rrr#r$r%) r r!r<from_wcsrrreplacer#r$r%)r'r8s r)to_ocszConstructionEllipse.to_ocssm $..!~~<< ,||DOO4<propertyrArCrIrOr`rwr{rrrrrFrrr+r)rr#s_ ! 88RRR R  R  RRR0 ( ( (  (  (  ( (  ( ( T      ( s#jDDE!*:$xN.&& :$  r+rcB||kr|tjz }||zdz S)Nr)r1rW)rLrMs r)rfrfs% U{ txx CK3 r+c\|j|j|j|zSr;)rcrbrd)rr!r#s r)r&r&s' ??: & 0 01E1E1M NNr+c|j}|j}|j}||z}tj||z|z} tj||z|z} || z| zSr;)rbrdr1r}r~) rNrr&rr#r\r]rrrrs r)r@r@sq ! ! #F  ! ! #F##H%H ("V+A ("V+A A:>r+c#K|dkr td||kr|tjz }tj|||D]}|tjzyw)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 r1rWnplinspace)rLrMrzrNs r)ryrysT  Qw$$ e| txxUC-dhh.sAActjtj||z tj|tjzS)uKReturns 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) )r1rVr~r}rW)r#angles r)rrs3 ::dhhuo-txx ?$(( JJr+ctjtj||ztj|S)uVReturns 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) )r1rVr~r})r#rNs r)rrs* ::dhhuo-txx ??r+c0t|}tj|jddr>tj|jddrt|j d}n;|j |}|j |j |j}|j|}|j}||z j |}||z }||z} |jts| jtr td||z j} | |z j} tj| dstj| dr td| | z } | j | } |j | }| || fS)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) rrQrRF)r(z.Conjugated axis required, invalid source data.r^) rr1rr orthogonalrcrbrdlerpr ArithmeticError)d1d2QP1r!Dr5 radius_vectorABmajor_axis_lengthminor_axis_lengthr#rr&s r)rr,sU( RA ||BDD!T*t||BDD!T/R "X U +HHRL __R * *2<< 8  A [[FV&&v.M MA MAyyQYYw/NOOQ))Q)) ||%s+t||rs#//    (&  TWWs]DGGTWWs]; ''C-C C L O   " 04 >B KP     K @+)r+