hB ddlmZddlmZmZmZmZmZddlZddl m Z ddl m Z m Z mZmZmZmZmZmZmZmZmZmZddlmZmZgdZ dK dLd Zdddej:df dMd Z dN dOd ZdPdQdZ dR dSdZ!dTdUdZ" dV dWdZ# dX dYdZ$ dZ d[dZ%Gdde Z& d\ d]dZ'e dddfd^dZ(d_d`dZ) da dbdZ*dcdddZ+ de dfdZ, dg dhdZ-e ddde ddde ddde ddde ddde ddde ddde dddgZ.e d d d e d!d d e d!d!d e d d!d e d d d!e d!d d!e d!d!d!e d d!d!gZ/gd"gd#gd$gd%gd&gd'gZ0didjd(Z1 dk dld)Z2dmd*Z3dnd+Z4dd d dd dd, dod-Z5 dpdd. dqd/Z6 drdd. dsd0Z7ddd d1 dtd2Z8 du dvd3Z9 dw dxd4Z: dwddd d1 dyd5Z; dzdd. d{d6Z< d|dd. d}d7Z=ej:d8fd d. d~d9Z> ddd; dd<Z?dd:d d=dej:fdd. dd>Z@ dd?ZA dd@ZB ddAZCefddBZDefddCZE ddDZF ddEZGddFZH ddGZI ddHZJ di ddIZKdddd1 ddJZLy)) annotations)IterableSequenceIteratorCallableOptionalN)IntEnum) Vec2Vec3UVecMatrix44global_bspline_interpolation EulerSpiralarc_angle_span_radNULLVECZ_AXISX_AXISUCSintersection_ray_ray_3d)MeshVertexMergerMeshTransformer)"circleellipse euler_spiralsquarebox open_arrowarrow2ngonstargearturtle translaterotatescale close_polygonhelixcubeextrudeextrude_twist_scalesweepcylinder cylinder_2pfrom_profiles_linearfrom_profiles_splinespline_interpolationspline_interpolated_profilesconecone_2p rotation_formspheretorusreference_frame_zreference_frame_extmake_next_reference_frameFc#Kt|}tj|z }d}t|D]F}tj||z}tj ||z}t |||||z }H|rt |d|yyw)aCreate polygon vertices for a `circle `_ with the given `radius` and approximated by `count` vertices, `elevation` is the z-axis for all vertices. Args: count: count of polygon vertices radius: circle radius elevation: z-axis for all vertices close: yields first vertex also as last vertex if ``True``. Returns: vertices in counter-clockwise orientation as :class:`~ezdxf.math.Vec3` objects rN)floatmathtaurangecossinr ) countradius elevationclosedeltaalphaindexxys 2lib/python3.12/site-packages/ezdxf/render/forms.pyrr>s$6]F HHu E Eu HHUOf $ HHUOf $1a##    61i(( sBB c#BKt|}t|}t|}t|}t|}||z |dz z }tj}tj}t |D]+} || |zz} t || |z|| |z|-yw)uCreate polygon vertices for an `ellipse `_ with given `rx` as x-axis radius and `ry` as y-axis radius approximated by `count` vertices, `elevation` is the z-axis for all vertices. The ellipse goes from `start_param` to `end_param` in counter clockwise orientation. Args: count: count of polygon vertices rx: ellipse x-axis radius ry: ellipse y-axis radius start_param: start of ellipse in range [0, 2π] end_param: end of ellipse in range [0, 2π] elevation: z-axis for all vertices Returns: vertices in counter clockwise orientation as :class:`~ezdxf.math.Vec3` objects r:N)r=intr>rArBr@r ) rCrxry start_param end_paramrErGrArBparamrHs rLrr]s6 rB rB $Ki I JE  $ 3E ((C ((Cueem+3u:?CJOY??sBBc#Kt|}|j||dz D]}|j|yw)aCreate polygon vertices for an `euler spiral `_ of a given `length` and radius of curvature. This is a parametric curve, which always starts at the origin (0, 0). Args: count: count of polygon vertices length: length of curve in drawing units curvature: radius of curvature elevation: z-axis for all vertices Returns: vertices as :class:`~ezdxf.math.Vec3` objects ) curvaturer:)zN)r approximatereplace)rClengthrUrEspiralvertexs rLrrs>"9 -F$$VUQY7nnyn))8s<>?c|r7|dz }t| | t|| t||t| |fStddt|dt||td|fS)zReturns 4 vertices for a square with a side length of the given `size`. The center of the square in (0, 0) if `center` is ``True`` otherwise the lower left corner is (0, 0), upper right corner is (`size`, `size`). @rr )sizecenteras rLrrsg  3JQB|T!aR[$q!*dA2qkAAAqz4a=$tT*:DDMIIc|r<|dz }|dz }t| | t|| t||t| |fStddt|dt||td|fS)zReturns 4 vertices for a box with a width of `sx` by and a height of `sy`. The center of the box in (0, 0) if `center` is ``True`` otherwise the lower left corner is (0, 0), upper right corner is (`sx`, `sy`). r^rr_)sxsyrarbbs rLrrso H HQB|T!aR[$q!*dA2qkAAAqz4A;R d1bkAArcctjtj|dz |z}t| |tddt| | fS)aFReturns 3 vertices for an open arrow `<` with a length of the given `size`, argument `angle` defines the enclosing angle in degrees. Vertex order: upward end vertex, tip (0, 0) , downward end vertex (counter- clockwise order) Args: size: length of arrow angle: enclosing angle in degrees r^r)r>rBradiansr )r`anglehs rLrrsI eck*+d2A q>41:tTEA2 66rcctjtj|dz |z}tjtj||z}t | |t ddt | | t | |zdfS)avReturns 4 vertices for an arrow with a length of the given `size`, and an enclosing `angle` in degrees and a slanted back side defined by angle `beta`:: **** **** * **** * **** angle X******************** **** * +beta **** * **** **** **** * **** * **** angle X*************** **** * -beta **** * **** Vertex order: upward end vertex, tip (0, 0), downward end vertex, bottom vertex `X` (anti clockwise order). Bottom vertex `X` is also the connection point to a continuation line. Args: size: length of arrow angle: enclosing angle in degrees beta: angle if back side in degrees r^r)r>rBritanr )r`rjbetark back_steps rLrrs}D eck*+d2Ad+,q0I dUA Q  dUQB dUY "  rcr<c#K|dkr td|=|dkr td|dz tjtj|z z }n||dkrtdtdtj|z }|}d}tj } tj} t |D].} t|| |z|| |z|} || }| ||z }0|r|yyw) aWReturns the corner vertices of a `regular polygon `_. The polygon size is determined by the edge `length` or the circum `radius` argument. If both are given `length` has the higher priority. Args: count: count of polygon corners >= 3 length: length of polygon side radius: circum radius rotation: rotation angle in radians elevation: z-axis for all vertices close: yields first vertex also as last vertex if ``True``. Returns: vertices as :class:`~ezdxf.math.Vec3` objects *Argument `count` has to be greater than 2.Nr<z+Argument `length` has to be greater than 0.r^+Argument `radius` has to be greater than 0.z'Argument `length` or `radius` required.) ValueErrorr>rBpir?rAr@r ) rCrYrDrotationrErFrGrjfirstrArB_vs rLrrs0 qyEFF  S=JK K#5 99   S=JK KBCC HHu E E E ((C ((C 5\ #e*$fs5z&99 E =E     sC(C*c#&K|dkr td|dkr td|dkr tdt||||d}t||tj|z |z|d}d}t ||D]\} } || }| | |r|yyw) aeReturns the corner vertices for a `star shape `_. The shape has `count` spikes, `r1` defines the radius of the "outer" vertices and `r2` defines the radius of the "inner" vertices, but this does not mean that `r1` has to be greater than `r2`. Args: count: spike count >= 3 r1: radius 1 r2: radius 2 rotation: rotation angle in radians elevation: z-axis for all vertices close: yields first vertex also as last vertex if ``True``. Returns: vertices as :class:`~ezdxf.math.Vec3` objects rqrrr<z'Argument `r1` has to be greater than 0.z'Argument `r2` has to be greater than 0.F)rDrvrErFN)rtrr>ruzip) rCr1r2rvrErFcorners1corners2rws1s2s rLr r %s4 qyEFF SyBCC SyBCC b8yH 58+ H Eh)B =E *    sBBceZdZdZdZdZdZy)_Gearrr:rqN)__name__ __module__ __qualname__ TOP_STARTTOP_END BOTTOM_START BOTTOM_ENDrcrLrr[sIGLJrcrc#K|dkr td|dkr td|dkr td|dkr td|dkr td||k\r td||z }tj|dz |z }tj|dz |z } | |z dz } tj|| zz |z } | dz } tj } d }tj }tj}td |zD]}| tj k(s| tjk(r|}n|}t||| z||| z|}| tj k(r| |z } nJ| tjk(r| | z } n1| tjk(r| | z } n| tjk(r| | z } ||}|| d z } | tjkDstj } |r|y y w) aReturns the corner vertices of a `gear shape `_ (cogwheel). .. warning:: This function does not create correct gears for mechanical engineering! Args: count: teeth count >= 3 top_width: teeth width at outside radius bottom_width: teeth width at base radius height: teeth height; base radius = outside radius - height outside_radius: outside radius elevation: z-axis for all vertices close: yields first vertex also as last vertex if True. Returns: vertices in counter clockwise orientation as :class:`~ezdxf.math.Vec3` objects rqrrr<rsz*Argument `width` has to be greater than 0.z+Argument `height` has to be greater than 0.z1Argument `height` has to be smaller than `radius`r^Nr:) rtr>asinr?rrrArBr@rr rr)rC top_width bottom_widthheightoutside_radiusrErF base_radius alpha_top alpha_bottomalpha_differencernrjstaterwrArBrxrDrys rLr!r!bs< qyEFFFGGCEFFsEFF }FGG LMM 6)K )c/N:;I99\C/+=>Ly    HHu|+ +u 4D J E OOE E ((C ((C 1u9  EOO #u '=#F F #e*$fs5z&99 E EOO # Y E emm # % %E e(( ( TME e&& & % %E =E   5## #OOE-0   s GG0G0c#K|}||jdD]}|j}|ddk(r&t|dk(r|dz }/|t|ddz }A|ddk(r&t|dk(r|dz}]|t|ddz}o|ddk(r=|ddjd \}}|t t|t|z }||t j |t|z }|yw) aReturns the 2D vertices of a polyline created by turtle-graphic like commands: - ```` - go units forward in current direction and yield vertex - ``r`` - turn right in degrees, a missing angle is 90 deg - ``l`` - turn left in degrees, a missing angle is 90 deg - ``@,`` - go relative , and yield vertex The command string ``"10 l 10 l 10"`` returns the 4 corner vertices of a square with a side length of 10 drawing units. Args: commands: command string, commands are separated by spaces start: starting point, default is (0, 0) angle: starting direction, default is 0 deg  rlr:ZNr@,)splitstriplenr=r from_deg_angle)commandsstartrjcursorcmdrJrKs rLr"r"s&F L~~c"iik q6S=3x1} s12w' Vs]3x1} s12w' Vs]qr7==%DAq d58U1X. .FL d))%s< Kt|}|D] }||z yw)zTranslate `vertices` along `vec`, faster than a Matrix44 transformation. Args: vertices: iterable of vertices vec: translation vector Returns: yields transformed vertices Nr_)verticesvec_vecps rLr#r#s$ 9D QhsTc4|r fd|DSfd|DS)a"Rotate `vertices` about to z-axis at to origin (0, 0), faster than a Matrix44 transformation. Args: vertices: iterable of vertices angle: rotation angle deg: True if angle in degrees, False if angle in radians Returns: yields transformed vertices c3RK|]}t|j ywN)r rotate_deg.0ryrjs rL zrotate..s!<8aQ""5)8$'c3RK|]}t|j ywr)r r$rs rLrzrotate..s8x!Qu%xrr)rrjdegs ` rLr$r$s <8<<8x88rcc#K|\}}}tj|D]8}t|j|z|j|z|j|z:yw)zScale `vertices` around the origin (0, 0), faster than a Matrix44 transformation. Args: vertices: iterable of vertices scaling: scale factors as tuple of floats for x-, y- and z-axis Returns: yields scaled vertices N)r generaterJrKrV)rscalingrerfszrys rLr%r%sMJBB ]]8 $1338QSS2XqssRx00%sAAcxt|}|dj|d||s|j|d|S)zgReturns list of :class:`~ezdxf.math.Vec3`, where the first vertex is equal to the last vertex. r)rel_tolabs_tol)listiscloseappend)rrrpolygons rLr&r&s? x.G 1:  gbk7G  Lwqz" Nrcc#NKdt|dz }|s| }t|t|z }t|dzD]e}||z}|tj z} t j | |z} t j| |z} t| | t||zgyw)aYields the vertices of a `helix `_. The center of the helix is always (0, 0), a positive `pitch` value creates a helix along the +z-axis, a negative value along the -z-axis. Args: radius: helix radius pitch: the height of one complete helix turn turns: count of turns resolution: vertices per turn ccw: creates a counter-clockwise turning (right-handed) helix if ``True`` r\r:N) maxrNabsr@r>r?rArBr ) rDpitchturns resolutionccwsteptotal_step_countrItrjrJrKs rLr'r's&J**D u53t9,-'!+, 5LDHH  HHUOf $ HHUOf $1aQ%(( -sB#B%g?)rrqrr:)r:r)rqrr)rrrrq)rr:rr)rrrrcdt}|rtnt}|j|t|S)a"Create a `cube `_ as :class:`~ezdxf.render.MeshTransformer` object. Args: center: 'mass' center of cube, ``(0, 0, 0)`` if ``True``, else first corner at ``(0, 0, 0)`` Returns: :class:`~ezdxf.render.MeshTransformer` )rfaces)r_cube0_vertices_cube_verticesadd_mesh cube_faces)rameshrs rLr(r(`s*  D"(nHMM8:M6 Krcct}tj|}|r t|}tj|}|r|j t |dd|d}|ddD]?}||z } |D cgc]} | | z } } t || D]} |j | | }|}A|r|j |ddtj|Scc} w)aExtrude a `profile` polygon along a `path` polyline, the vertices of `profile` should be in counter-clockwise order. The sweeping profile will not be rotated at extrusion! Args: profile: sweeping profile as list of (x, y, z) tuples in counter-clockwise order path: extrusion path as list of (x, y, z) tuples close: close profile polygon if ``True`` caps: close hull with top- and bottom faces (ngons) Returns: :class:`~ezdxf.render.MeshTransformer` Nrrr:) rr rr&add_facereversed_quad_connection_facesr from_builder) profilepathrFcapsrsweeping_profileextrusion_path start_point target_pointtranslation_vectorrtarget_profilefaces rLr)r)qs"  Dyy) ()9:YYt_N  h/456 #K&qr* )K7>NO>Ns# 22>NO*+;^LD MM$ M)" +  &s+,  ' ' --Ps7 Cct||ddDcgc]\}}|j|}}}t|}dg}d}|D]}||z }|j||z |Scc}}w)Nr:r<)r{distancesumr)rv1v2partial_lengths total_lengthfactors partial_sumpls rL_partial_path_factorsrsy58tABx5HI5H62rr{{25HOI'LeGKr {\12 NJsA#c2|dg}t||ddD]~\}}||z }|j}||kDrRttj||z }|d|z z}t |dz D]} ||z }|j ||j ||S)Nrr:r\)r{ magnituderNr>ceilr@r) r max_step_sizenew_pathv0r segment_vecrYpartsrrxs rL_divide_path_into_stepsrs G9HdDH%B2g && M ! &="89:E#+.D519%d #& & Orc)twistr% step_sizerFrquadscJdfd }t} tj|} |r t| } |r| j t | ddtj|} |dk7r t | |} t| } | d| } |rtnt}t| dd| ddD]F\}t||j| }|| |D]}| j ||} H|r| j | ddtj| S)a6Extrude a `profile` polygon along a `path` polyline, the vertices of `profile` should be in counter-clockwise order. This implementation can scale and twist the sweeping profile along the extrusion path. The `path` segment points are fix points, the `max_step_size` is used to create intermediate profiles between this fix points. The `max_step_size` is adapted for each segment to create equally spaced distances. The twist angle is the rotation angle in radians and the scale `argument` defines the scale factor of the final profile. The twist angle and scaling factor of the intermediate profiles will be linear interpolated between the start and end values. Args: profile: sweeping profile as list of (x, y, z) tuples in counter-clockwise order path: extrusion path as list of (x, y, z) tuples twist: rotate sweeping profile up to the given end rotation angle in radians scale: scale sweeping profile gradually from 1.0 to given value step_size: rough distance between automatically created intermediate profiles, the step size is adapted to the distances between the path segment points, a value od 0.0 disables creating intermediate profiles close: close profile polygon if ``True`` caps: close hull with top- and bottom faces (ngons) quads: use quads for "sweeping" faces if ``True`` else triangles, the top and bottom faces are always ngons Returns: :class:`~ezdxf.render.MeshTransformer` cddz |zz} |z}z }|tj|z}|tj|z}t||dd| |dddd|d|j|j |j dgS)Nr\r<)r>rArBr rJrKrV) fac current_scalecurrent_rotation translation scale_cos_a scale_sin_ar%rrrs rLmatrixz#extrude_twist_scale..matrixsus{c11  3;"[0 #dhh/?&@@ #dhh/?&@@  c3 L+sC mS MM;==+--    rcNrr<rr:)rr=returnr )rr rr&rrrrr_tri_connection_facesr{transform_verticesrr)rrrr%rrFrrrrrrr prev_profileface_generatorfactorrrrrs `` @@rLr*r*s!V     Dyy) ()9:  h/456YYt_NC0K#N3G #K#L/4+:ON #N12$6 D ffVn??@PQR"<@D MM$ A% !E   l3B'(  ' ' --rc)rc ||}tj|drt|||Stt ||d}tt t ||d|}t ||gdd|S)aCreate a `cylinder `_ as :class:`~ezdxf.render.MeshTransformer` object, the base center is fixed in the origin (0, 0, 0). Args: count: profiles edge count radius: radius for bottom profile top_radius: radius for top profile, if ``None`` top_radius == radius top_center: location vector for the center of the top profile caps: close hull with top- and bottom faces (ngons) r<)rCrDapexTrFFrFrr)r>rr2rrr#r.)rCrD top_radius top_centerr base_profile top_profiles rLr,r,sw(  ||J$%Z@@ufD9:Lyz!F STK  {#   rccZt|}t||z }|jr tdt||dd|jf|} t |t j||}|j|j|S#t$rt |t|}Y:wxYw)aKCreates a `cylinder `_ as :class:`~ezdxf.render.MeshTransformer` object from two points, `base_center` is the center of the base circle and, `top_center` the center of the top circle. Args: count: cylinder profile edge count radius: radius for bottom profile base_center: center of base circle top_center: center of top circle caps: close hull with top- and bottom faces (ngons) Raises: ValueError: the cylinder orientation cannot be detected (base center == top center) zCcylinder orientation cannot be detected (base center == top center)r)rroriginuyuzruxr) r is_nullrtr,rrrcrossZeroDivisionErrorr transformr) rCrD base_centerrrrheadingrucss rLr-r-(s0+ F:'G Q   E6q!W5F5F.Gd SD8FLL$9gF NN3:: K 8Fw78!B B*)B*rcpt}|r|Dcgc] }t|}}|r|jt|d|rtnt }t ||ddD]$\}}|||D]} |j| &|r|j|dtj|Scc}w)aQReturns a :class:`~ezdxf.render.MeshTransformer` instance from linear connected `profiles`. Args: profiles: list of profiles close: close profile polygon if ``True`` quads: use quadrilaterals as connection faces if ``True`` else triangles caps: close hull with top- and bottom faces (ngons) rr:Nr) rr&rrrr r{rr) profilesrFrrrrr p0p1rs rLr.r.Ps"  D .67hM!$h7  hx{+,/4+:ONh -B"2r*D MM$ +.  hrl#  ' ' --8sB3ct|}t|||}t|jt|dz |zS)aB-spline interpolation, vertices are fit points for the spline definition. Only method 'uniform', yields vertices at fit points. Args: vertices: fit points degree: degree of B-spline method: "uniform", "chord"/"distance", "centripetal"/"sqrt_chord" or "arc" calculation method for parameter t subdivide: count of sub vertices + 1, e.g. 4 creates 3 sub-vertices Returns: list of vertices )degreemethodr:)segments)rrrWr)rr*r+ subdividesplines rLr0r0osB*H~H )(6& QF ""S]Q->),K"L MMrcc#tKttd|Ddk7r tdt|d}g}t|D]0}|Dcgc]}|| }}|j t ||2t|d}t|D]}|D cgc]} | | c} ycc}wcc} ww)a&Profile interpolation by cubic B-spline interpolation. Args: profiles: list of profiles subdivide: count of interpolated profiles + 1, e.g. 4 creates 3 sub-profiles between two main profiles (4 face loops) Returns: yields profiles as list of vertices c32K|]}t|ywr)r)rrs rLrz/spline_interpolated_profiles..s(x!s1vxsr:z/All profiles have to have the same vertex countr)r-N)rsetrtr@rr0) r&r- vertex_countedgesrIr edge_vertices profile_count profile_indexedges rLr1r1s 3(x( ()Q.JKKx{#L E|$+348a58 4 )-9MN%aMM}- /45uttM"u55. 5 6sA B8 B.AB8 B3&B8c~t|dkDrtt||}n tdt ||||S)a6Returns a :class:`~ezdxf.render.MeshTransformer` instance by spline interpolation between given `profiles`. Requires at least 4 profiles. A `subdivide` value of 4, means, create 4 face loops between two profiles, without interpolation two profiles create one face loop. Args: profiles: list of profiles subdivide: count of face loops close: close profile polygon if ``True`` quads: use quadrilaterals as connection faces if ``True`` else triangles caps: close hull with top- and bottom faces (ngons) rqz1Spline interpolation requires at least 4 profilesr)rrr1rtr.)r&r-rFrrs rLr/r/sG, 8}q4XyIJLMM    rcct}tt||d}t||ddD]\}}|j |||g|r|j t |t j|S)aUCreate a `cone `_ as :class:`~ezdxf.render.MeshTransformer` object, the base center is fixed in the origin (0, 0, 0). Args: count: edge count of basis_vector radius: radius of basis_vector apex: tip of the cone caps: add a bottom face as ngon if ``True`` Trr:N)rrrr{rrrr)rCrDrrr base_circler(p2s rLr2r2sq$  DveV489Kk;qr?3B r2tn%4  h{+,  ' ' --rccZt|}t||z }|jr tdt||dd|jf|} t |t j||}|j|j|S#t$rt |t|}Y:wxYw)aCreate a `cone `_ as :class:`~ezdxf.render.MeshTransformer` object from two points, `base_center` is the center of the base circle and `apex` as the tip of the cone. Args: count: edge count of basis_vector radius: radius of basis_vector base_center: center point of base circle apex: tip of the cone caps: add a bottom face as ngon if ``True`` Raises: ValueError: the cone orientation cannot be detected (base center == apex) z=the cone orientation cannot be detected (base center == apex)r)rrrr) r rrtr2rrrrrrr r) rCrDr!rrrr"rr#s rLr3r3s.+ F4j6!G K   vQ7+<+<$=D ID8FLL$9gF NN3:: K 8Fw78r$)r:rrcf|dkr tdt||z }tjt ||}|Dcgc] }t |}}|g}t t |D]-} t|j|}|j|/t|dd|} | Scc}w)a`Returns a :class:`~ezdxf.render.MeshTransformer` instance created by rotating a `profile` around an `axis`. Args: count: count of rotated profiles profile: profile to rotate as list of vertices angle: rotation angle in radians axis: rotation axis caps: close hull with start- and end faces (ngons) rqz count >= 2FTr) rtr=r axis_rotater r@rNrr rr.) rCrrjaxisrrGmrr&rxrs rLr4r4 s& qy&& %L5 ET$Z/A '(1tAwG(yH 3u: q++G45     D K)sB.)rc tt|t|dz}tjtz tjt|z t d fd d fd d fd }|| dzdt | dz|dz D]&}|dz}|}|} tj|zz} tj|zz} t D]} | || } | dz|| }| dz| | }| | | }|rj| |||gI| dz|dztj|dzzz}j| ||gj|||gj|||gj|| |g)||dz d tjS) a_Create a `sphere `_ as :class:`~ezdxf.render.MeshTransformer` object, the center of the sphere is always at (0, 0, 0). Args: count: longitudinal slices stacks: latitude slices radius: radius of sphere quads: use quadrilaterals as faces if ``True`` else triangles rc:tj|zzSr)r>rA)stack delta_phirDs rLradius_of_stackzsphere..radius_of_stackEsU!2333rcc|z}ttj||ztj||z|Sr)r r>rArB)slice_rrV actual_theta delta_thetas rLr[zsphere..vertexHs8"V+ DHH\*Q.0F0JANNrcFc*tj|z z}|r tdd n tdd } |}t D]D} |||} |dz||}|r j |||f1 j |||fFyNrr:)r>rBr r@r)rDtoprV cap_vertexr|rHrrrErrDrFslicesr[s rL cap_triangleszsphere..cap_trianglesLs HHUY& '& 0+.T!Q'DAw4G U #FmFA&B B*B r2z23 z2r23 $rcr:)rMrT)rDr=rr=)rHr=rr=rVr=rr )F) r=rNr>r?rurr@rBrrr)rCstacksrDrstacks_2rP actual_stack next_stackr|r}z1z2irrv3v4rarErJrrFrOr[s ` @@@@@@rLr5r50s6]F ZF6{aH((U6]*K%-'I  D4O 4 48)a-U+xi!mX\: !A% \ * Z ( XXi,. /& 8 XXi*, - 6vA2r"BAr2&BAr2&B2r"B r2r2./G#L3$67HHY,*<=>G  r2v./ r2v./ r2v./ r2v./! ;2(Q,D)  ' ' --rcg?c|dkr td|dkr tdtjt|}tjt|}|dkr td|dkr td||k\r tdt|tjz}|tjk7rt|tjz}t ||}tj |tj}||z } tt||d t|d d D cgc]#} t| jd | j%} } | j|dkDr| D cgc]} | j|} } t} | } | D cgc]} | j| }} |s|r| jt!| t#|D]D}t%| |D]}| j||} |D cgc]} | j| }} F|s|r| j| t'j(| Scc} wcc} wcc} wcc} w) aVCreate a `torus `_ as :class:`~ezdxf.render.MeshTransformer` object, the center of the torus is always at (0, 0, 0). The `major_radius` has to be bigger than the `minor_radius`. Args: major_count: count of circles minor_count: count of circle vertices major_radius: radius of the circle center minor_radius: radius of circle start_angle: start angle of torus in radians end_angle: end angle of torus in radians caps: close hull with start- and end faces (ngons) if the torus is open r:zmajor_count < 1rqzminor_count < 3& .>zmajor_radius is 0zminor_radius is 0zminor_radius >= major_radiusTrr)rtr>fabsr=r?rrr#rr rJrKreverser$rrrr@rrr) major_count minor_count major_radius minor_radius start_angle end_angler angle_span closed_torus step_anglerycircle_profiler start_profile end_profilerxrs rLr6r6zs72Q?,,Q?,,99U<01L99U<01Ld,--d,--|#788 $txx/KDHH)$txx/ #K;J<< DHH5Lk)J ; D 9 q! $  A QSS!QSS T9GHA!((;/H  D"M1?@A188J'K@ D h}-. ; *=+FD MM$ G# 5@A[qxx +[ A  D m$  ' ' --9IABs2(I5II I"c#Kt|t|k(sJd|rt||Ed{yt||Ed{y77w)Nzprofiles differ in vertex count)rrr )rhriquads rLconnection_facesrlsS } [!1 1T3TT 1 )-EEE( DDD FDs!0AA AAAAc#lK|d}|d}t|dd|ddD]\}}||||f|}|}ywrLr{rhriv0_prevv1_prevrrs rLrrsVAG!nGmAB'QR9Br2w&&:s24c#xK|d}|d}t|dd|ddD]\}}|||f|||f|}|}ywrLrnros rLr r s`AG!nGmAB'QR9B'7##r2o :s8:cDttj|||S)aReturns a reference frame as UCS from the given heading and the WCS z-axis as reference "up" direction. The z-axis of the reference frame is pointing in heading direction, the x-axis is pointing right and the y-axis is pointing upwards. The reference frame is used to project vertices in xy-plane (construction plane) onto the normal plane of the given heading. Use the :func:`reference_frame_ext` if heading is parallel to the WCS Z_AXIS. Args: heading: WCS direction of the reference frame z-axis origin: new UCS origin Raises: ZeroDivisionError: heading is parallel to WCS Z_AXIS rrr)rrr)r"rs rLr7r7s( &,,w'GF CCrcc ttj|jt|S#t$r2t|j jtt|cYSwxYw)zReference frame calculation if heading vector is parallel to the WCS Z_AXIS. Args: frame: previous reference frame origin: new UCS origin rt)rrr)rrrrrr)framers rLr8r8sQHfll588,GG HehhnnV,GGHs.18A,+A,c#Kt||D]a\}}t||}t|}|dk(r|d*|dk(r|dj|dI|dj|dcyw)Nr:rrr)r{rrlerp) prev_rays next_raysray1ray2iprCs rL_intersect_raysr~ sw)Y/ d $T4 0B A:Q%K aZQ%**RU# #r(--Q( (0sA2A4c N|dg}t||Dcgc]&\}}t||Dcgc] \}}||f c}}(}}}}}t||ddD])\}} |jtt|| +|j|d|Scc}}wcc}}}}w)Nrr:r)r{rrr~) start_profiles end_profilesr&r'r(rrraysryrzs rL_intersection_profilesrs'5Q&7%8H.,7 7FB!$B , fb""b ,7  !$D$qr( 3 9_Y BCD!4 OOL$% O - sB BB B c t||}|jj|jdkr#t||j|j }|S#t $rt ||cYSwxYw)aReturns the following reference frame next to the current reference `frame`. Args: frame: the current reference frame heading: z-axis direction of the following frame in WCS origin: origin of the following reference frame r)rrr)r7rdotrrrr8)rvr"r next_frames rLr9r9(sj 2&w7  ==  UXX & *Fz}}*--PJ 2"5&112sAAA32A3cjtj|}tj|}g}g}t}t||ddD]a\}} | |z } ||| |}t|j |} |j | |j | D cgc]} | | z c} c||fScc} w)Nr:)r rrr{ points_to_wcsr) r sweeping_pathnext_ref_framespathreference_profilerr ref_framertargetr"rhrys rL"_make_sweep_start_and_end_profilesr>s IIm $E '*NLIeU12Y/6/"9gv> Y445FGH m,-@-QQ[-@A 0 < ''As B0 c0tt||tS)aReturns the intermediate profiles of sweeping a profile along a 3D path where the sweeping path defines the final location in the `WCS`. The profile is defined in a reference system. The origin of this reference system will be moved along the sweeping path where the z-axis of the reference system is pointing into the moving direction. Returns the start-, end- and all intermediate profiles along the sweeping path. )rrr9)rrs rL sweep_profilerQs! " + ]$=  rcc|r t|}g}tt||tD]'\}}|j ||j |)|Sr)r&r{rr9r)rrrFr&speps rLdebug_sweep_profilesrgsZ  (%'H + ]$= B   Orcc8t||}t||||S)aeReturns the mesh from sweeping a profile along a 3D path, where the sweeping path defines the final location in the `WCS`. The profile is defined in a reference system. The origin of this reference system will be moved along the sweeping path where the z-axis of the reference system is pointing into the moving direction. Returns the mesh as :class:`ezdxf.render.MeshTransformer` object. Args: profile: sweeping profile defined in the reference system as iterable of (x, y, z) coordinates in counter-clockwise order sweeping_path: the sweeping path defined in the WCS as iterable of (x, y, z) coordinates close: close sweeping profile if ``True`` quads: use quadrilaterals as connection faces if ``True`` else triangles caps: close hull with top- and bottom faces (ngons) r)rr.)rrrFrrr&s rLr+r+ys)6Wm4H    rc)r:rF) rCrNrDr=rEr=rFboolrIterable[Vec3])rCrNrOr=rPr=rQr=rRr=rEr=rr)r:r:r) rCrNrYr=rUr=rEr=rr)r\F)r`r=rtuple[Vec3, Vec3, Vec3, Vec3])r\r\F)rer=rfr=rr)r\>@)r`r=rjr=rztuple[Vec3, Vec3, Vec3])r\rgF@)r`r=rjr=rnr=rr)NNr<r<F)rCrNrYOptional[float]rDrrvr=rEr=rFrrr)r<r<F)rCrNr|r=r}r=rvr=rEr=rFrrr)rF)rCrNrr=rr=rr=rr=rEr=rFrrr)rstrrjr=rzIterator[Vec2])rrr)rIterable[UVec]rr rr)r<T)rrrjr=rrrr))r\r\r\)rrrr)r[g-q=)rrrr=rr=r list[Vec3])rT) rDr=rr=rr=rrNrIterator[Vec3])T)rarrr)TF)rrrrrr)rrrz list[float])rSequence[Vec3]rr=rr) rrrrrr=r%r=rr=rr)rr\Nrrr:) rCrNrDr=rrrr rr)rr:rr) rCrNrDr=r!r rr rr)r&Sequence[Sequence[Vec3]]rr)rqchordr) rrr*rNr+rr-rNrr)r)r&rr-rNrzIterable[list[Vec3]])r&rr-rNrr)rr\r)rCrNrDr=rr rr)rr\rr) rCrNrDr=r!r rr rr) rCrNrrrjr=r?r rr)rrAr:)rCrNrQrNrDr=rr) r^rNr_rNrbr=rcr=rr)rhrrirrkrrIterator[Sequence[Vec3]])rhrrirrr)r"r rr rr)rvrrr rr)ryrrzrrr)rrrrrlist[Sequence[Vec3]])rvrr"r rr rr)rrrrrz Callable[[UCS, Vec3, Vec3], UCS]rz)tuple[list[list[Vec3]], list[list[Vec3]]])rrrrrr)rrrrrr)M __future__rtypingrrrrrr>enumr ezdxf.mathr r r r rrrrrrrrezdxf.render.meshrr__all__rr?rrrrrrrr rr!r"r#r$r%r&r'rrrr(r)rrr*r,r-r.r0r1r/r2r3r4r5r6rlrr r7r8r~rr9rrrr+rrcrLrs#CC     @# NHM) )).3)@D))Bxx %@ %@ %@ %@ %@  %@  %@%@RMN* **.3*DI**, J.3 B  B B" B 7 ;?) )#)27)")\#" 1 1 1 1 1  1  11p 3 3 3 3 3  3  33lGP PPP  P  P  P PPf!%Q 1'T  ?C99%*97;99( 1"GL  ', >C    ) ) ) ) )  )B AqMAqMAqMAqMAqMAqMAqMAqM  tTtTtTtTtTtTtTtT   $EJ#. #.#1#.#.L &   P. P. P.  P.  P.  P.P.h"& !  ! ! ! ! !!J! %  % % %% %%V    .&.  .B NN N N N  N6:;6&63666<    &F.  . . . .  .:! %  % % %%  %%V88 "  " " " "  ""L78G.BFG. G. G..3G.G.Vxx G. G.G.G.  G.  G.G.TEE,6E>BEE!0> ! 0>  5<D.4; H )' )4L ) ) , *  2,( (!(5(/ (& !2  ! ,   ! !!!!rc