'j ddlmZddlmZmZmZmZmZddlZddl m Z ddl m Z m Z mZmZmZmZmZmZmZmZmZmZddlmZmZgdZ dddZdddejdfddZ dddZdddZ ddd"Z!ddd&Z" ddd)Z# ddd-Z$ ddd0Z%Gd1d2e Z& ddd7Z'e dddfdd;Z(dddAZ) dddDZ*dddFZ+ dddLZ, dddRZ-e ddde ddde ddde ddde ddde ddde ddde dddgZ.e dSdSdSe dTdSdSe dTdTdSe dSdTdSe dSdSdTe dTdSdTe dTdTdTe dSdTdTgZ/gdUgdVgdWgdXgdYgdZgZ0ddd]Z1 ddd`Z2ddbZ3ddeZ4d*dddBd dBdfddjZ5 ddBdlddoZ6 ddBdlddqZ7dBdBd drdduZ8 ddd|Z9 ddd~Z: ddBdBd drddZ; ddBdlddZ< ddBdlddZ=ejdfd dlddZ> ddBdddZ?dMdddd*ejfdBdlddZ@ddZAddZBddZCefddZDefddZEddZFddZGddZHddZIddZJ dddZKdBdBdBdrddZLdS)) 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_frameFcountintradiusfloat elevationcloseboolreturnIterable[Vec3]c#(Kt|}tj|z }d}t|D]H}tj||z}tj||z}t |||V||z }I|rt |d|VdSdS)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)r>mathtaurangecossinr ) r;r=r?r@deltaalphaindexxys L/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/render/forms.pyrr>s$6]]F Hu E Eu HUOOf $ HUOOf $1a#####  )61i((((((())rxry start_param end_paramc#pKt|}t|}t|}t|}t|}||z |dz z }tj}tj}t |D]5} || |zz} t || |z|| |z|V6dS)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>r<rFrIrJrHr ) r;rRrSrTrUr?rKrIrJparamrLs rPrr]s6 rB rB $$Ki  I JJE  $ 3E (C (Cu@@eem+33u::?CCJJOY??????@@rQlength curvaturec#Kt|}|||dz D]}||VdS)aCreate polygon vertices for an `euler spiral `_ of a given `length` and radius of curvature. This is a parametric curve, which always starts at the origin (0, 0). Args: count: count of polygon vertices length: length of curve in drawing units curvature: radius of curvature elevation: z-axis for all vertices Returns: vertices as :class:`~ezdxf.math.Vec3` objects )rYr:)zN)r approximatereplace)r;rXrYr?spiralvertexs rPrrsb"9 - - -F$$VUQY77**nnyn))))))**rQ?sizetuple[Vec3, Vec3, Vec3, Vec3]c|rG|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 )racenteras rPrrs~ J 3JQB||T!aR[[$q!**dA2qkkAAAqzz4a==$tT*:*:DDMMIIrQsxsyc|rL|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`). rdrre)rhrirfrgbs rPrrsB H HQB||T!aR[[$q!**dA2qkkAAAqzz4A;;R d1bkkAArQ>@angletuple[Vec3, Vec3, Vec3]ctjtj|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 rdr)rFrJradiansr )rarmhs rPrrsQ eck**++d2A q>>41::tTEA2 66rQF@betac6tjtj|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 rdr)rFrJrptanr )rarmrsrq back_steps rPrrsD eck**++d2Ad++,,q0I dUA Q  dUQB dUY ""  rQrEOptional[float]rotationc#K|dkrtd|=|dkrtd|dz tjtj|z z }n'||dkrtdntdtj|z }|}d}tj} tj} t |D]8} t|| |z|| |z|} || }| V||z }9|r|VdSdS) 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.NrEz+Argument `length` has to be greater than 0.rd+Argument `radius` has to be greater than 0.z'Argument `length` or `radius` required.) ValueErrorrFrJpirGrIrHr ) r;rXr=rxr?r@rKrmfirstrIrJ_vs rPrrs30 qyyEFFF  S==JKK K#5 9 99   S==JKK K BCCC Hu E E E (C (C 5\\ ##e**$fss5zz&99 E E =E   rQr1r2c#PK|dkrtd|dkrtd|dkrtdt||||d}t||tj|z |z|d}d}t ||D]\} } || }| V| V|r|VdSdS) 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 rzr{rEz'Argument `r1` has to be greater than 0.z'Argument `r2` has to be greater than 0.F)r=rxr?r@N)r}rrFr~zip) r;rrrxr?r@corners1corners2rs1s2s rPr r %s4 qyyEFFF SyyBCCC SyyBCCC b8yH 58+ H Eh))B =E  rQceZdZdZdZdZdZdS)_Gearrr:rzN)__name__ __module__ __qualname__ TOP_STARTTOP_END BOTTOM_START BOTTOM_ENDrQrPrr[s"IGLJJJrQr top_width bottom_widthheightoutside_radiusc#K|dkrtd|dkrtd|dkrtd|dkrtd|dkrtd||krtd||z }tj|dz |z }tj|dz |z } | |z dz } tj|| zz |z } | dz } tj} d }tj}tj}td |zD]}| tjks| tj kr|}n|}t||| z||| z|}| tjkr| |z } nA| tj kr| | z } n+| tj kr| | z } n| tj kr| | z } ||}|V| d z } | tj kr tj} |r|Vd Sd S) 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 rzr{rEr|z*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`rdNr:) r}rFasinrGrrrIrJrHrr rr)r;rrrrr?r@ base_radius alpha_top alpha_bottomalpha_differencersrmstaterrIrJrr=rs rPr!r!bsM< qyyEFFFFGGGCEFFFsEFFF }}FGGG LMMM 6)K )c/N:;;I9\C/+=>>Ly    Hu|+ +u 4D J E OE E (C (C 1u9  $$ EO # #u '='=#FF F ##e**$fss5zz&99 E E EO # # Y EE em # # % %EE e( ( ( TMEE e& & & % %E =E   5# # #OE  rQcommandsstrIterator[Vec2]c#K|}|V|dD]}|}|ddkr4t|dkr|dz }<|t|ddz }W|ddkr4t|dkr|dz}||t|ddz}|ddkrR|ddd \}}|t t|t|z }|V|t j|t|z }|V dS) 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)rstartrmcursorcmdrNrOs rPr"r"sG&F LLL~~c""iikk q6S==3xx1}} s122w' Vs]]3xx1}} s122w' Vs]]qrr7==%%DAq d588U1XX.. .FLLLL d)%s<< zrotate..s7<.s588!Qu%%888888rQr)rrmrs ` rPr$r$sA 9<<<<8<<<<8888x8888rQr`r`r`c#K|\}}}tj|D]-}t|j|z|j|z|j|zV.dS)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 generaterNrOr[)rscalingrhriszrs rPr%r%scJBB ]8 $ $11138QS2XqsRx00000011rQ& .>-q=rel_tolabs_tol list[Vec3]ct|}|d|d||s||d|S)zgReturns list of :class:`~ezdxf.math.Vec3`, where the first vertex is equal to the last vertex. r)rr)listiscloseappend)rrrpolygons rPr&r&sO x..G 1:  gbk7G  L L#wqz""" NrQpitchturns resolutionIterator[Vec3]c#lKdt|dz }|s| }t|t|z }t|dzD]g}||z}|tjz} t j| |z} t j| |z} t| | t||zVhdS)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) maxr<absrHrFrGrIrJr ) r=rrrccwsteptotal_step_countrMtrmrNrOs rPr'r's&J***D u53t99,--'!+,,)) 5LDH  HUOOf $ HUOOf $1aQ%(((((( ))rQg?)rrzrr:)r:r)rzrr)rrrrz)rr:rr)rrrrrfrczt}|rtnt}||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)rfmeshrs rPr(r(`s8   D"(<nHMM8:M666 KrQprofilepathc t}tj|}|rt|}tj|}|r*|t |dd|d}|ddD]A}||z fd|D} t || D]} || | }|}B|r||ddtj|S)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:cg|]}|zSrr)rrtranslation_vectors rP zextrude..sOOOs# 22OOOrQ) rr rr&add_facereversed_quad_connection_facesr from_builder) rrr@capsrsweeping_profileextrusion_path start_point target_pointtarget_profilefacers @rPr)r)qs("   Dy)) ;()9::Yt__N 7 h/455666 #K&qrr*## )K7OOOO>NOOO*+;^LL  D MM$    )"  - &ss+,,,  ' - --rQ list[float]cdt||ddD}t|}dg}d}|D]}||z }|||z  |S)Nc>g|]\}}||Sr)distance)rv1v2s rPrz)_partial_path_factors..s&III62rr{{2IIIrQr:rE)rsumr)rpartial_lengths total_lengthfactors partial_sumpls rP_partial_path_factorsrsxIIStABBx5H5HIIIO''LeGK33r {\12222 NrQSequence[Vec3] max_step_sizecX|dg}t||ddD]\}}||z }|j}||kr[ttj||z }|d|z z}t |dz D]} ||z }|||||S)Nrr:r`)r magnituder<rFceilrHr) rrnew_pathv0r segment_vecrXpartsrrs rP_divide_path_into_stepsrs G9HdDH%%  B2g & M ! ! &="899::E#+.D519%% $ $d #### OrQ)twistr% step_sizer@rquadsrr%rcd fd }t} tj|} |rt| } |r*| t | ddtj|} |dkrt | |} t| } | d | } |rtnt}t| d d| d dD]V\}t|| | }|| |D]}| ||} W|r| | 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` facr>rBr cddz |zz} |z}z }|tj|z}|tj|z}t||dd| |dddd|d|j|j|jdgS)Nr`rE)rFrIrJr rNrOr[) r current_scalecurrent_rotation translation scale_cos_a scale_sin_ar%rrrs rPmatrixz#extrude_twist_scale..matrixsus{c11  3;"[0 #dh/?&@&@@ #dh/?&@&@@  c3 L+sC mS M;=+-     rQNrrErr:)rr>rBr )rr rr&rrrrr_tri_connection_facesrtransform_verticesrr)rrrr%rr@rrrrrrr prev_profileface_generatorfactorrrrrs `` @@rPr*r*sV             Dy)) ;()9:: 7 h/455666Yt__NC0KK#N33G #K#L/4O++:ON #N122$6 D D&& fffVnn??@PQQRR"N<@@  D MM$    %  ) l3B3'(((  ' - --rQrrr:)r top_radius top_centerc ||}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) NrE)r;r=apexTr@Fr@rr)rFrr2rrr#r.)r;r=r#r$r base_profile top_profiles rPr,r,s(  |J$$A%Z@@@@ufD999::Lyz!F!F!F SSTTK  {#     rQ base_centercxt|}t||z }|jrtdt||dd|jf|} t |t j||}n'#t$rt |t|}YnwxYw| |j |S)aKCreates a `cylinder `_ as :class:`~ezdxf.render.MeshTransformer` object from two points, `base_center` is the center of the base circle and, `top_center` the center of the top circle. Args: count: cylinder profile edge count radius: radius for bottom profile base_center: center of base circle top_center: center of top circle caps: close hull with top- and bottom faces (ngons) Raises: ValueError: the cylinder orientation cannot be detected (base center == top center) zCcylinder orientation cannot be detected (base center == top center)r)r$roriginuyuzr.uxr0) r is_nullr}r,r rrcrossZeroDivisionErrorr transformr) r;r=r+r$rr.headingrucss rPr-r-(s0+  F:'G  Q    E6q!W5F.Gd S S SD8FL$9$9gFFF 888Fw7778 NN3: K$A99!BBr(profilesSequence[Sequence[Vec3]]ct}|r d|D}|r(|t|d|rtnt}t ||ddD])\}}|||D]}||*|r||dt j|S)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) c,g|]}t|Sr)r&rrs rPrz(from_profiles_linear..cs 777M!$$777rQrr:Nr)rrrrrrrr) r:r@rrrr p0p1rs rPr.r.Ps"   D 877h777 - hx{++,,,/4O++:ONh --  B"N2r**  D MM$      $ hrl###  ' - --rQrzchordrdegreemethod subdividect|}t|||}t|t|dz |zS)aB-spline interpolation, vertices are fit points for the spline definition. Only method 'uniform', yields vertices at fit points. Args: vertices: fit points degree: degree of B-spline method: "uniform", "chord"/"distance", "centripetal"/"sqrt_chord" or "arc" calculation method for parameter t subdivide: count of sub vertices + 1, e.g. 4 creates 3 sub-vertices Returns: list of vertices )rBrCr:)segments)rrr\r)rrBrCrDsplines rPr0r0osR*H~~H )(6& Q Q QF ""S]]Q->),K"LL M MMrQIterable[list[Vec3]]c#Kttd|Ddkrtdt|d}g}t|D]4fd|D}|t ||5t|d}t|D]fd|DVdS) a&Profile interpolation by cubic B-spline interpolation. Args: profiles: list of profiles subdivide: count of interpolated profiles + 1, e.g. 4 creates 3 sub-profiles between two main profiles (4 face loops) Returns: yields profiles as list of vertices c34K|]}t|VdSr)rr>s rPrz/spline_interpolated_profiles..s(((!s1vv((((((rQr:z/All profiles have to have the same vertex countrc g|] }| Srr)rrrMs rPrz0spline_interpolated_profiles..s444a5444rQ)rDc g|] }| Srr)redge profile_indexs rPrz0spline_interpolated_profiles..s555ttM"555rQN)rsetr}rHrr0)r:rD vertex_countedges edge_vertices profile_countrMrNs @@rPr1r1s 3((x((( ( ())Q..JKKKx{##L E|$$OO44448444  )-9MMMNNNNaMMM}--66 5555u555555566rQct|dkrtt||}ntdt ||||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) rzz1Spline interpolation requires at least 4 profilesr()rrr1r}r.)r:rDr@rrs rPr/r/sa, 8}}q4XyIIJJLMMM      rQr&c8t}tt||d}t||ddD]\}}||||g|r"|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`` Tr'r:N)rrrrrrrr)r;r=r&rr base_circler@p2s rPr2r2s$   DveV488899Kk;qrr?33&&B r2tn%%%% - h{++,,,  ' - --rQcxt|}t||z }|jrtdt||dd|jf|} t |t j||}n'#t$rt |t|}YnwxYw| |j |S)aCreate a `cone `_ as :class:`~ezdxf.render.MeshTransformer` object from two points, `base_center` is the center of the base circle and `apex` as the tip of the cone. Args: count: edge count of basis_vector radius: radius of basis_vector base_center: center point of base circle apex: tip of the cone caps: add a bottom face as ngon if ``True`` Raises: ValueError: the cone orientation cannot be detected (base center == apex) z=the cone orientation cannot be detected (base center == apex)r)r&rr-r1) r r3r}r2r rrr4r5rr6r) r;r=r+r&rr.r7rr8s rPr3r3s.+  F4jj6!G  K    vQ7+<$=D I I ID8FL$9$9gFFF 888Fw7778 NN3: Kr9)r:rraxisc|dkrtdt||z }tjt ||}d|D}|g}t t |D]9}t||}| |:t|dd|} | S)a`Returns a :class:`~ezdxf.render.MeshTransformer` instance created by rotating a `profile` around an `axis`. Args: count: count of rotated profiles profile: profile to rotate as list of vertices angle: rotation angle in radians axis: rotation axis caps: close hull with start- and end faces (ngons) rzz count >= 2c,g|]}t|Srrer>s rPrz!rotation_form.."s(((1tAww(((rQFTr() r}r>r axis_rotater rHr<rrrr.) r;rrmrYrrKmr:rrs rPr4r4 s& qyy&&& %LL5 ET$ZZ//A(((((GyH 3u::  !!q++G4455         D KrQ)rstacksc jtt|t|dz}tjtz tjt|z t dfd dfd dfd }|| d zd t | d z|d z D]Q}|d z}|}|} tj|zz} tj|zz} t D]} | || } | d z|| }| d z| | }| | | }|r| |||gX| dz|dztj|dzzz}| ||g|||g|||g|| |gS||d z dtj S)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 rstackr>rBc8tj|zzSr)rFrI)ra delta_phir=s rPradius_of_stackzsphere..radius_of_stackEsU!23333rQslice_rr[r c|z}ttj||ztj||z|Sr)r rFrIrJ)rerr[ actual_theta delta_thetas rPr_zsphere..vertexHs="V+ DH\**Q.0F0F0JANNNrQFc`tj|z z}|rtdd ntdd } |}t D]R} |||} |dz||}|r |||f: |||fSdSNrr:)rFrJr rHr)ratopr[ cap_vertexrrerrrcrr=rdslicesr_s rP cap_triangleszsphere..cap_trianglesLs HUY& ' '& 0+.GT!Q'''DAw4G4G _U # #Fmm 4 4FA&&B B**B 4 r2z23333 z2r23333  4 4rQr:)rkrT)rar>rBr>)rer>rr>r[r>rBr )F) r>r<rFrGr~rrHrJrrr)r;r_r=rstacks_2rn actual_stack next_stackrrz1z2irrv3v4rfrcrhrrdrmr_s ` @@@@@@rPr5r50s6]]F ZZF6{{aH(U6]]*K%--'I   D4444444OOOOOO 4 4 4 4 4 4 4 4 4 4 4M8)a-U++++xi!mX\::00 !A% _\ * * _Z ( ( Xi,. / /& 8 Xi*, - - 6v 0 0A2r""BAr2&&BAr2&&B2r""B 0 r2r2.////G#OL3$677HY,*<=>>G  r2v./// r2v./// r2v./// r2v.////! 0&M(Q,D))))  ' - --rQg? major_count minor_count start_angle end_anglec |dkrtd|dkrtdtjt|}tjt|}|dkrtd|dkrtd||krtdttjz|tjkrt|tjz}t |}tj|tj}||z d tt||d t|d d D} | dkrfd | D} t} | } fd| D} |s$|r"| t| t|D]:} t| | D]}| || } fd| D} ;|s|r| | t!j| S)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 < 1rzzminor_count < 3rzmajor_radius is 0zminor_radius is 0zminor_radius >= major_radiuscDg|]}t|jd|jS)r)r rNrO)rrs rPrztorus..s8  QS!QSrQTr'rc:g|]}|Srr$)rrrys rPrztorus..s%HHHA!((;//HHHrQc:g|]}|Srr~rr step_angles rPrztorus..s%@@@A188J''@@@rQc:g|]}|Srr~rs rPrztorus..s%AAAqxx ++AAArQ)r}rFfabsr>rGrrr#rr reverserrrrHrrr)rwrx major_radius minor_radiusryrzr angle_span closed_toruscircle_profiler start_profile end_profilerrrs ` @rPr6r6zs2Q+,,,Q+,,,9U<0011L9U<0011Ld,---d,---|##7888 $$tx/KDH)$$tx/ #K;;J< DH55Lk)J ; D 9 9 9 q! $ $  NTHHHHHHH   D"M@@@@@@@K /D/ h}--... ;  BB*=+FF  D MM$    # AAAA[AAA %D% m$$$  ' - --rQrrquadIterator[Sequence[Vec3]]c#Kt|t|ks Jd|rt||Ed{VdSt||Ed{VdS)Nzprofiles differ in vertex count)rrr)rrrs rPconnection_facesrs }  [!1!1 1 1 13T 1 1 1 E)-EEEEEEEEEEE( DDDDDDDDDDDrQc#K|d}|d}t|dd|ddD]\}}||||fV|}|}dSrjrrrv0_prevv1_prevr rs rPrrstAG!nGmABB'QRR99Br2w&&&&rQc#K|d}|d}t|dd|ddD]\}}|||fV|||fV|}|}dSrjrrs rPrrsAG!nGmABB'QRR99B'7####r2o rQr7r r.rcJttj|||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 r/r0r.)rrr4)r7r.s rPr7r7s#( &,w''GF C C CCrQframec ttj|jt|S#t$r7t|jtt|cYSwxYw)zReference frame calculation if heading vector is parallel to the WCS Z_AXIS. Args: frame: previous reference frame origin: new UCS origin r)r2r0r.)rrr4r2r5r/)rr.s rPr8r8sqHfl58,,GGGG HHHehnnV,,GGGGGGHs-0>A10A1 prev_rays next_raysc#0Kt||D]\}}t||}t|}|dkr |dV5|dkr$|d|dV_|d|dVdS)Nr:rrr)rrrlerp)rrray1ray2ipr;s rP_intersect_raysr s)Y//)) d $T4 0 0B A::Q%KKKK aZZQ%**RU## # # # #r(--Q(( ( ( ( ())rQstart_profiles end_profileslist[Sequence[Vec3]]c |dg}dt||D}t||ddD]5\}}|tt||6||d|S)NrcHg|]\}}dt||D S)cg|] \}}||f Srr)rr rs rPrz5_intersection_profiles...s ,,,fb""b,,,rQr)rr?r@s rPrz*_intersection_profiles..sB    B -,B ,,,   rQr:r)rrrr)rrr:raysrrs rP_intersection_profilesrs'5Q&7%8H  .,77   D!$D$qrr( 3 3EE 9_Y BBCCDDDD OOL$%%% OrQc t||}|j|jdkrt||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)r.r0r/)r7r/dotrr0r5r8)rr7r. next_frames rPr9r9(s 2&w77  =  UX & & * *Fz}*-PPPJ 222"5&111112sAAA10A1 sweeping_pathnext_ref_frame Callable[[UCS, Vec3, Vec3], UCS])tuple[list[list[Vec3]], list[list[Vec3]]]c tj|}tj|}g}g}t}t||ddD]o\}} | |z || |}t||} || | fd| Dp||fS)Nr:cg|]}|zSrr)rrr7s rPrz6_make_sweep_start_and_end_profiles..Ms@@@QQ[@@@rQ)r rrr points_to_wcsr) rrrspathreference_profilerr ref_framer.targetrr7s @rP"_make_sweep_start_and_end_profilesr>s Im $ $E '**NLIeU122Y//BB6/"N9gv>> Y445FGGHH m,,,@@@@-@@@AAAA < ''rQc<tt||tS)aReturns the intermediate profiles of sweeping a profile along a 3D path where the sweeping path defines the final location in the `WCS`. The profile is defined in a reference system. The origin of this reference system will be moved along the sweeping path where the z-axis of the reference system is pointing into the moving direction. Returns the start-, end- and all intermediate profiles along the sweeping path. )rrr9)rrs rP sweep_profilerQs& " + ]$=   rQc|rt|}g}tt||tD]/\}}||||0|Sr)r&rrr9r)rrr@r:speps rPdebug_sweep_profilesrgsy  )((%'H + ]$=  B  OrQcHt||}t||||S)aeReturns the mesh from sweeping a profile along a 3D path, where the sweeping path defines the final location in the `WCS`. The profile is defined in a reference system. The origin of this reference system will be moved along the sweeping path where the z-axis of the reference system is pointing into the moving direction. Returns the mesh as :class:`ezdxf.render.MeshTransformer` object. Args: profile: sweeping profile defined in the reference system as iterable of (x, y, z) coordinates in counter-clockwise order sweeping_path: the sweeping path defined in the WCS as iterable of (x, y, z) coordinates close: close sweeping profile if ``True`` quads: use quadrilaterals as connection faces if ``True`` else triangles caps: close hull with top- and bottom faces (ngons) r()rr.)rrr@rrr:s rPr+r+ys66Wm44H      rQ)r:rF) r;r<r=r>r?r>r@rArBrC)r;r<rRr>rSr>rTr>rUr>r?r>rBrC)r:r:r) r;r<rXr>rYr>r?r>rBrC)r`F)rar>rBrb)r`r`F)rhr>rir>rBrb)r`rl)rar>rmr>rBrn)r`rlrr)rar>rmr>rsr>rBrb)NNrErEF)r;r<rXrwr=rwrxr>r?r>r@rArBrC)rErEF)r;r<rr>rr>rxr>r?r>r@rArBrC)rF)r;r<rr>rr>rr>rr>r?r>r@rArBrC)rrrmr>rBr)r)rrrr rBrC)rET)rrrmr>rrArBrC)r)rrrBrC)rr)rrCrr>rr>rBr)rT) r=r>rr>rr>rr<rBr)T)rfrArBr)TF)rrrrrBr)rrrBr)rrrr>rBr) rrrrrr>r%r>rr>rBr)rr`Nr") r;r<r=r>r#rwr$r rBr)rr:rr") r;r<r=r>r+r r$r rBr)r:r;rBr)rzrAr) rrrBr<rCrrDr<rBr)r)r:r;rDr<rBrH)r:r;rDr<rBr)rr`r")r;r<r=r>r&r rBr)rr`rr") r;r<r=r>r+r r&r rBr) r;r<rrrmr>rYr rBr)rr^r:)r;r<r_r<r=r>rBr) rwr<rxr<ryr>rzr>rBr)rrrrrrArBr)rrrrrBr)r7r r.r rBr)rrr.r rBr)rr;rr;rBr)rr;rr;rBr)rrr7r r.r rBr)rrrrrrrBr)rrrrrBr)rrrrrBr)M __future__rtypingrrrrrrFenumr ezdxf.mathr r r r rrrrrrrrezdxf.render.meshrr__all__rrGrrrrrrrr rr!r"r#r$r%r&r'rrrr(r)rrr*r,r-r.r0r1r/r2r3r4r5r6rrrr7r8rrr9rrrr+rrQrPrs#"""""CCCCCCCCCCCCCC                             @???????# # # NHM)))))Bx %@%@%@%@%@RMN*****, J J J J J.3 B B B B B 7 7 7 7 7 ;?)))))\#" 11111p 33333lGPPPPPf!%Q 1'''''T      ?C99999( 1 1 1 1 1"GL       )))))B DAqMMDAqMMDAqMMDAqMMDAqMMDAqMMDAqMMDAqMM  DtTDtTDtTDtTDtTDtTDtTDtT LLLLLLLLLLLL  $EJ#.#.#.#.#.L    &   P.P.P.P.P.P.h"& !  !!!!!!J! %  %%%%%%V    ......B NNNNN6:;66666<    F.  ......:! %  %%%%%%V8 "  """"""L78G.BFG.G.G.G.G.G.Vx G. G.G.G.G.G.G.TEEEE    5<DDDDD.4; H H H H H ) ) ) )    2222,((((&2 ,   !!!!!!!!rQ