'j- UddlmZddlmZmZmZmZmZmZddl Z ddl m Z m Z ddl mZddlmZer ddlmZdd lmZgd Zed e e ZGd d eeZ d$d%dZe jdz Zded< d&d'dZd Zd!ZeZ d&d(d#Z dS))) annotations) TYPE_CHECKINGIterableIteratorSequenceTypeVarGenericN)Vec3Vec2)Matrix44)arc_angle_span_deg)UVec)ConstructionEllipse)Bezier4Pcubic_bezier_arc_parameterscubic_bezier_from_arccubic_bezier_from_ellipseTceZdZdZdZddZed dZd!d Zd!d Z d"dZ d#d$dZ d!dZ d!dZ d%d&dZd'dZd(dZdS))ruImplements an optimized cubic `Bézier curve`_ for exact 4 control points. A `Bézier curve`_ is a parametric curve, parameter `t` goes from 0 to 1, where 0 is the first control point and 1 is the fourth control point. The class supports points of type :class:`Vec2` and :class:`Vec3` as input, the class instances are immutable. Args: defpoints: sequence of definition points as :class:`Vec2` or :class:`Vec3` compatible objects. _control_points_offset defpoints Sequence[T]ct|dkrtd|dj}|jdvrt d|j|d|_t fd|D|_dS)NzFour control points required.r)r r zinvalid point type: c3"K|] }|z V dSN).0poffsets N/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/math/_bezier4p.py z$Bezier4P.__init__..=s'3R3R1AJ3R3R3R3R3R3R)len ValueError __class____name__ TypeErrorrtupler)selfr point_typer#s @r$__init__zBezier4P.__init__2s y>>Q  <== =q\+ "&666H:3FHHII IaL  .33R3R3R3R 3R3R3R.R.Rr&returncF|j\}}}}|j}|||z||z||zfS)zBControl points as tuple of :class:`Vec3` or :class:`Vec2` objects.r)r-p0p1p2p3r#s r$control_pointszBezier4P.control_points?s6-BBrF{BKf<Q # 677 7&&q)))r&chd|cxkrdksntd||S)uReturns point for location `t` at the Bèzier-curve. Args: t: curve position in the range ``[0, 1]`` rr:r;)r(_get_curve_pointr=s r$pointzBezier4P.pointSs>Q # 677 7$$Q'''r&segmentsint Iterator[T]c#K|dkrt|d|z }|j}|dVtd|D]}|||zV|dVdS)uApproximate `Bézier curve`_ by vertices, yields `segments` + 1 vertices as ``(x, y[, z])`` tuples. Args: segments: count of segments for approximation r r:rN)r(r6ranger@)r-rBdelta_tcpsegments r$ approximatezBezier4P.approximate^s a<<X&& &.  e Q)) ; ;G'''(9:: : : : :e r&rdistancec#Kg}d|z }d}|j}|d}|V|dkr||z}tj|dr |d} d}n||} ||zdz} || } || } | | } | |kr#| V|}| }|r|\}} nn||| f| }| } |dkdSdS)a>Adaptive recursive flattening. The argument `segments` is the minimum count of approximation segments, if the distance from the center of the approximation segment to the curve is bigger than `distance` the segment will be subdivided. Args: distance: maximum distance from the center of the cubic (C3) curve to the center of the linear (C1) curve between two approximation points to determine if a segment should be subdivided. segments: minimum segment count r:rrFTg?N)r6mathiscloser@lerprLpopappend)r-rLrBstackdtt0rI start_pointt1 end_pointmid_t mid_point chk_pointds r$ flatteningzBezier4P.flatteningos@(*(N  A 3hhbB|B$$ 6qE  11"55  * "R3#44U;; *// :: &&y11x<<#OOOB"+K(- IILL"i111B )I# *3hhhhhhr&c|j\}}}}||z}d|z }d|z|z|z}d|z|z} ||z} ||z|| zz|| zz|jzS)Nr:@r) r-r7_r3r4r5t2 _1_minus_tbcr]s r$r@zBezier4P._get_curve_pointst, 2r2 U1W * z )A - * r ! FAvQa'$,66r&c|j\}}}}||z}ddd|zz d|zzz}d|zdd|zz z}d|z} ||z||zz|| zzS)Nr`r:@@)r) r-r7rar3r4r5rbrdrer]s r$r<zBezier4P._get_curve_tangentsr, 2r2 U 3q=38+ , !GsS1W} % "HAvQa''r&cvd}d}||D]}||||z }|}|S)u_Returns estimated length of Bèzier-curve as approximation by line `segments`. rNN)rKrL)r-rBlength prev_pointrAs r$approximated_lengthzBezier4P.approximated_lengthsU %%h//  E%*--e444JJ r& Bezier4P[T]c^ttt|jS)u>Returns a new Bèzier-curve with reversed control point order.)rlistreversedr6)r-s r$reversezBezier4P.reverses#Xd&9::;;<<>???r&N)rr)r0r)r7r8r0r)rBrCr0rD)r)rLr8rBrCr0rD)ri)rBrCr0r8)r0rn)rsr r0rt)r* __module__ __qualname____doc__ __slots__r/propertyr6r>rArKr^r@r<rmrrrxr r&r$rr!s"  /I S S S S===X= * * * * ( ( ( ("0*0*0*0*0*d 7 7 7 7 ( ( ( (     ==== @ @ @ @ @ @r&rrrrhcenterrradiusr8 start_angle end_anglerBrCr0Iterator[Bezier4P[Vec3]]c# Kt| tt||}t|dkrdS|}t j|tjz}t j||z}||kr|tjz }||kt|||D]"} fd|D}t|V#dS)uReturns an approximation for a circular 2D arc by multiple cubic Bézier-curves. Args: center: circle center as :class:`Vec3` compatible object radius: circle radius start_angle: start angle in degrees end_angle: end angle in degrees segments: count of Bèzier-curve segments, at least one segment for each quarter (90 deg), 1 for as few as possible. & .>Nc g|] }|zz Sr r )r!r"center_rs r$ z)cubic_bezier_from_arc..s"DDDWF +DDDr&) r r8rabsrOradianstaurr) rrrrrB angle_spansr6rrs ` @r$rrs&LLG 6]]F*; BBJ :A,q//DH,K Q^,,I  ! !TX   ! !6k9hWW""DDDDD^DDD y!!!!!!""r&rhPI_2ellipse'ConstructionEllipse'c#.Kj}t|dkrdSjtjz}||z}||kr|tjz }||kdfd }t |||D])}t t||V*dS) uMReturns an approximation for an elliptic arc by multiple cubic Bézier-curves. Args: ellipse: ellipse parameters as :class:`~ezdxf.math.ConstructionEllipse` object segments: count of Bèzier-curve segments, at least one segment for each quarter (π/2), 1 for as few as possible. rNpointsIterable[Vec3]r0Iterator[Vec3]c3Ktj}j}j}|D]}|||jzz||jzzVdSr)r r major_axis minor_axisxy)rrx_axisy_axisr"rs r$rxz,cubic_bezier_from_ellipse..transformsdgn%%)) 7 7A6AC<'&13,6 6 6 6 6 7 7r&)rrr0r) param_spanr start_paramrOrrrr,)rrBrrrrxrs` r$rrs *J : ,tx7K"Z/I  ! !TX   ! !7777771iRR44 uYYy112233333344r&gUUUUUU?gI`Q?'Iterator[tuple[Vec3, Vec3, Vec3, Vec3]]c# K|dkrtd||z }|dkr3ttj|tjz dz|}ntd||z }t tj|dz z}|}tj|}t|D]U} |} ||z }tj|}| | j |z| j |zfz} ||j |z|j |zfz} | | | |fVVdS)uYields cubic Bézier-curve parameters for a circular 2D arc with center at (0, 0) and a radius of 1 in the form of [start point, 1. control point, 2. control point, end point]. Args: start_angle: start angle in radians end_angle: end angle in radians (end_angle > start_angle!) segments: count of Bèzier-curve segments, at least one segment for each quarter (π/2) r z!Invalid argument segments (>= 1).rrhz3Delta angle from start- to end angle has to be > 0.rgN) r(maxrOceilpiTANGENT_FACTORtanr from_anglerGrr) rrrB delta_angle arc_count segment_angletangent_lengthanglerYrarWcontrol_point_1control_point_2s r$rr)sI!||<==="[0KQ +"7#"=>>II NOOO&2M*TXmc6I-J-JJNEoe,,I 9   G G  OE** % ]N^ + MN *)  $ K. ( [L> )'  ?OYFFFFF G Gr&)r~r rrr ) rrrr8rr8rr8rBrCr0r)r )rrrBrCr0r)rr8rr8rBrCr0r)! __future__rtypingrrrrrr rO_vectorr r _matrix44r _constructr ezdxf.mathrezdxf.math.ellipser__all__rrrrr__annotations__rDEFAULT_TANGENT_FACTOROPTIMIZED_TANGENT_FACTORrrr r&r$rs#""""""  ******7666666    GCtr@r@r@r@r@wqzr@r@r@l !"!"!"!"!"Hgm5644444H#-(;<'G'G'G'G'G'G'Gr&