hd.DUddlmZddlmZmZmZmZmZmZddl Z ddl m Z m Z ddl mZddlmZer ddlmZdd lmZgd Zed e e ZGd d eeZ d ddZe j2dz Zded< d ddZdZdZeZ d ddZ y)) annotations) TYPE_CHECKINGIterableIteratorSequenceTypeVarGenericN)Vec3Vec2)Matrix44)arc_angle_span_deg)UVec)ConstructionEllipse)Bezier4Pcubic_bezier_arc_parameterscubic_bezier_from_arccubic_bezier_from_ellipseTczeZdZdZdZddZeddZddZddZ ddZ dddZ dd Z dd Z ddd Zdd Zdd Zy)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_offsetct|dk7r td|dj}|jdvrt d|j|d|_t fd|D|_y)NzFour control points required.r)r r zinvalid point type: c3(K|] }|z  ywN).0poffsets 4lib/python3.12/site-packages/ezdxf/math/_bezier4p.py z$Bezier4P.__init__..=s3R 1AJ s)len ValueError __class____name__ TypeErrorrtupler)self defpoints point_typer!s @r"__init__zBezier4P.__init__2sx y>Q <= =q\++ ""&662:3F3F2GHI IaL  .33R 3R.RcZ|j\}}}}|j}|||z||z||zfS)zBControl points as tuple of :class:`Vec3` or :class:`Vec2` objects.r)r*p0p1p2p3r!s r"control_pointszBezier4P.control_points?s;--BBrF{BKf<Adaptive recursive flattening. The argument `segments` is the minimum count of approximation segments, if the distance from the center of the approximation segment to the curve is bigger than `distance` the segment will be subdivided. Args: distance: maximum distance from the center of the cubic (C3) curve to the center of the linear (C1) curve between two approximation points to determine if a segment should be subdivided. segments: minimum segment count r6rr@g?N)r4mathiscloser=lerpdistancepopappend)r*rLrBstackdtt0rD start_pointt1 end_pointmid_t mid_point chk_pointds r" flatteningzBezier4P.flatteningos(*(N  A 3hbB||B$qE  11"5  "R3#44U; *// : &&y1x<#OB"+K(- ILL"i1B )I#3hs CCCc|j\}}}}||z}d|z }d|z|z|z}d|z|z} ||z} ||z|| zz|| zz|jzS)Nr6@r) r*r:_r1r2r3t2 _1_minus_tbcrXs r"r=zBezier4P._get_curve_pointsy,, 2r2 U1W * z )A - * r ! FAvQa'$,,66r.c|j\}}}}||z}ddd|zz d|zzz}d|zdd|zz z}d|z} ||z||zz|| zzS)Nr[r6@@)r) r*r:r\r1r2r3r]r_r`rXs r"r8zBezier4P._get_curve_tangentsu,, 2r2 U 3q=38+ , !GsS1W} % "HAvQa''r.cjd}d}|j|D]}|||j|z }|}|S)u_Returns estimated length of Bèzier-curve as approximation by line `segments`. rHN)rFrL)r*rBlength prev_pointr>s r"approximated_lengthzBezier4P.approximated_lengthsJ %%h/E%*--e44J0 r.cPttt|jS)u>Returns a new Bèzier-curve with reversed control point order.)rlistreversedr4)r*s r"reversezBezier4P.reversesXd&9&9:;<??r.N)r+ Sequence[T])returnrq)r:floatrrr)rBintrr Iterator[T])r)rLrsrBrtrrru))rBrtrrrs)rrz Bezier4P[T])ror rrzBezier4P[Vec3])r' __module__ __qualname____doc__ __slots__r-propertyr4r;r>rFrYr=r8rgrkrprr.r"rr!sW /I S== * ("0*d 7 ( = @r.rrsc#Kt|}t|}t||}t|dkry|}t j |tj z}t j ||z}||kDr|tj z }||kDrt|||D]$}|D cgc] } || |zz } } t| &ycc} ww)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. & .>N) r rsrabsrIradianstaurr) centerradius start_angle end_anglerBcenter_ angle_spansr4r r+s r"rrs&LG 6]F*; BJ :A,,q/DHH,K Q^,I  !TXX   !6k9hW5CD^WF +^ Dy!!XDsBC C &C5C rcPI_2c#,Kj}t|dkryjtjz}||z}||kDr|tjz }||kDrdfd }t |||D]}t t|| yw)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. r}Nc3Ktj}j}j}|D]&}|||jzz||j zz(ywr)r r major_axis minor_axisxy)pointsrx_axisy_axisr ellipses r"rpz,cubic_bezier_from_ellipse..transformsUgnn%))))A6ACC<'&133,6 6sAA)rzIterable[Vec3]rrzIterator[Vec3]) param_spanr~ start_paramrIrrrr))rrBrrrrpr+s` r"rrs **J : ,,txx7K"Z/I  !TXX   !71iR uYy1233Ss AB5BgUUUUUU?gI`Q?c#$K|dkr td||z }|dkDr4ttj|tjz dz|}n td||z }t tj |dz z}|}tj|}t|D]j} |} ||z }tj|}| | j |z| j|zfz} ||j|z|j |zfz} | | | |flyw)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).rrcz3Delta angle from start- to end angle has to be > 0.rbN) r%maxrIceilpiTANGENT_FACTORtanr from_anglerArr) rrrB delta_angle arc_count segment_angletangent_lengthanglerTr\rRcontrol_point_1control_point_2s r"rr)s!!|<=="[0KQ +"7#"=>I NOO&2M*TXXmc6I-JJNEooe,I 9   OOE* % ]]N^ + MMN *)  $ KK. ( [[L> )'  ?OYFFsDD))rrrr rihr ) rrrrsrrsrrsrBrtrrIterator[Bezier4P[Vec3]])r )rz'ConstructionEllipse'rBrtrrr)rrsrrsrBrtrrz'Iterator[tuple[Vec3, Vec3, Vec3, Vec3]])! __future__rtypingrrrrrr rI_vectorr r _matrix44r _constructr ezdxf.mathrezdxf.math.ellipser__all__rrrrr__annotations__rDEFAULT_TANGENT_FACTOROPTIMIZED_TANGENT_FACTORrrrr.r"rs##  *6  Ctr@wqzr@l !" !" !"!" !"  !"  !"Hggme564 "4.144H#-(;<'G'G#('G47'G,'Gr.