h-Z%SSKJr SSKJrJrJrJrJrJr SSK r SSK J r J r SSK Jr SSKJr \(a SSKJr SS KJr /S Qr\"S \ \ 5r"S S \\5rSSSjjr\ R2S- rS\S'SSSjjrSrSr\rSSSjjr g)) annotations) TYPE_CHECKINGIterableIteratorSequenceTypeVarGenericN)Vec3Vec2)Matrix44)arc_angle_span_deg)UVec)ConstructionEllipse)Bezier4Pcubic_bezier_arc_parameterscubic_bezier_from_arccubic_bezier_from_ellipseTc\rSrSrSrSrSSjr\SSj5rSSjr SSjr SSjr SSS jjr SS jr SS jrSSS jjrSS jrSSjrSrg)r!uImplements 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_offsetc^[U5S:wa [S5eUSRnURS;a[ SUR35eUSmTUl[ U4SjU55Ulg)NzFour control points required.r)r r zinvalid point type: c3,># UH oT- v M g7fN).0poffsets F/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/_bezier4p.py $Bezier4P.__init__..=s3R 1J s)len ValueError __class____name__ TypeErrorrtupler)self defpoints point_typer"s @r#__init__Bezier4P.__init__2sx y>Q <= =q\++ ""&662:3F3F2GHI IaL  .33R 3R.RcPURupp4URnXRU-X5-XE-4$)zBControl points as tuple of :class:`Vec3` or :class:`Vec2` objects.r)r,p0p1p2p3r"s r#control_pointsBezier4P.control_points?s1--F{BK<_r4r5r6t2 _1_minus_tbcr_s r#rBBezier4P._get_curve_pointsk,, r U1W * z )A - * r ! Fv'$,,66r1cURup#pEX-nSSSU-- SU---nSU-SSU-- -nSU-n X7-XH--XY--$)Nrcr:@@)r) r,r>rdr4r5r6rergrhr_s r#r<Bezier4P._get_curve_tangentsi,, r U 3q=38+ , !GsS1W} % "Hv''r1cnSnSnURU5HnUbX#RU5- nUnM U$)uOReturns estimated length of Bèzier-curve as approximation by line `segments`. rON)rLrS)r,rHlength prev_pointrCs r#approximated_lengthBezier4P.approximated_lengthsH %%h/E%--e44J0 r1cP[[[UR555$)u>Returns a new Bèzier-curve with reversed control point order.)rlistreversedr7)r,s r#reverseBezier4P.reversesXd&9&9:;<??r1N)r- Sequence[T])returnr~)r>floatrr)rHintr Iterator[T])r)rSrrHrrr))rHrrr)rz Bezier4P[T])r{r rzBezier4P[Vec3])r) __module__ __qualname____firstlineno____doc__ __slots__r/propertyr7r?rCrLr`rBr<rqrvr|__static_attributes__rr1r#rr!sW /I S== * ("0*d 7 ( = @r1rrc## [U5n[U5n[X#5n[U5S:agUn[R "U5[R -n[R "Xv-5nX#:aU[R - nX#:aM[X#U5H&nUV s/sH oX--PM n n [U 5v M( gs sn f7f)u}Returns 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 rrabsrPradianstaurr) centerradius start_angle end_anglerHcenter_ angle_spansr7r!r-s r#rrs&LG 6]F*;BJ :A,,q/DHH,K Q^,I  !TXX   !6khW5CD^ +^ Dy!!XDsBCC'C 7CrlPI_2c#4^# TRn[U5S:agTR[R-nX2-nX4:aU[R- nX4:aMSU4Sjjn[ X4U5Hn[ [U"U555v M! g7f)u1Returns 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. rNc3># [TR5nTRnTRnUH%nXUR--X4R --v M' g7fr)r r major_axis minor_axisxy)pointsrx_axisy_axisr!ellipses r#r|,cubic_bezier_from_ellipse..transformsPgnn%))))AACC<'&33,6 6sAA)rzIterable[Vec3]rzIterator[Vec3]) param_spanr start_paramrPrrrr+)rrHrrrr|r-s` r#rrs **J : ,,txx7K"/I  !TXX   !71R uYy1233Ss AB 8BgUUUUUU?gI`Q?c#*# US:a [S5eX- nUS:a5[[R"U[R- S-5U5nO [S5eX4- n[ [R "US- 5-nUn[R"U5n[U5Hin Un Xu- n[R"U5nU U R*U-U RU-4-n UURU-UR*U-4-n XX4v Mk g7f)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).rrlz3Delta angle from start- to end angle has to be > 0.rkN) r'maxrPceilpiTANGENT_FACTORtanr from_anglerGrr) rrrH delta_angle arc_count segment_angletangent_lengthangler[rdrYcontrol_point_1control_point_2s r#rr)s!|<=="0KQ +"7#"=>I NOO&2M*TXXmc6I-JJNEooe,I 9   OOE* % ]]N^ + MMN *)  $ KK. ( [[L> )'  OFFsDD))rrrr rihr ) rrrrrrrrrHrrIterator[Bezier4P[Vec3]])r )rz'ConstructionEllipse'rHrrr)rrrrrHrrz'Iterator[tuple[Vec3, Vec3, Vec3, Vec3]])! __future__rtypingrrrrrr rP_vectorr r _matrix44r _constructr ezdxf.mathrezdxf.math.ellipser__all__rrrrr__annotations__rDEFAULT_TANGENT_FACTOROPTIMIZED_TANGENT_FACTORrrrr1r#rs##  *6  Ctr@wqzr@l !" !" !"!" !"  !"  !"Hggme564 "4.144H#-(;<'G'G#('G47'G,'Gr1