hnSSKJr SSKJrJrJrJrJr SSKrSSK J r J r SSK J r S/rS Sjr\"S \ \ 5r"S S\\5rg) ) annotations)IteratorSequenceOptionalGenericTypeVarN)Vec3Vec2)Matrix44Bezier3Pc8SUs=::aS::d O [S5eg)N?zt not in range [0 to 1]) ValueError)ts F/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/_bezier3p.pycheck_if_in_valid_rangers !?s?233 Tc\rSrSrSrSrSSjr\SSj5rSSjr SSjr SSjr SSS jjr SSS jjr SS jrSS jrSS jrSSjrSrg)r u2Implements an optimized quadratic `Bézier curve`_ for exact 3 control points. 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)NzThree control points required.r)r r zinvalid point type: c3,># UH oT- v M g7f)N).0poffsets r $Bezier3P.__init__..8s3R 1J s)lenr __class____name__ TypeErrorrtupler)self defpoints point_typer"s @r__init__Bezier3P.__init__-sx y>Q => >q\++ ""&662:3F3F2GHI IaL  .33R 3R.RrcJURupnURnXBU-X4-4$)zBControl points as tuple of :class:`Vec3` or :class:`Vec2` objects.r)r*_p1p2r"s rcontrol_pointsBezier3P.control_points:s-(( rF{BK//rc:[U5 URU5$)uReturns direction vector of tangent for location `t` at the Bèzier-curve. Args: t: curve position in the range ``[0, 1]`` )r_get_curve_tangentr*rs rtangentBezier3P.tangentBs "&&q))rc:[U5 URU5$)ukReturns point for location `t` at the Bèzier-curve. Args: t: curve position in the range ``[0, 1]`` )r_get_curve_pointr7s rpointBezier3P.pointMs "$$Q''rc## US:a [U5eSU- nURnUSv [SU5HnURX$-5v M USv g7f)uApproximate `Bézier curve`_ by vertices, yields `segments` + 1 vertices as ``(x, y[, z])`` tuples. Args: segments: count of segments for approximation r rrN)rr3ranger;)r*segmentsdelta_tcpsegments r approximateBezier3P.approximateWsd a<X& &x  e Q)G''(9: :*e sAAcnSnSnURU5HnUbX#RU5- nUnM U$)uOReturns estimated length of Bèzier-curve as approximation by line `segments`. rN)rEdistance)r*rAlength prev_pointr<s rapproximated_lengthBezier3P.approximated_lengthhsH"& %%h/E%--e44J0 rc## /nSU- nSnURnUSnUv US:aXT-n[R"US5(aUSn SnOURU5n XX-S-n URU 5n UR U 5n U R U 5n X:a#U v UnU nU(aUR 5upOOURX45 U nU n MzUS:aMgg7f)aAdaptive recursive flattening. The argument `segments` is the minimum count of approximation segments, if the distance from the center of the approximation segment to the curve is bigger than `distance` the segment will be subdivided. Args: distance: maximum distance from the center of the quadratic (C2) curve to the center of the linear (C1) curve between two approximation points to determine if a segment should be subdivided. segments: minimum segment count rrrr?g?N)r3mathiscloser;lerprHpopappend)r*rHrAstackdtt0rC start_pointt1 end_pointmid_t mid_point chk_pointds r flatteningBezier3P.flatteningts(*(N  A 3hB||B$$qE  11"5  "3#44U; *// : &&y1<#OB"+K(- ILL"1B )I#3hs CC%#C%cnURup#nSU- nSU-U-nX-nX6-XG--UR-$)Nr@r)r*rr0r1r2 _1_minus_tbcs rr;Bezier3P._get_curve_pointsH(( r1W !Gj  Ev--rcLURup#nSSU-- nSU-nX5-XF--$)Nr`g@)r)r*rr0r1r2rbrcs rr6Bezier3P._get_curve_tangents7(( r #'M !GvrcP[[[UR555$)u>Returns a new Bèzier-curve with reversed control point order.)r listreversedr3)r*s rreverseBezier3P.reversesXd&9&9:;<??rN)r+ Sequence[T])returnrr)rfloatrsr)rAintrs Iterator[T]))rArursrt))rHrtrArursrv)rsz Bezier3P[T])ror rszBezier3P[Vec3])r' __module__ __qualname____firstlineno____doc__ __slots__r-propertyr3r8r<rErKr]r;r6rjrp__static_attributes__rrrr r sW /I S00 *(" 0*d .= @r)rrtrsNone) __future__rtypingrrrrrrN_vectorr r _matrix44r __all__rrr rrrrsS#   ,4  Ctj@wqzj@r