h6ddlmZddlmZmZmZmZmZddlZddl m Z m Z ddl m Z dgZd dZed e e ZGd deeZy) ) annotations)IteratorSequenceOptionalGenericTypeVarN)Vec3Vec2)Matrix44Bezier3PcHd|cxkrdkstdtdy)N?zt not in range [0 to 1]) ValueError)ts 4lib/python3.12/site-packages/ezdxf/math/_bezier3p.pycheck_if_in_valid_rangers/ !?s?233 233 TczeZdZdZdZddZeddZddZddZ ddZ dddZ ddd Z dd Z dd Zdd Zdd Zy)r uNImplements 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_offsetct|dk7r td|dj}|jdvrt d|j|d|_t fd|D|_y)NzThree control points required.r)r r zinvalid point type: c3(K|] }|z  yw)N).0poffsets r z$Bezier3P.__init__..8s3R 1AJ s)lenr __class____name__ TypeErrorrtupler)self defpoints point_typer!s @r__init__zBezier3P.__init__-sx y>Q => >q\++ ""&662:3F3F2GHI IaL  .33R 3R.RrcP|j\}}}|j}|||z||zfS)zBControl points as tuple of :class:`Vec3` or :class:`Vec2` objects.r)r(_p1p2r!s rcontrol_pointszBezier3P.control_points:s3(( 2rrF{BK//rc:t||j|S)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 rtangentzBezier3P.tangentBs "&&q))rc:t||j|S)uReturns point for location `t` at the Bèzier-curve. Args: t: curve position in the range ``[0, 1]`` )r_get_curve_pointr3s rpointzBezier3P.pointMs "$$Q''rc#K|dkr t|d|z }|j}|dtd|D]}|j||z|dyw)uApproximate `Bézier curve`_ by vertices, yields `segments` + 1 vertices as ``(x, y[, z])`` tuples. Args: segments: count of segments for approximation r rrN)rr0ranger6)r(segmentsdelta_tcpsegments r approximatezBezier3P.approximateWsg a<X& &x  e Q)G'''(9: :*e sAAcjd}d}|j|D]}|||j|z }|}|S)u_Returns estimated length of Bèzier-curve as approximation by line `segments`. rN)r?distance)r(r;length prev_pointr7s rapproximated_lengthzBezier3P.approximated_lengthhsJ"& %%h/E%*--e44J0 rc#Kg}d|z }d}|j}|d}||dkr||z}tj|dr|d} d}n|j|} ||zdz} |j| } |j | } | j | } | |kr| |}| }|r|j \}} nn|j|| f| }| } w|dkryyw)aBAdaptive 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 rrrr9g?N)r0mathiscloser6lerprApopappend)r(rAr;stackdtt0r= start_pointt1 end_pointmid_t mid_point chk_pointds r flatteningzBezier3P.flatteningts(*(N  A 3hbB||B$qE  11"5  "R3#44U; *// : &&y1x<#OB"+K(- ILL"i1B )I#3hs CCCcv|j\}}}d|z }d|z|z}||z}||z||zz|jzS)Nr@r)r(rr-r.r/ _1_minus_tbcs rr6zBezier3P._get_curve_pointsP(( 2r1W !Gj  EAvQ--rcR|j\}}}dd|zz }d|z}||z||zzS)NrWg@)r)r(rr-r.r/rYrZs rr2zBezier3P._get_curve_tangents=(( 2r #'M !GAvQrcPttt|jS)u>Returns a new Bèzier-curve with reversed control point order.)r listreversedr0)r(s rreversezBezier3P.reversesXd&9&9:;<??rN)r) Sequence[T])returnre)rfloatrfr)r;intrf Iterator[T]))r;rhrfrg))rArgr;rhrfri)rfz Bezier3P[T])rcr rfzBezier3P[Vec3])r% __module__ __qualname____doc__ __slots__r+propertyr0r4r7r?rDrUr6r2r_rdrrrr r sW /I S00 *(" 0*d .= @r)rrgrfNone) __future__rtypingrrrrrrF_vectorr r _matrix44r __all__rrr rrrrwsS#   ,4  Ctj@wqzj@r