'jnddlmZddlmZmZmZmZmZddlZddl m Z m Z ddl m Z dgZdd Zed e e ZGddeeZdS)) annotations)IteratorSequenceOptionalGenericTypeVarN)Vec3Vec2)Matrix44Bezier3PtfloatreturnNonecBd|cxkrdksntddS)N?zt not in range [0 to 1]) ValueError)rs N/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/math/_bezier3p.pycheck_if_in_valid_rangers/ !????s????2333 ?TceZdZdZdZddZed dZd!d Zd!d Z d"dZ d#d$dZ d%d&dZ d!dZ d!dZd'dZd(dZdS))r uNImplements an optimized quadratic `Bézier curve`_ for exact 3 control points. The class supports points of type :class:`Vec2` and :class:`Vec3` as input, the class instances are immutable. Args: defpoints: sequence of definition points as :class:`Vec2` or :class:`Vec3` compatible objects. _control_points_offset defpoints Sequence[T]ct|dkrtd|dj}|jdvrt d|j|d|_t fd|D|_dS)NzThree control points required.r)r r zinvalid point type: c3"K|] }|z V dS)N).0poffsets r z$Bezier3P.__init__..8s'3R3R1AJ3R3R3R3R3R3Rr)lenr __class____name__ TypeErrorrtupler)selfr point_typer&s @r__init__zBezier3P.__init__-s y>>Q  =>> >q\+ "&666H:3FHHII IaL  .33R3R3R3R 3R3R3R.R.Rrrc<|j\}}}|j}|||z||zfS)zBControl points as tuple of :class:`Vec3` or :class:`Vec2` objects.r)r-_p1p2r&s rcontrol_pointszBezier3P.control_points:s.( 2rrF{BK//rrrrcJt|||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)))rcJt|||S)uReturns point for location `t` at the Bèzier-curve. Args: t: curve position in the range ``[0, 1]`` )r_get_curve_pointr7s rpointzBezier3P.pointMs& """$$Q'''rsegmentsint Iterator[T]c#K|dkrt|d|z }|j}|dVtd|D]}|||zV|dVdS)uApproximate `Bézier curve`_ by vertices, yields `segments` + 1 vertices as ``(x, y[, z])`` tuples. Args: segments: count of segments for approximation r rrN)rr4ranger:)r-r<delta_tcpsegments r approximatezBezier3P.approximateWs a<<X&& &x  e Q)) ; ;G'''(9:: : : : :e rcvd}d}||D]}||||z }|}|S)u_Returns estimated length of Bèzier-curve as approximation by line `segments`. rN)rEdistance)r-r<length prev_pointr;s rapproximated_lengthzBezier3P.approximated_lengthhsU"& %%h//  E%*--e444JJ rrHc#Kg}d|z }d}|j}|d}|V|dkr||z}tj|dr |d} d}n||} ||zdz} || } || } | | } | |kr#| V|}| }|r|\}} nn||| f| }| } |dkdSdS)aBAdaptive recursive flattening. The argument `segments` is the minimum count of approximation segments, if the distance from the center of the approximation segment to the curve is bigger than `distance` the segment will be subdivided. Args: distance: maximum distance from the center of the quadratic (C2) curve to the center of the linear (C1) curve between two approximation points to determine if a segment should be subdivided. segments: minimum segment count rrrr@Tg?N)r4mathiscloser:lerprHpopappend)r-rHr<stackdtt0rC start_pointt1 end_pointmid_t mid_point chk_pointds r flatteningzBezier3P.flatteningts@(*(N  A 3hhbB|B$$ 6qE  11"55  * "R3#44U;; *// :: &&y11x<<#OOOB"+K(- IILL"i111B )I# *3hhhhhhrcb|j\}}}d|z }d|z|z}||z}||z||zz|jzS)Nr@r)r-rr1r2r3 _1_minus_tbcs rr:zBezier3P._get_curve_pointsK( 2r1W !Gj  EAvQ--rcH|j\}}}dd|zz }d|z}||z||zzS)Nr_g@)r)r-rr1r2r3rarbs rr6zBezier3P._get_curve_tangents:( 2r #'M !GAvQr Bezier3P[T]c^ttt|jS)u>Returns a new Bèzier-curve with reversed control point order.)r listreversedr4)r-s rreversezBezier3P.reverses#Xd&9::;;<<>???rN)rr)rr)rrrr)r<r=rr>)rF)r<r=rr)rL)rHrr<r=rr>)rrd)rir rrj)r* __module__ __qualname____doc__ __slots__r/propertyr4r8r;rErKr]r:r6rhrnr#rrr r s"  /I S S S S000X0 * * * *(((("     0*0*0*0*0*d . . . .==== @ @ @ @ @ @r)rrrr) __future__rtypingrrrrrrN_vectorr r _matrix44r __all__rrr r#rrrys#"""""   ,4444  GCtj@j@j@j@j@wqzj@j@j@j@j@r