hZ#SSKJr SSKJrJr SSKJr SSKrSSKr SSK J r J r J r Jr S/r"SS5rS Sjr\"SS 9S S j5rg) ) annotations)IterableSequence) lru_cacheN)Vec3NULLVECMatrix44UVecBezierc\rSrSrSrSSjr\SSj5rSSSjjrSSSjjr SSjr SSjr SS jr SS jr SS jrSS jrSS jrSrg)r Lu Generic `Bézier curve`_ of any degree. A `Bézier curve`_ is a parametric curve used in computer graphics and related fields. Bézier curves are used to model smooth curves that can be scaled indefinitely. "Paths", as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves. Paths are not bound by the limits of rasterized images and are intuitive to modify. (Source: Wikipedia) This is a generic implementation which works with any count of definition points greater than 2, but it is a simple and slow implementation. For more performance look at the specialized :class:`Bezier4P` and :class:`Bezier3P` classes. Objects are immutable. Args: defpoints: iterable of definition points as :class:`Vec3` compatible objects. c:[R"U5UlgN)rtuple _defpoints)self defpointss C/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/bezier.py__init__Bezier.__init__bs*.**Y*?cUR$)z1Control points as tuple of :class:`Vec3` objects.rrs rcontrol_pointsBezier.control_pointsesrcBURURU55$)zXApproximates curve by vertices as :class:`Vec3` objects, vertices count = segments + 1. )pointsparamsrsegmentss r approximateBezier.approximatejs{{4;;x011rc#,^^^# SUUU4SjjmSU- nSnTRSnUv US:aaXC-n[R"US5(aTRSnSnOTRU5nT"XWXF5ShvN UnUnUS:aM`ggN7f)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 curve (Cn) to the center of the linear (C1) curve between two approximation points to determine if a segment should be subdivided. segments: minimum segment count c3># X#-S-nTRU5nURU5nURU5T:aUv gT "XX$5ShvN T "XQXC5ShvN gNN7f)Ng?)pointlerpdistance) start_point end_pointstart_tend_tmid_t mid_point chk_pointr(rsubdivs rr0!Bezier.flattening..subdivss_+E 5)I#((3I!!),x7!+'III!)EEEJEs$AA.A*A.$A,%A.,A.?rN)r+floatr,r5)rmathiscloser&) rr(r!dtt0r)t1r*r0s `` @r flatteningBezier.flatteningps F F8^ ooa( 3hB||B$$ OOB/  JJrN kb= = =B#K3h >sA:B?BBBc#V# [R"SSUS-5ShvN gN7f)zCYield evenly spaced parameters from 0 to 1 for given segment count.r3r2N)nplinspacer s rr Bezier.paramss;;sCA666s )')cUS:dUS:a [S5eSU- S:aSn[nURn[U5n[ U5HnU[ US- XQ5X5-- nM U$)zKReturns a point for parameter `t` in range [0, 1] as :class:`Vec3` object. r3r2Parameter t not in range [0, 1]h㈵>r>) ValueErrorrrlenrangebernstein_basis)rtr&ptsnis rr& Bezier.pointst s7a#g>? ? !Gt Aoo HqA _QUA1CF: :E rc#D# UHnURU5v M g7f)zuYields multiple points for parameters in vector `t` as :class:`Vec3` objects. Parameters have to be in range [0, 1]. N)r&rrIus rr Bezier.pointssA**Q-  cfUS:dUS:a [S5eSU- S:aSnURn[U5nUS- n[n[n[nX-nUS- n US:Xa&XBSUS- -nXI-USSUS-- US--n[ U5Hn [ XJU5n X[X*-- nSUs=:aS:aHO OESU- n XU-- n XmX-- U -X*-- nUX-XH-- U SSU-- -- X-U -- U -X*-- nUS:XdMuXBUX)- -nXI-X$SX)-- X$S- --nM XVU4$) zrReturns (point, 1st derivative, 2nd derivative) tuple for parameter `t` in range [0, 1] as :class:`Vec3` objects. r3r2rCrDr>rg@)rErrFrrGrH)rrIrJrKn0r&d1d2t2n0_1rLtmp_bas_1_ti_n0_ts r derivativeBezier.derivatives s7a#g>? ? !Gt Aoo H U   UAv 81vA'Bc!fsSV|3c!f<=BqA%bQ/G sv% %EQ}}Qw!V)G3cf<<_rw.cC!Gm1DDy4')f Cxr7SY./Y#'A M"9CQK"GH "}rc#D# UHnURU5v M g7f)zReturns multiple (point, 1st derivative, 2nd derivative) tuples for parameter vector `t` as :class:`Vec3` objects. Parameters in range [0, 1] N)r]rOs r derivativesBezier.derivativess A//!$ $rRcP[[[UR555$)u>Returns a new Bèzier-curve with reversed control point order.)r listreversedrrs rreverseBezier.reversesd8D$7$789::rc`[URUR55n[U5$)zGeneral transformation interface, returns a new :class:`Bezier` curve. Args: m: 4x4 transformation matrix (:class:`ezdxf.math.Matrix44`) )rtransform_verticesrr )rmrs r transformBezier.transforms*!..t/B/BCD i  rrN)rzIterable[UVec])returnzSequence[Vec3]))r!intrlIterable[Vec3]))r(r5r!rnrlro)r!rnrlIterable[float])rIr5rlr)rIrqrlro)rIr5rlztuple[Vec3, Vec3, Vec3])rIrqrlz!Iterable[tuple[Vec3, Vec3, Vec3]])rlr )rir rlr )__name__ __module__ __qualname____firstlineno____doc__rpropertyrr"r;rr&rr]r`rerj__static_attributes__rrr r Ls`*@2 ($T7  $L% % *%;!rcUS:Xa US:XaSnO [X!5nX:Xa US:XaSnO[SU- X- 5n[U5[U5[X- 5-- nXS-U-$)Nr3rr2)pow factorial)rKrLrItitniNis rrHrHsiCxAF  Yv!s(37ae% 11 !%(88 9B 7S=r)maxsizec.[R"U5$r)r6r|)rKs rr|r|s >>! r)rKrnrLrnrIr5rlr5)rKrn) __future__rtypingrr functoolsrr6numpyr? ezdxf.mathrrr r __all__r rHr|ryrrrsV#% 44 *:ze!e!P  4r