h^$ddlmZddlmZmZddlmZddlZddlZ ddl m Z m Z m Z mZdgZ GddZd dZed d d Zy) ) annotations)IterableSequence) lru_cacheN)Vec3NULLVECMatrix44UVecBezierc~eZdZdZddZeddZdddZdddZddZ ddZ ddZ dd Z dd Z dd Zdd Zy )r uCGeneric `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. c8tj||_yN)rtuple _defpoints)self defpointss 1lib/python3.12/site-packages/ezdxf/math/bezier.py__init__zBezier.__init__bs*.**Y*?c|jS)z1Control points as tuple of :class:`Vec3` objects.)rrs rcontrol_pointszBezier.control_pointsesrcB|j|j|S)zhApproximates curve by vertices as :class:`Vec3` objects, vertices count = segments + 1. )pointsparamsrsegmentss r approximatezBezier.approximatejs{{4;;x011rc#Kdfd d|z }d}jd}||dkr\||z}tj|drjd}d}nj|}||||Ed{|}|}|dkr[yy7w)a8Adaptive 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 c3K||zdz}j|}|j|}|j|kr|y ||||Ed{ ||||Ed{y77w)Ng?)pointlerpdistance) start_point end_pointstart_tend_tmid_t mid_point chk_pointr#rsubdivs rr+z!Bezier.flattening..subdivsu_+E 5)I#((3I!!),x7!+y'5III!)YuEEEJEs$AA2A.A2(A0)A20A2?rN)r&floatr'r/)rmathiscloser!) rr#rdtt0r$t1r%r+s `` @r flatteningzBezier.flatteningps F8^ ooa( 3hbB||B$ OOB/  JJrN k9b"= = =B#K3h >sA4B 9B : B B c#TKtjdd|dzEd{y7w)zCYield evenly spaced parameters from 0 to 1 for given segment count.r-r,N)nplinspacers rrz Bezier.paramss ;;sCA666s (&(c|dks|dkDr tdd|z dkrd}t}|j}t|}t |D]}|t |dz ||||zz }|S)z[Returns a point for parameter `t` in range [0, 1] as :class:`Vec3` object. r-r,Parameter t not in range [0, 1]h㈵>r7) ValueErrorrrlenrangebernstein_basis)rtr!ptsnis rr!z Bezier.pointsx s7a#g>? ? !Gt Aoo HqA _QUAq1CF: :E rc#@K|D]}|j|yw)zYields multiple points for parameters in vector `t` as :class:`Vec3` objects. Parameters have to be in range [0, 1]. N)r!rrAus rrz Bezier.pointss A**Q- c||dks|dkDr tdd|z dkrd}|j}t|}|dz }t}t}t}||z}|dz } |dk(r(||d|dz z}|| z|dd|dzz |dzz}t |D]} t || |} || || zz }d|cxkrdkrPnnMd|z } | ||zz } || || zz | z|| zz }|| | z||zz | dd|zz zz || z| zz | z|| zz }|dk(s|||||| z z}|| z||d|| zz ||dz zz}|||fS) zReturns (point, 1st derivative, 2nd derivative) tuple for parameter `t` in range [0, 1] as :class:`Vec3` objects. r-r,r;r<r7rg@)r=rr>rr?r@)rrArBrCn0r!d1d2t2n0_1rDtmp_bas_1_ti_n0_ts r derivativezBezier.derivatives s7a#g>? ? !Gt Aoo H U   UAv 8s1vA'Bdc!fsSV|3c!f<=BqA%b!Q/G Ws1v% %EQ}}QwR!VfD)G3c!f<<f_rBw.cC!Gm1DDDy4')!f Cx3r7SY./$Y#b'AD M"9CQK"GH b"}rc#@K|D]}|j|yw)zReturns multiple (point, 1st derivative, 2nd derivative) tuples for parameter vector `t` as :class:`Vec3` objects. Parameters in range [0, 1] N)rSrFs r derivativeszBezier.derivativess!A//!$ $rHcPttt|jS)u>Returns a new Bèzier-curve with reversed control point order.)r listreversedrrs rreversezBezier.reversesd8D$7$789::rc`t|j|j}t|S)zGeneral transformation interface, returns a new :class:`Bezier` curve. Args: m: 4x4 transformation matrix (:class:`ezdxf.math.Matrix44`) )rtransform_verticesrr )rmrs r transformzBezier.transforms*!..t/B/BCD i  rN)rzIterable[UVec])returnzSequence[Vec3]))rintr^Iterable[Vec3]))r#r/rr`r^ra)rr`r^Iterable[float])rAr/r^r)rArcr^ra)rAr/r^ztuple[Vec3, Vec3, Vec3])rArcr^z!Iterable[tuple[Vec3, Vec3, Vec3]])r^r )r\r r^r )__name__ __module__ __qualname____doc__rpropertyrrr5rr!rrSrUrYr]rrr r Ls`*@2 ($T7  $L% % *%;!rc|dk(r|dk(rd}n t||}||k(r|dk(rd}ntd|z ||z }t|t|t||z zz }||z|zS)Nr-rr,)pow factorial)rCrDrAtitniNis rr@r@ssCxAF  AYAv!s(37a!e% 11 !a%(88 9B 7S=r)maxsizec,tj|Sr)r0rl)rCs rrlrls >>! r)rCr`rDr`rAr/r^r/)rCr`) __future__rtypingrr functoolsrr0numpyr8 ezdxf.mathrrr r __all__r r@rlrirrrxsV#% 44 *:ze!e!P  4r