hddlmZddlmZmZddlZddlmZddlm Z m Z ddl m Z gdZ dd Zdd Zdd Zdd Zdd ZddZddZddZddZ d d!dZ d" d#dZ d$ d%dZ d& d'dZd(dZ d& d'dZd)dZy)*) annotations)IterableSequenceN)Vec3)#tangents_cubic_bezier_interpolationcubic_bezier_interpolation)circle_radius_3p)estimate_tangentsestimate_end_tangent_magnitudecreate_t_vector chord_lengthc|dk(rtt|S|dvr t|S|dvr t|S|dk(r t |St dj |)Nuniform)distancechord) centripetal sqrt_chordarczUnknown method: {})uniform_t_vectorlendistance_t_vectorcentripetal_t_vector arc_t_vector ValueErrorformat) fit_pointsmethods 6lib/python3.12/site-packages/ezdxf/math/parametrize.pyr r sj J00 ( ( ,, 0 0#J// 5J''-44V<==c`t|dz }t|Dcgc]}||z  c}Scc}wNr)floatrange)lengthnts rrr"s0 fqjA = )=aAE= )) )s +c<ttt|SN)_normalize_distanceslistlinear_distances)rs rrr's %5j%A B CCr c t||ddDcgc])\}}tj|j|+}}}t |Scc}}wr")zipmathsqrtrr*)rp1p2 distancess rrr+sS14ZAB1P1Pvr2 "++b/"1P **s.Act|}t|dkrgSdg}d}|ddD]}||z }|j||z |jd|S)Ng-q=?)sumabsappend)r3 total_lengthparamssds rr*r*2sfy>L <E! %F A s^ Q a,&' MM# Mr c#RKd}|D]}||}|j||}ywr)r)pointsprevps rr,r,?s6 D  <D mmA s%'c*tt|Sr))r8r,)rAs rrrIs ' ((r c@tt|}t|Sr))r+ arc_distancesr*)rr3s rrrMs]:./I  **r c#tK|dfd }t|}t|dk(ry|j|dtdtdz D]]}|dz|z j}||}t j |dr|;t j|dz |z dz|z_yw)Nc3Kttdz D]#} t||dz|dz}|%y#t$rd}YwxYww)Nrr5)r$rr ZeroDivisionError)iradiusrCs r_radiizarc_distances.._radiiUsas1vz"A )!A$!a%!AE(CL #%  s'AAA A AAArr6r@)returnIterable[float])r+rr:r$ magnituder/iscloseasin)rrMrkrrkrCs @rrFrFRsA&(^A 1v{HHQrUO 1c!fqj !a!eHqtO.. qT <<A N))HsNR/036; ; "sB5B8c.|j}|jdr t||S|jdr t||S|jdr t ||S|jdr t ||St d|)aBEstimate tangents for curve defined by given fit points. Calculated tangents are normalized (unit-vectors). Available tangent estimation methods: - "3-points": 3 point interpolation - "5-points": 5 point interpolation - "bezier": tangents from an interpolated cubic bezier curve - "diff": finite difference Args: points: start-, end- and passing points of curve method: tangent estimation method normalize: normalize tangents if ``True`` Returns: tangents as list of :class:`Vec3` objects bez normalizez3-pz5-pdifzUnknown method: )lower startswithrtangents_3_point_interpolationtangents_5_point_interpolationfinite_difference_interpolationr)rArrZs rr r js,\\^F 26YOO   5 !-f JJ   5 !-f JJ   5 !.vKK+F8455r c ^|dk(r#tdt||ddD}||fS|dk(rtt|}||fS|jdrJt |dd}d}t |D](}|tt |j|z }*||fStd |) aEstimate tangent magnitude of start- and end tangents. Available estimation methods: - "chord": total chord length, curve approximation by straight segments - "arc": total arc length, curve approximation by arcs - "bezier-n": total length from cubic bezier curve approximation, n segments per section Args: points: start-, end- and passing points of curve method: tangent magnitude estimation method rc3DK|]\}}|j|ywr)r@).0p0r1s r z1estimate_end_tangent_magnitude..sQ9Pvr22;;r?9Ps rNrzbezier-r5z.Unknown tangent magnitude calculation method: ) r8r.rFr]intr r, approximater)rArr;countr=curves rr r s"QVVABZ9PQQ \)) 5=01 \))   9 %F12J /7E %e&7&7&>?@ @A8!t I&RSSr c t||ddDcgc] \}}||z  }}}tt||}t||ddDcgc] \}}||z  } }}t|| D cgc] \} } | | z  } } } t| | ddD cgc] \} }| | |zz }} }tg}|j t t | dz Dcgc]}d||z | |z||| |dzzz!c}d| dz|dz |d<|jd| dz|dz |r|Dcgc]}|j}}|Scc}}wcc}}wcc} } wcc}} wcc}wcc}w)zTReturns from 3 points interpolated and optional normalized tangent vectors. rNr7rNrr6) r.r+r rextendr$rr:rZ)rrrZQ0Q1qr't0t1delta_tqkdtkr>dt0dt1alphatangentsrUvs rr^r^s #:z!"~>?>VRb>A? _Z 01A%(AabE]3]62rrBw]G3!$Q1gb#cA1/27GABK/H I/H83SC#I /HE I F8H OO@Ec!fqj@QR@Q1#a.AaD 58aAh#6 6@QR!*x{*HQK OOC!B%K(2,./+348aAKKM84 O @31 I S 5s#E E-EE!$E'4E,ct|}t|}t}t|D]d}||dz j ||j }||dzj ||dzj }|j |||zz fg}t|D]0}d||z ||z||||dzzz} |j | 2|r|D cgc]} | j}} |Scc} w)zTReturns from 5 points interpolated and optional normalized tangent vectors. rrIr7)r_delta_qr+r$crossrQr:rZ) rrZr&rorwrUv1v2rxvkrys rr_r_s JAA FE 1XAhnnQqT" - -AhnnQq1uX& 1 1 R27^$ H 1XE!Hn! $uQx!AE(': :+348aAKKM84 O5sC4ct|}tg}|jt|dz Dcgc]}||dz||z c}d|dz|dz |d<|j d||dz z||dz z |j d||z||dz z |j d|dz|dz |Scc}w)NrrNrIr)rrrlr$r:)rAr&rorUs rr{r{s F A AHHq1u >AfQUmfQi' >? 1:! AaDHHS1QU8^aAh &'HHS1Q4Z!AE( "#HHS1Q4Z!A$  H ?sCcLd}|}|d|dz |z g}tdt|dz D]4}|j||||dz z |z ||dz||z |z z6|j|d|dz |z |r|Dcgc]}|j}}|Scc}w)NrNrrr6)r$rr:rZ)rrZfrCr'rUrys rr`r`s AA A$1+ A 1c*o) * !A$1q5/Q&!AE(QqT/Q)>>?+HHaeaemq !$% &AqQ[[]A & H 'sB!c fd}||d|dg}tdt|dz D]&}|j|||dz||dz (|j||d|d|S)Nc2||z jdz S)Nr7rY)rdr1tensions rtangentz'cardinal_interpolation..tangentsR""3=11r rrr6r)r$rr:)rrrr'rUs ` rcardinal_interpolationrs2 A 1 ./A 1c*o) * AE*Jq1u,=>?+HHWZ^Z^ 45 Hr )r list[Vec3]rstrrO list[float])r%rgrOr)rrrOr)r3zSequence[float]rOr)rAIterable[Vec3]rOrP)rArrOr#)rrrOrP)z5-pointsT)rArrrrOr)r)rArrrrOztuple[float, float])rT)rrrrrOr)T)rrrOr)rArrOr)rrrr#rOr) __future__rtypingrrr/ ezdxf.mathrbezier_interpolationrr construct2dr __all__r rrrr*r,rrrFr r r^r_r{r`rr rrs#% *  >* D+ )+ <2=A 6  6 # 6 6H'.T T #TTD>B$'.'+0 '+        r