+ iiJRt^RIHt^RIt^RIt^RIt^RIHt]P]!^R7R44t !RR] 4t Rt R tR tR tRR lt!R R4tRRltRRltRtRtRRltRtRtRRltR#)uP A module providing some utility functions regarding Bézier path manipulation. ) lru_cacheN)_api)maxsizecW8d^#\WV, 4p\P!^V^,4p\P!V^,V, V, 4P \ 4#))minnparangeprodastypeint)nkis&& q/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/matplotlib/bezier.py_combrsS u A1u A !QUA 77AEAIq= ! ( ( --c]tRt^tRtR#)NonIntersectingPathExceptionN)__name__ __module__ __qualname____firstlineno____static_attributes__rrrrrsrrcZaW0,W!,, pWt,We,, p Y2)rYv)rW,W,, o\S4R8d \R4hY)rV )T ppV3RlWVV34wrppW,W,,pVV,VV ,,pVV3#)z Return the intersection between the line through (*cx1*, *cy1*) at angle *t1* and the line through (*cx2*, *cy2*) at angle *t2*. g-q=zcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.c34<"TF qS, xK R#5i)Nr).0rad_bcs& r #get_intersection..9s:)9A%ii)9s)abs ValueError)cx1cy1cos_t1sin_t1cx2cy2cos_t2sin_t2 line1_rhs line2_rhsabcda_b_c_d_xyrs&&&&&&&& @rget_intersectionr7 s v|+I v|+I 7q 7q EAEME 5zENO ORB:""b)9:NBB 'A Yi'A a4KrcVR8XdWW3#Y2)reV)TrWE,V,WF,V,rWG,V,WH,V,rWW3#)z For a line passing through (*cx*, *cy*) and having an angle *t*, return locations of the two points located along its perpendicular line at the distance of *length*. r) cxcycos_tsin_tlengthr%r&r)r*x1y1x2y2s &&&&& rget_normal_pointsrCAsY|r~FFVUF _r !6?R#7 _r !6?R#7 2>rcVVRR^V, ,VR,V,,pV#)NNNr)betat next_betas&& r_de_casteljau1rKZs)Sb QU#d2hl2I rc\P!V4pV.p\W4pVPV4\ V4^8XgK/TUu.uF q^,NK pp\ T4Uu.uF qR,NK ppY43#uupiuupi)u Split a Bézier segment defined by its control points *beta* into two separate segments divided at *t* and return their control points. rG)rasarrayrKappendlenreversed)rHrI beta_list left_beta right_betas&& rsplit_de_casteljaurT_s ::d DI d& t9> %./YTaYI/'/ ':;':tr((':J;   0;s B.B cV!V4pV!V4pV!V4pV!V4pWx8XdWV8wd \R4h\P!V^,V^,, V^,V^,, 4V8dW#3#RW#,,p V!V 4p V!V 4p W{, 'dT pWj8XdW#3#T pKT pWZ8XdW#3#T pT pK)u$ Find the intersection of the Bézier curve with a closed path. The intersection point *t* is approximated by two parameters *t0*, *t1* such that *t0* <= *t* <= *t1*. Search starts from *t0* and *t1* and uses a simple bisecting algorithm therefore one of the end points must be inside the path while the other doesn't. The search stops when the distance of the points parametrized by *t0* and *t1* gets smaller than the given *tolerance*. Parameters ---------- bezier_point_at_t : callable A function returning x, y coordinates of the Bézier at parameter *t*. It must have the signature:: bezier_point_at_t(t: float) -> tuple[float, float] inside_closedpath : callable A function returning True if a given point (x, y) is inside the closed path. It must have the signature:: inside_closedpath(point: tuple[float, float]) -> bool t0, t1 : float Start parameters for the search. tolerance : float Maximal allowed distance between the final points. Returns ------- t0, t1 : float The Bézier path parameters. z3Both points are on the same side of the closed path?)rrhypot) bezier_point_at_tinside_closedpatht0t1 tolerancestartend start_inside end_insidemiddle_tmiddle middle_insides &&&&& r*find_bezier_t_intersecting_with_closedpathrdqsL b !E B C$U+L"3'J!el* AC C  88E!Hs1v%uQx#a&'8 9I E6M"'?"8,)&1  ' 'B}v CBv E(Lrc|a]tRt^toRtRtRtRt]R4t ]R4t ]R4t ]R4t R t R tVtR #) BezierSegmentu A d-dimensional Bézier segment. Parameters ---------- control_points : (N, d) array Location of the *N* control points. c \\P!V4VnVPPwVnVn\P !VP4Vn\VP4Uu.uFxp\P!VP^, 4\P!V4\P!VP^, V, 4,,NKz ppVPPV,PVn R#uupi)rFN) rrM_cpointsshape_N_dr _ordersrangemath factorialT_px)selfcontrol_pointsrcoeffs&& r__init__BezierSegment.__init__s >2 ==..yy)  .*(Q! ,^^A&! a)HHJJ( *MMOOe+..*s;A>D)c "\P!V4p\PP^V, VPRRR1,4\PPWP4,VP ,#)u Evaluate the Bézier curve at point(s) *t* in [0, 1]. Parameters ---------- t : (k,) array-like Points at which to evaluate the curve. Returns ------- (k, d) array Value of the curve for each point in *t*. NrG)rrMpowerouterrlrqrrrIs&&r__call__BezierSegment.__call__s^ JJqMq1udll4R4&89((..LL1259XX> >rc $\V!V44#)zH Evaluate the curve at a single point, returning a tuple of *d* floats. )tuplerzs&&r point_at_tBezierSegment.point_at_tsT!W~rc VP#)z The control points of the curve.)rhrrs&rrsBezierSegment.control_pointss}}rc VP#)zThe dimension of the curve.)rkrs&r dimensionBezierSegment.dimensions wwrc (VP^, #)z@Degree of the polynomial. One less the number of control points.)rjrs&rdegreeBezierSegment.degreesww{rc vVPpV^ 8d\P!R\4VPp\ P !V^,4R,p\ P !V^,4R,pRWC,,\W44,p\W4V,V,#)u: The polynomial coefficients of the Bézier curve. .. warning:: Follows opposite convention from `numpy.polyval`. Returns ------- (n+1, d) array Coefficients after expanding in polynomial basis, where :math:`n` is the degree of the Bézier curve and :math:`d` its dimension. These are the numbers (:math:`C_j`) such that the curve can be written :math:`\sum_{j=0}^n C_j t^j`. Notes ----- The coefficients are calculated as .. math:: {n \choose j} \sum_{i=0}^j (-1)^{i+j} {j \choose i} P_i where :math:`P_i` are the control points of the curve. zFPolynomial coefficients formula unstable for high order Bezier curves!NNNN)NrrG)rwarningswarnRuntimeWarningrsrr r)rrr Pjr prefactors& rpolynomial_coefficients%BezierSegment.polynomial_coefficientss2 KK r6 MM12@ B    IIacN7 # IIacN7 #15ME!K/ Q{Y&**rc VPpV^8:d-\P!.4\P!.43#VPp\P!^V^,4R,VR,,p.p.p\ VP 4F[wrg\P!VRRR1,4pVPV4VP\P!W44K] \P!V4p\P!V4p\P!V4V^8,V^8*,p WI,\P!V4V ,3#)a Return the dimension and location of the curve's interior extrema. The extrema are the points along the curve where one of its partial derivatives is zero. Returns ------- dims : array of int Index :math:`i` of the partial derivative which is zero at each interior extrema. dzeros : array of float Of same size as dims. The :math:`t` such that :math:`d/dx_i B(t) = 0` NrErrG) rrarrayrr enumeraterprootsrN full_like concatenateisrealreal) rrr CjdCjdimsrrpirin_ranges & raxis_aligned_extrema"BezierSegment.axis_aligned_extremas  KK 688B<"- -  ) )ii1Q3(2b61suu%EADbD"A LLO KK Q* +&u%~~d#99U#uz2eqjA~rwwu~h777r)rjrhrkrlrqN)rrrr__doc__rur{rpropertyrsrrrrr__classdictcell__) __classdict__s@rrfrfst/>$ !+!+F88rrfc\V4pVPp\WAVR7wrV\WV,R, 4wrxWx3#)u2 Split a Bézier curve into two at the intersection with a closed path. Parameters ---------- bezier : (N, 2) array-like Control points of the Bézier segment. See `.BezierSegment`. inside_closedpath : callable A function returning True if a given point (x, y) is inside the closed path. See also `.find_bezier_t_intersecting_with_closedpath`. tolerance : float The tolerance for the intersection. See also `.find_bezier_t_intersecting_with_closedpath`. Returns ------- left, right Lists of control points for the two Bézier segments. )r\g@)rfrrdrT) bezierrYr\bzrXrZr[_left_rights &&& r)split_bezier_intersecting_with_closedpathr<sH, v B  7 CFB'vR2~>ME =rc ^RIHpVP4p\V4wrgV!VRR4pTp ^p ^p VFOwrgT p V \ V4^,, p V!VRR4V8wd\ P !V RRV.4p MTp KQ \R4hV PR4p \WV4wr\ V4^8Xd'VP.pVPVP.pM\ V4^8Xd=VPVP.pVPVPVP.pMm\ V4^8XdSVPVPVP.pVPVPVPVP.pM \R4hVR,pVR,pVPfXV!\ P !VP RV V.44pV!\ P !VVP V R.44pMV!\ P !VP RV V.4\ P !VPRV V.44pV!\ P !VVP V R.4\ P !VVPV R.44pV'd V'gTTppVV3#) zT Divide a path into two segments at the point where ``inside(x, y)`` becomes False. )PathNz*The path does not intersect with the patchzThis should never be reachedrEr)rG)pathr iter_segmentsnextrOrrr"reshaperLINETOMOVETOCURVE3CURVE4AssertionErrorcodesvertices)rinsider\ reorder_inoutr path_iter ctl_pointscommand begin_insidectl_points_oldioldr bezier_pathbpleftright codes_left codes_right verts_left verts_rightpath_inpath_outs&&&& rsplit_path_inoutr_sw ""$Iy/J*RS/*LN D A(  S_ !! *RS/ "l 2...*=z)JKK # )EFF   W %B; IKD 4yA~kk] {{DKK0 Takk4;;/ {{DKK= Takk4;; < {{DKKdkkJ ;<<bJ(K zzr~~t}}Ra'8*&EFG T]]125F'GHIr~~t}}Ud';Z&HI~~tzz%4'8*&EFH T]]125F'GH TZZ^'DEG\$g H rc.aaaV^,oVVV3RlpV#)z Return a function that checks whether a point is in a circle with center (*cx*, *cy*) and radius *r*. The returned function has the signature:: f(xy: tuple[float, float]) -> bool c\<VwrVS, ^,VS, ^,,S8#)rr)xyr5r6r:r;r2s& r_finside_circle.._fs*B1}B1},r11rr)r:r;rrrsff& @r inside_circlers aB2 IrcW , W1, rTWD,WU,,R,pV^8XdR#WF, WV, 3#)rV)r9r9r)x0y0r?r@dxdyr0s&&&& r get_cos_sinrs: Wbg 27 r!AAv 626>rc\P!W4p\P!W#4p\WV, 4pWt8d^#\V\P, 4V8dR#R#)a Check if two lines are parallel. Parameters ---------- dx1, dy1, dx2, dy2 : float The gradients *dy*/*dx* of the two lines. tolerance : float The angular tolerance in radians up to which the lines are considered parallel. Returns ------- is_parallel - 1 if two lines are parallel in same direction. - -1 if two lines are parallel in opposite direction. - False otherwise. FrG)rarctan2r!r)dx1dy1dx2dy2r\theta1theta2dthetas&&&&& rcheck_if_parallelrsR&ZZ !F ZZ !F  !F  Vbee^ y ( rc V^,wr#V^,wrEV^,wrg\W$, W5, WF, WW, 4pVR8Xd(\P!R4\W#Wg4wrYrM\W#WE4wr\WEWg4wr\ W#WV4wrpp\ WgWV4wpppp\ WV V VVW4wpp\ VVV V VVW4wppW3VV3VV3.pVV3VV3VV3.pVV3# \ dDRT T,,RTT,,ppRTT,,RTT,,ppLfi;i)u Given the quadratic Bézier control points *bezier2*, returns control points of quadratic Bézier lines roughly parallel to given one separated by *width*. z8Lines do not intersect. A straight line is used instead.rVrG)rr warn_externalrrCr7r")bezier2widthc1xc1ycmxcmyc2xc2y parallel_testr%r&r)r*c1x_leftc1y_left c1x_right c1y_rightc2x_leftc2y_left c2x_right c2y_rightcmx_leftcmy_left cmx_right cmy_right path_left path_rights&& r get_parallelsrsqzHCqzHCqzHC%ci&)i( 0 9f06 906 @ 9 %H%H%'Ii(i(i(*J j  )   8h& '80C)D 9y( )3)i2G+H 9  s6'C66A EEcR^V,W,, ,pR^V,W,, ,pW3Wg3WE3.#)u Find control points of the Bézier curve passing through (*c1x*, *c1y*), (*mmx*, *mmy*), and (*c2x*, *c2y*), at parametric values 0, 0.5, and 1. rVr)rrmmxmmyrrrrs&&&&&& rfind_control_pointsr sA C39% &C C39% &C J SJ //rc2V^,wrVV^,wrxV^,wr\WVWx4wr\WxW4wr\WVWW,4wpppp\WWW,4wppppWW,R,Wh,R,ppWy,R,W,R,ppVV,R,VV,R,pp\VVVV4wpp\VVVVW,4wpp p!p"\VVVV VV4p#\VVV!V"VV4p$V#V$3#)u Being similar to `get_parallels`, returns control points of two quadratic Bézier lines having a width roughly parallel to given one separated by *width*. rV)rrCr)%rrw1wmw2rrrrc3xc3yr%r&r)r*rrrrc3x_leftc3y_left c3x_right c3y_rightc12xc12yc23xc23yc123xc123ycos_t123sin_t123 c123x_left c123y_left c123x_right c123y_rightrrs%&&&&& rmake_wedged_bezier2r*sAqzHCqzHCqzHC!34NF 34NF #FEJ?-Hh 9 #FEJ?-Hh 9 )r!CI#3$D)r!CI#3$D4K2%t r'95E%T4t<Hh %(EJG5J K$Hh$. $,h8I%Y %0+%. ;J j  r)r9?{Gz?)r)rF)gh㈵>)rrVr9)r functoolsrrnrnumpyr matplotlibr vectorizerr"rr7rCrKrTrdrfrrrrrrrrrrrr#s  3.. : B2 !$I)X|8|8~F:z&