jWdZddlmZddlZddlZddlZddlmZdZ dZ edd Z Gd d e Z d Zd ZdZdZ d!dZGddZ d"dZd#dZdZdZd$dZdZdZd%d ZdS)&uP A module providing some utility functions regarding Bézier path manipulation. ) lru_cacheN)_apict|dkrft|dkrtjgS| |z }d|cxkrdkrnntj|gntjgS||zd|z|zz }|dkrtjgStj|}|dkr d||zz}nd||z z}g}t|dkr|||z t|dkr|||z tj|}||dk|dkzS)z,Real roots of c0 + c1*x + c2*x**2 in [0, 1].-q=rg)absnparraysqrtappendasarray)c0c1c2rootdisc sqrt_discqrootss ?C:\Projects\DSCons\.venv\Lib\site-packages\matplotlib\bezier.py_quadratic_roots_in_01rsG 2ww r77U??8B<< sRx#$>>>>>>>>>rxrx||C 7QVb[ D axxx|| I Qww BN # BN # E 1vv~~ R!V 2ww QV Ju  E %1*!, --c tj|t}t|dz }|dkr=t ||dkr$|dz}|dkrt ||dk$|dkrtjgS|dkrK|d |dz }d|cxkrdkrnntj|gntjgS|dkr$t |d|d|d}nvd}tj||dd}tj|j|k}||j }|| k|d|zkz}tj ||dd}tj |S) a Find real roots of a polynomial in the interval [0, 1]. For polynomials of degree <= 2, closed-form solutions are used. For higher degrees, `numpy.roots` is used as a fallback. In practice, matplotlib only ever uses cubic bezier curves and axis_aligned_extrema() differentiates, so we only ever find roots for degree <= 2. Parameters ---------- coeffs : array-like Polynomial coefficients in ascending order: ``c[0] + c[1]*x + c[2]*x**2 + ...`` Note this is the opposite convention from `numpy.roots`. Returns ------- roots : ndarray Sorted array of real roots in [0, 1]. )dtyperrrg|=N) r rfloatlenr r rrimagrealclipsort) coeffsdegrreps all_roots real_mask real_rootsin_ranges r_real_roots_in_01r++s*Ze , , ,F f++/C ''c&+&&.. q ''c&+&&.. axxx|| q zF1I%#$>>>>>>>>>rxrx||C &vay&)VAYGGHVCGG_-- F9>**S0 y). 3$&:S+@A 8,a33 75>>r)maxsizecd}tj|dzdddf}tj|dzdddf}d||zz|||z}||||ztS)a& Compute the matrix for converting Bezier control points to polynomial coefficients for a curve of degree n. The matrix M is such that M @ control_points gives polynomial coefficients. Entry M[j, i] = C(n, j) * (-1)^(i+j) * C(j, i) where C is the binomial coefficient. cRtjtj||SN)r vectorizemathcomb)nks r_combz _get_coeff_matrix.._combds &r|DI&&q!,,,rrNr)r arangeastyper)r4r6ji prefactors r_get_coeff_matrixr<Zs--- !a%D!A !a%qqq!AQ%%1++-I E!QKK) # + +E 2 22rceZdZdS)NonIntersectingPathExceptionN)__name__ __module__ __qualname__rrr>r>msDrr>c||z||zz }||z||zz } || } } || } } | | z| | zz tdkrtd| | }}| | }}fd||||fD\}}}}||z|| zz}||z|| zz}||fS)z Return the intersection between the line through (*cx1*, *cy1*) at angle *t1* and the line through (*cx2*, *cy2*) at angle *t2*. rzcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.c3"K|] }|z V dSr0rB).0r5ad_bcs r z#get_intersection..s'::Aa%i::::::r)r ValueError)cx1cy1cos_t1sin_t1cx2cy2cos_t2sin_t2 line1_rhs line2_rhsabcda_b_c_d_xyrFs @rget_intersectionr]ts v|+I v|+I F7qA F7qA EAEME 5zzENOO OBRB::::"b"b)9:::NBB Yi'A Yi'A a4Krcz|dkr||||fS|| }}| |}}||z|z||z|z} } ||z|z||z|z} } | | | | fS)z For a line passing through (*cx*, *cy*) and having an angle *t*, return locations of the two points located along its perpendicular line at the distance of *length*. rB) cxcycos_tsin_tlengthrKrLrOrPx1y1x2y2s rget_normal_pointsrisu||2r2~UFFFVUFF f_r !6F?R#7B f_r !6F?R#7B r2r>rcB|ddd|z z|dd|zz}|S)NrrrB)betat next_betas r_de_casteljau1rns/SbS QU#d122hl2I rctj|}|g} t||}||t |dkrn:d|D}dt |D}||fS)u Split a Bézier segment defined by its control points *beta* into two separate segments divided at *t* and return their control points. Trcg|] }|d S)rrBrErks r z&split_de_casteljau..s///Ta///rcg|] }|d S)rrBrqs rrrz&split_de_casteljau..s;;;t$r(;;;r)r rrnr rreversed)rkrl beta_list left_beta right_betas rsplit_de_casteljaurxs :d  DIdA&& t99>>   0/Y///I;;x ':':;;;J j  rr_?{Gz?c||}||}||}||}||kr||krtd tj|d|dz |d|dz |kr||fSd||zz} || } || } || z r| }|| kr||fS| }n| }|| kr||fS| }| }~)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 pathTrr?)r>r hypot) bezier_point_at_tinside_closedpatht0t1 tolerancestartend start_inside end_insidemiddle_tmiddle middle_insides r*find_bezier_t_intersecting_with_closedpathrs5L  b ! !E  B  C$$U++L""3''Jz!!esll* ACC C) 8E!Hs1v%uQx#a&'8 9 9I E Er6M"r'?""8,,))&11 - ' )Bf}}2v CCB2v E(L3)rceZdZdZdZdZejdddZe dZ e d Z e d Z e d Z d Zd S) BezierSegmentu* A d-dimensional Bézier segment. A BezierSegment can be called with an argument, either a scalar or an array-like object, to evaluate the curve at that/those location(s). Parameters ---------- control_points : (N, d) array Location of the *N* control points. ctj|_jj\__tjj_fdtjD}jj |zj _ dS)Ncg|]S}tjjdz tj|tjjdz |z zzTS)r)r2 factorial_N)rEr:selfs rrrz*BezierSegment.__init__.."se***! ,,^A&&! a)H)HHJ***r) r r_cpointsshaper_dr7_ordersrangeT_px)rcontrol_pointscoeffs` r__init__zBezierSegment.__init__s >22 =.y)) ****..***MOe+.rctj|}tjd|z |jdddtj||jz|jzS)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*. rNr)r rpowerouterrrrrls r__call__zBezierSegment.__call__'s^ JqMMq1udl44R4&899(..DL11259X> >rz3.11z/Call the BezierSegment object with an argument.) alternativec2t||S)zX Evaluate the curve at a single point, returning a tuple of *d* floats. tuplers r point_at_tzBezierSegment.point_at_t9s TT!WW~~rc|jS)z The control points of the curve.)rrs rrzBezierSegment.control_pointsAs }rc|jS)zThe dimension of the curve.)rrs r dimensionzBezierSegment.dimensionFs wrc|jdz S)z@Degree of the polynomial. One less the number of control points.r)rrs rdegreezBezierSegment.degreeKsw{rc~|j}|dkrtjdtt ||jzS)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!)rwarningswarnRuntimeWarningr<r)rr4s rpolynomial_coefficientsz%BezierSegment.polynomial_coefficientsPsI2 K r66 M12@ B B B ##d&999rc|j}|dkr(tjgtjgfS|j}tjd|dzdddf|ddz}g}g}t |jD]q\}}t|}t|dkrJ| || tj t||r|s(tjgtjgfStj |tj |fS)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` rNr) rr r rr7 enumeraterr+rr full concatenate) rr4CjdCjall_dimsr'r:pirs raxis_aligned_extremaz"BezierSegment.axis_aligned_extremaps$ K 668B<<"- -  )i1q5!!!!!T'*RV3 su%% 4 4EAr!"%%A1vvzz  ###A 2 2333 .8B<<"- -~h'' )B)BBBrN)r?r@rA__doc__rrr deprecatedrpropertyrrrrrrBrrrrs  ///>>>$T_MOOOOO XXX::X:>"C"C"C"C"Crrct|tfd||\}}t|||zdz \}}||fS)ur 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. c4t|Sr0r)rlbzs rz;split_bezier_intersecting_with_closedpath..s%1,,r)rg@)rrrx)bezierrrrr_left_rightrs @r)split_bezier_intersecting_with_closedpathrse, v  B 7 1YHHHFB'vR2~>>ME6 &=rFc Fddlm}|}t|\}}||dd}|} d} d} |D]U\}}| } | t |dzz } ||dd|kr t j| dd|g} n|} Vtd| d} t| ||\}}t |dkr|j g}|j |j g}nt |d kr#|j |j g}|j |j |j g}nQt |d kr/|j |j |j g}|j |j |j |j g}ntd |dd}|dd}|jY|t j|jd| |g}|t j||j| dg}n|t j|jd| |gt j|jd| |g}|t j||j| dgt j||j| dg}|r|s||}}||fS) z` Divide a path into two segments at the point where ``inside(x, y)`` becomes False. r)PathNrrz*The path does not intersect with the patch)rrrzThis should never be reached)pathr iter_segmentsnextrr rrHreshaperLINETOMOVETOCURVE3CURVE4AssertionErrorcodesvertices)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_inoutrs ""$$Iy//J6*RSS/**LN D A(GG G S__ !! 6*RSS/ " "l 2 2..*=z)JKKK E#EFFF   W % %B; FIKD% 4yyA~~k] {DK0 Tak4;/ {DK= Tak4; < {DKdkJ ;<<<abbJ(K z$r~t}RaR'8*&EFFGG4 T]1225F'GHHII$r~t}UdU';Z&HII~tz%4%'8*&EFFHH4 T]1225F'GHH TZ^'DEEGG.\.$g H rc$|dzfd}|S)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 rc8|\}}|z dz|z dzzkS)NrrB)xyr[r\r`rar2s r_fzinside_circle.._fs,1B1}B1},r11rrB)r`rarrrs`` @r inside_circlers: aB2222222 IrcV||z ||z }}||z||zzdz}|dkrdS||z ||z fS)Nr|r)r_r_rB)x0y0rerfdxdyrVs r get_cos_sinrsJ "Wb2gB b27 r!AAvvx 626>rh㈵>ctj||}tj||}t||z }||krdSt|tjz |krdSdS)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. rrF)r arctan2r r)dx1dy1dx2dy2rtheta1theta2dthetas rcheck_if_parallelrsj&ZS ! !F ZS ! !F & ! !F q Vbe^  y ( (rurc |d\}}|d\}}|d\}}t||z ||z ||z ||z }|dkr.tjdt||||\} } | | } } n*t||||\} } t||||\} } t ||| | |\} }}}t ||| | |\}}}} t | || | ||| | \}}t ||| | ||| | \}}n0#t $r#d| |zzd||zz}}d||zzd||zz}}YnwxYw| |f||f||fg}||f||f||fg}||fS)u Given the quadratic Bézier control points *bezier2*, returns control points of quadratic Bézier lines roughly parallel to given one separated by *width*. rrrrz8Lines do not intersect. A straight line is used instead.r|)rr warn_externalrrir]rH)bezier2widthc1xc1ycmxcmyc2xc2y parallel_testrKrLrOrPc1x_leftc1y_left c1x_right c1y_rightc2x_leftc2y_left c2x_right c2y_rightcmx_leftcmy_left cmx_right cmy_right path_left path_rights r get_parallelsr.sqzHCqzHCqzHC%cCis&)Cis<>( 0 9f06 906 @ @ 99     8h& '80C)D 9y( )3)i2G+H   H%H%H%'Ii(i(i(*J j  s2D*D/.D/cPdd|z||zz z}dd|z||zz z}||f||f||fgS)u Find control points of the Bézier curve passing through (*c1x*, *c1y*), (*mmx*, *mmy*), and (*c2x*, *c2y*), at parametric values 0, 0.5, and 1. r|rrB)rrmmxmmyrr rrs rfind_control_pointsrxsK C39% &C C39% &C #Jc S#J //rr|c|d\}}|d\}}|d\} } t||||\} } t||| | \} }t||| | ||z\}}}}t| | | |||z\}}}}||zdz||zdz}}|| zdz|| zdz}}||zdz||zdz}}t||||\}}t||||||z\}} }!}"t|||| ||}#t|||!|"||}$|#|$fS)u Being similar to `get_parallels`, returns control points of two quadratic Bézier lines having a width roughly parallel to given one separated by *width*. rrrr|)rrir)%rrw1wmw2rrrrc3xc3yrKrLrOrPr r r rc3x_leftc3y_left c3x_right c3y_rightc12xc12yc23xc23yc123xc123ycos_t123sin_t123 c123x_left c123y_left c123x_right c123y_rightrrs% rmake_wedged_bezier2r4sqzHCqzHCqzHC!c344NFF c344NFF #sFFEBJ??-Hh 9 #sFFEBJ??-Hh 9 )r!C#I#3$D)r!C#I#3$D4K2%t r'95E%T4t<<Hh %(EBJGG5J K$Hh$. $,h88I%Y %0+%. ;;J j  r)r_ryrz)rz)rzF)r)ryr|r_)r functoolsrr2rnumpyr matplotlibrrr+r<rHr>r]rirnrxrrrrrrrrrr4rBrrr8s  ...:,,,^ 2333$     :   B2 !!!&GKI)I)I)I)XACACACACACACACACJ.2D::::z&