P/PhiJdZddlmZddlZddlZddlZddlmZej eddZ Gdd e Z d Z d Zd Zd Z ddZGddZ d dZd!dZdZdZd"dZdZdZd#dZdS)$uP A module providing some utility functions regarding Bézier path manipulation. ) lru_cacheN)_api)maxsizec||krdSt|||z }tjd|dz}tj|dz|z |z t S)Nr)minnparangeprodastypeint)nkis Q/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/matplotlib/bezier.py_combrsb 1uuq Aq1u A !QUA 7AEAIq= ! ! ( ( - --ceZdZdS)NonIntersectingPathExceptionN)__name__ __module__ __qualname__rrrrsDrrc||z||zz }||z||zz } || } } || } } | | z| | zz tdkrtd| | }}| | }}fd||||fD\}}}}||z|| zz}||z|| zz}||fS)z Return the intersection between the line through (*cx1*, *cy1*) at angle *t1* and the line through (*cx2*, *cy2*) at angle *t2*. g-q=zcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.c3"K|] }|z V dS)Nr).0rad_bcs r z#get_intersection..9s'::Aa%i::::::r)abs ValueError)cx1cy1cos_t1sin_t1cx2cy2cos_t2sin_t2 line1_rhs line2_rhsabcda_b_c_d_xyrs @rget_intersectionr6 s v|+I v|+I F7qA F7qA EAEME 5zzENOO OBRB::::"b"b)9:::NBB Yi'A Yi'A a4Krcz|dkr||||fS|| }}| |}}||z|z||z|z} } ||z|z||z|z} } | | | | fS)z For a line passing through (*cx*, *cy*) and having an angle *t*, return locations of the two points located along its perpendicular line at the distance of *length*. r) cxcycos_tsin_tlengthr$r%r(r)x1y1x2y2s rget_normal_pointsrBAsu||2r2~UFFFVUFF f_r !6F?R#7B f_r !6F?R#7B r2r>rcB|ddd|z z|dd|zz}|S)Nrr)betat next_betas r_de_casteljau1rHZs/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)rrrrEs r z&split_de_casteljau..ks///Ta///rcg|] }|d S)rDrrKs rrLz&split_de_casteljau..ls;;;t$r(;;;r)r asarrayrHappendlenreversed)rErF beta_list left_beta right_betas rsplit_de_casteljaurU_s :d  DIdA&& t99>>   0/Y///I;;x ':':;;;J j  rr8?{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?)rr hypot) bezier_point_at_tinside_closedpatht0t1 tolerancestartend start_inside end_insidemiddle_tmiddle middle_insides r*find_bezier_t_intersecting_with_closedpathrgqs5L  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)rceZdZdZdZdZdZedZedZ edZ edZ d Z d S) BezierSegmentu A d-dimensional Bézier segment. 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)math factorial_N)rrselfs rrLz*BezierSegment.__init__..se***! ,,^A&&! a)H)HHJ***r) r rN_cpointsshapern_dr _ordersrangeT_px)rocontrol_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*. rNrD)r rNpowerouterrsrvrorFs r__call__zBezierSegment.__call__s^ JqMMq1udl44R4&899(..DL11259X> >rc2t||S)zX Evaluate the curve at a single point, returning a tuple of *d* floats. )tupler}s r point_at_tzBezierSegment.point_at_tsTT!WW~~rc|jS)z The control points of the curve.)rpros rrwzBezierSegment.control_pointss }rc|jS)zThe dimension of the curve.)rrrs r dimensionzBezierSegment.dimensions wrc|jdz S)z@Degree of the polynomial. One less the number of control points.r)rnrs rdegreezBezierSegment.degreesw{rc@|j}|dkrtjdt|j}t j|dzdddf}t j|dzdddf}d||zzt||z}t|||z|zS)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!rNrD)rwarningswarnRuntimeWarningrwr r r)rorPjr prefactors rpolynomial_coefficientsz%BezierSegment.polynomial_coefficientss2 K r66 M12@ B B B   IacNN111d7 # IacNN47 #1q5ME!QKK/ Q{{Y&**rc|j}|dkr(tjgtjgfS|j}tjd|dzdddf|ddz}g}g}t |jD]_\}}tj|ddd}|||tj ||`tj |}tj |}tj ||dkz|dkz} || 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` rNrDr) rr arrayrr enumeraterurootsrO full_like concatenateisrealreal) rorCjdCjdimsrrpirin_ranges raxis_aligned_extremaz"BezierSegment.axis_aligned_extremas1 K 668B<<"- -  )i1Q34(2abb61su%% , ,EArDDbD""A LLOOO KK Q** + + + +u%%~d##9U##uz2eqjAH~rwu~~h777rN) rrr__doc__ryr~rpropertyrwrrrrrrrriris///>>>$ XXX!+!+X!+F88888rrict|}|j}t|||\}}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. )r_g@)rirrgrU) bezierr\r_bzr[r]r^_left_rights r)split_bezier_intersecting_with_closedpathr<sc, v  B  7, CCCFB'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)PathNrz*The path does not intersect with the patch)rDrzThis should never be reached)pathr iter_segmentsnextrPr rr!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_s ""$$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)Nrr)xyr4r5r9r:r2s r_fzinside_circle.._fs,1B1}B1},r11rr)r9r:rrrs`` @r inside_circlers: aB2222222 IrcV||z ||z }}||z||zzdz}|dkrdS||z ||z fS)NrYr)r8r8r)x0y0r>r?dxdyr/s 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. rrDF)r arctan2r r)dx1dy1dx2dy2r_theta1theta2dthetas 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 $r#d| |zzd||zz}}d||zzd||zz}}YnwxYw| |f||f||fg}||f||f||fg}||fS)u Given the quadratic Bézier control points *bezier2*, returns control points of quadratic Bézier lines roughly parallel to given one separated by *width*. rrrrDz8Lines do not intersect. A straight line is used instead.rY)rr warn_externalrrBr6r!)bezier2widthc1xc1ycmxcmyc2xc2y parallel_testr$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%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. rYrr)rrmmxmmyrrrrs rfind_control_pointsr sK C39% &C C39% &C #Jc S#J //rrYc|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*. rrrrY)rrBr)%rrw1wmw2rrrrc3xc3yr$r%r(r)rrrrc3x_leftc3y_left c3x_right c3y_rightc12xc12yc23xc23yc123xc123ycos_t123sin_t123 c123x_left c123y_left c123x_right c123y_rightrrs% rmake_wedged_bezier2r*sqzHCqzHCqzHC!c344NFF c344NFF #sFFEBJ??-Hh 9 #sFFEBJ??-Hh 9 )r!C#I#3$D)r!C#I#3$D4K2%t r'95E%T4t<<Hh %(EBJGG5J K$Hh$. $,h88I%Y %0+%. ;;J j  r)r8rVrW)rW)rWF)r)rVrYr8)r functoolsrrlrnumpyr matplotlibr vectorizerr!rr6rBrHrUrgrirrrrrrrrrrrrs   3...     :   B2 !!!&GKI)I)I)I)X|8|8|8|8|8|8|8|8@.2F::::z&