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Ñò Y¬Jc@sdZddkZddklZddklZddklZd„Z d„Z d„Z d „Z d d d d „Z ddd„ƒYZd d„Zd d d d„Zd ed„Zd„Zd„Zd„Zdd„Zd„Zd dd d„Zd„Zd„ZdS(sO A module providing some utility functions regarding bezier path manipulation. iÿÿÿÿN(tsqrt(tPath(txorcCsö||||}||||} || } } || } } | | | | }|djotdƒ‚n| | }}| | }}g}||||gD]}|||q¢~\}}}}|||| }|||| }||fS(s‡ return a intersecting point between a line through (cx1, cy1) and having angle t1 and a line through (cx2, cy2) and angle t2. gsGiven lines do not intersect(t ValueError(tcx1tcy1tcos_t1tsin_t1tcx2tcy2tcos_t2tsin_t2t line1_rhst line2_rhstatbtctdtad_bcta_tb_tc_td_t_[1]tktxty((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pytget_intersections  =c Cs„|djo||||fS|| }}| |}}||||||} } ||||||} } | | | | fS(s² For a line passing through (*cx*, *cy*) and having a angle *t*, return locations of the two points located along its perpendicular line at the distance of *length*. g(( tcxtcytcos_ttsin_ttlengthRRR R tx1ty1tx2ty2((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pytget_normal_points0s cCs"|d d||d|}|S(Niÿÿÿÿi((tbetattt next_beta((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt_de_casteljau1MscCsµti|ƒ}|g}x@to8t||ƒ}|i|ƒt|ƒdjoPqqWg}|D]}||dqf~}g}t|ƒD]}||dq‘~}||fS(sŽsplit a bezier segment defined by its controlpoints *beta* into two separate segment divided at *t* and return their control points. iiiÿÿÿÿ(tnptasarraytTrueR)tappendtlentreversed(R&R't beta_listRt left_betat_[2]t right_beta((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pytsplit_de_casteljauQs   %+ggð?g{®Gáz„?c Csø||ƒ}||ƒ}||ƒ}||ƒ}t||ƒptdƒ‚nx¡|d|dd|d|dd|djo ||fSd||} || ƒ} || ƒ} t|| ƒo| }| }| }qS| }| }| }qSdS(s$ Find a parameter t0 and t1 of the given bezier path which bounds the intersecting points with a provided closed path(*inside_closedpath*). Search starts from *t0* and *t1* and it uses a simple bisecting algorithm therefore one of the end point must be inside the path while the orther doesn't. The search stop when |t0-t1| gets smaller than the given tolerence. value for - bezier_point_at_t : a function which returns x, y coordinates at *t* - inside_closedpath : return True if the point is insed the path s6the segment does not seemed to intersect with the pathiiigà?N(RR( tbezier_point_at_ttinside_closedpathtt0tt1t tolerencetstarttendt start_insidet end_insidetmiddle_ttmiddlet middle_inside((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt*find_bezier_t_intersecting_with_closedpathhs&    5    t BezierSegmentcBsqeZdZheiddgƒd6eidddgƒd6eiddddgƒd6Zd„Zd„ZRS( s: A simple class of a 2-dimensional bezier segment gð?ig@ig@icCsˆt|ƒ}ti|ƒ|_ti|d}ti|ƒ}|dd…df}|dd…df}|||_|||_dS(s³ *control_points* : location of contol points. It needs have a shpae of n * 2, where n is the order of the bezier line. 1<= n <= 3 is supported. iNi( R.R*taranget_ordersRBt _binom_coeffR+t_pxt_py(tselftcontrol_pointst_ot_coefft_control_pointstxxtyy((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt__init__¥s  cCsutid||iƒddd…}ti||iƒ}||}t||iƒ}t||iƒ}||fS(sevaluate a point at tgð?Niÿÿÿÿ(R*tpowerRDtsumRFRG(RHR'tone_minus_t_powerstt_powerstttt_xt_y((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt point_at_t¶s & (t__name__t __module__t__doc__R*tarrayRERORW(((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyRBšs  c CsWt|ƒ}|i}t||d|ƒ\}}t|||dƒ\}}||fS(s bezier : control points of the bezier segment inside_closedpath : a function which returns true if the point is inside the path R9g@(RBRWRAR4( tbezierR6R9tbzR5R7R8t_leftt_right((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt)split_bezier_intersecting_with_closedpathÂs  c sG|\‰‰‡‡‡‡fd†}t||d|d|d|ƒdS(sç Find a radius r (centered at *xy*) between *rmin* and *rmax* at which it intersect with the path. inside_closedpath : function cx, cy : center cos_t, sin_t : cosine and sine for the angle rmin, rmax : csˆ|ˆˆ|ˆfS(N((tr(RRRR(s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt_fåsR7R8R9N(RA(R6txyRRtrmintrmaxR9Rb((RRRRs7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt find_r_to_boundary_of_closedpath×s  cCsÞ|iƒ}|iƒ\}}||dƒ}d}|} ti} d} d} xf|D]^\}}| } | t|ƒd7} ||dƒ|jo| | d|gƒ}Pn|} qVW|djotdƒ‚nt|ddd…|ddd…ƒ} t| ||ƒ\}}t|ƒdjo"t i g}t i t i g}n˜t|ƒdjo.t i t i g}t i t i t i g}nWt|ƒdjo:t i t i t i g}t i t i t i t i g}n tƒ‚|d}|}|idjoBt | |i| |gƒƒ}t | ||i| gƒƒ}nkt | |i| |gƒ| |i| |gƒƒ}t | ||i| gƒ| ||i| gƒƒ}|o|tjo||}}n||fS( sW divide a path into two segment at the point where inside(x, y) becomes False. iþÿÿÿiiis2The path does not seem to intersect with the patchNii(t iter_segmentstnexttNoneR*t concatenateR.RtzipR`RtLINETOtMOVETOtCURVE3tCURVE4tcodestverticestFalse(tpathtinsideR9t reorder_inoutt path_itert ctl_pointstcommandt begin_insidet bezier_pathtctl_points_oldtconcattioldtitbptlefttrightt codes_leftt codes_rightt verts_leftt verts_righttpath_intpath_out((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pytsplit_path_inoutïsX     ) "  #cs#|d‰‡‡‡fd†}|S(Nics*|\}}|ˆd|ˆdˆjS(Ni((RcRR(tr2RR(s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyRb8s ((RRRaRb((RRR‰s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt inside_circle6s cCs=||||}}||||d}||||fS(Ngà?((tx0ty0R!R"tdxtdyR((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt get_cos_sinAsc CsH|d\}}|d\}}|d\}}t||||ƒ\}} t||||ƒ\} } t|||| |ƒ\} } }}t||| | |ƒ\}}}}t| | || ||| | ƒ\}}t|||| ||| | ƒ\}}| | f||f||fg}||f||f||fg}||fS(s« Given the quadraitc bezier control points *bezier2*, returns control points of quadrativ bezier lines roughly parralel to given one separated by *width*. iii(RR%R(tbezier2twidthtc1xtc1ytcmxtcmytc2xtc2yRRR R tc1x_lefttc1y_leftt c1x_rightt c1y_righttc2x_lefttc2y_leftt c2x_rightt c2y_righttcmx_lefttcmy_leftt cmx_rightt cmy_rightt path_leftt path_right((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyt get_parallelsGs $$!!gà?cCs–|d\}}|d\}}|d\}}||} } ||} } t| | d| | dƒ} | | | | | | }}t| | |||ƒ\}}}}||d||d}}||d||d}}t||d||dƒ} ||| ||| }}t||||||ƒ\}}}}||f||f||fg}||f||f||fg}||fS(s© Being similar to get_parallels, returns control points of two quadrativ bezier lines having a width roughly parralel to given one separated by *width*. iiig@(RR%(RR t shrink_factortxx1tyy1txx2tyy2txx3tyy3RRR‹RŒtdistRRR!R"R#R$txx12tyy12txx23tyy23txm1tym1txm2tym2tl_plustl_minus((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pytmake_wedged_bezier2us    $ (!!cCsKdd|||}dd|||}||f||f||fgS(s’ Find control points of the bezier line throught c1, mm, c2. We simply assume that c1, mm, c2 which have parameteric value 0, 0.5, and 1. gà?i((R’R“tmmxtmmyR–R—R”R•((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pytfind_control_points–sc%Cs|d\}}|d\}}|d\} } t||||ƒ\} } t||| | ƒ\} }t||| | ||ƒ\}}}}t| | | |||ƒ\}}}}||d||d}}|| d|| d}}||d||d}}t||||ƒ\}}t||||||ƒ\}} }!}"t|||| ||ƒ}#t|||!|"||ƒ}$|#|$fS(s© Being similar to get_parallels, returns control points of two quadrativ bezier lines having a width roughly parralel to given one separated by *width*. iiigà?(RR%R¼(%RR‘tw1twmtw2R’R“R”R•tc3xtc3yRRR R R˜R™RšR›tc3x_lefttc3y_leftt c3x_rightt c3y_righttc12xtc12ytc23xtc23ytc123xtc123ytcos_t123tsin_t123t c123x_leftt c123y_leftt c123x_rightt c123y_rightR¤R¥((s7/usr/lib64/python2.6/site-packages/matplotlib/bezier.pyR¹¡s&(((    cCsh|i}|djoJti|iid dƒ}|itiƒti |ds,    1* G  . ! 6