m[c@`sSdZddlmZmZmZmZddlZddlZddl m Z ddl m Z ddl Z defdYZdZd Zd Zd Zd d ddZdefdYZddZd d ddZdedZdZdZddZdZdZd dd dZ dZ!dZ"dS(uO A module providing some utility functions regarding bezier path manipulation. i(tabsolute_importtdivisiontprint_functiontunicode_literalsN(tPath(txortNonIntersectingPathExceptioncB`seZRS((t__name__t __module__(((s0lib/python2.7/site-packages/matplotlib/bezier.pyRscC`s||||}||||} || } } || } } | | | | }|dkrmtdn| | }}| | }}g||||gD]}||^q\}}}}|||| }|||| }||fS(u return a intersecting point between a line through (cx1, cy1) and having angle t1 and a line through (cx2, cy2) and angle t2. guGiven lines do not intersect(t ValueError(tcx1tcy1tcos_t1tsin_t1tcx2tcy2tcos_t2tsin_t2t line1_rhst line2_rhstatbtctdtad_bcta_tb_tc_td_tktxty((s0lib/python2.7/site-packages/matplotlib/bezier.pytget_intersections  5c C`s|dkr||||fS|| }}| |}}||||||} } ||||||} } | | | | fS(u 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_ttlengthR R RRtx1ty1tx2ty2((s0lib/python2.7/site-packages/matplotlib/bezier.pytget_normal_points6s cC`s"|d d||d|}|S(Nii((tbetattt next_beta((s0lib/python2.7/site-packages/matplotlib/bezier.pyt_de_casteljau1OscC`stj|}|g}x<trVt||}|j|t|dkrPqqWg|D]}|d^q^}gt|D]}|d^q}||fS(usplit a bezier segment defined by its controlpoints *beta* into two separate segment divided at *t* and return their control points. iii(tnptasarraytTrueR.tappendtlentreversed(R+R,t beta_listt left_betat right_beta((s0lib/python2.7/site-packages/matplotlib/bezier.pytsplit_de_casteljauTs   #gg?g{Gz?c C`s||}||}||}||}||krW||krWtdnxtrtj|d|d|d|d|kr||fSd||} || } || } t|| r| }| }| }qZ| }| }| }qZWdS(u% 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 inside the path u3Both points are on the same side of the closed pathiig?N(RR1R/thypotR( tbezier_point_at_ttinside_closedpathtt0tt1t tolerencetstarttendt start_insidet end_insidetmiddle_ttmiddlet middle_inside((s0lib/python2.7/site-packages/matplotlib/bezier.pyt*find_bezier_t_intersecting_with_closedpathgs(      0    t BezierSegmentcB`sqeZdZiejddgd6ejdddgd6ejddddgd6ZdZdZRS( u: A simple class of a 2-dimensional bezier segment g?ig@ig@icC`set|}tj||_tj|d}tj|j\}}|||_|||_ dS(u *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. iN( R3R/taranget_ordersRGt _binom_coeffR0tTt_pxt_py(tselftcontrol_pointst_ot_coefftxxtyy((s0lib/python2.7/site-packages/matplotlib/bezier.pyt__init__s   cC`s]d||jddd||j}tj||j}tj||j}||fS(uevaluate a point at tiNi(RIR/tdotRLRM(RNR,tttt_xt_y((s0lib/python2.7/site-packages/matplotlib/bezier.pyt point_at_ts)(RRt__doc__R/tarrayRJRTRY(((s0lib/python2.7/site-packages/matplotlib/bezier.pyRGs  c C`sWt|}|j}t||d|\}}t|||d\}}||fS(u bezier : control points of the bezier segment inside_closedpath : a function which returns true if the point is inside the path R>g@(RGRYRFR8( tbezierR;R>tbzR:R<R=t_leftt_right((s0lib/python2.7/site-packages/matplotlib/bezier.pyt)split_bezier_intersecting_with_closedpaths  c `sG|\fd}t||d|d|d|dS(u 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 : c`s||fS(N((tr(R#R!R"R$(s0lib/python2.7/site-packages/matplotlib/bezier.pyt_fsR<R=R>N(RF(R;txyR#R$trmintrmaxR>Rb((R#R!R"R$s0lib/python2.7/site-packages/matplotlib/bezier.pyt find_r_to_boundary_of_closedpaths   cC`s|j}t|\}}||d}|}tj} d} d} xp|D]\\}}| } | t|d7} ||d|kr| |d|g} Pn|}qPWtd| jd } t| ||\}}t|dkrtj g}tj tj g}nt|dkrUtj tj g}tj tj tj g}nWt|dkrtj tj tj g}tj tj tj tj g}n t d |d}|}|jd kr t| |j| |g}t| ||j| g}njt| |j| |g| |j| |g}t| ||j| g| ||j| g}|r|tkr||}}n||fS( uW divide a path into two segment at the point where inside(x, y) becomes False. iiiiu*The path does not intersect with the patchiiiuThis should never be reached(iiN(t iter_segmentstnextR/t concatenateR3R treshapeR`RtLINETOtMOVETOtCURVE3tCURVE4tAssertionErrortcodestNonetverticestFalse(tpathtinsideR>t reorder_inoutt path_itert ctl_pointstcommandt begin_insidetctl_points_oldtconcattioldtit bezier_pathtbptlefttrightt codes_leftt codes_rightt verts_leftt verts_righttpath_intpath_out((s0lib/python2.7/site-packages/matplotlib/bezier.pytsplit_path_inoutsP     !  "c`s#|dfd}|S(Nic`s*|\}}|d|dkS(Ni((RcRR(R!R"tr2(s0lib/python2.7/site-packages/matplotlib/bezier.pyRb(s ((R!R"RaRb((R!R"Rs0lib/python2.7/site-packages/matplotlib/bezier.pyt inside_circle%s cC`sM||||}}||||d}|dkr;dS||||fS(Ng?ig(gg((tx0ty0R&R'tdxtdyR((s0lib/python2.7/site-packages/matplotlib/bezier.pyt get_cos_sin0s  gh㈵>cC`sotj||}tj||}tj||}||krGdStj|tj|krgdStSdS(u returns * 1 if two lines are parralel in same direction * -1 if two lines are parralel in opposite direction * 0 otherwise iiN(R/tarctan2tabstpiRs(tdx1tdy1tdx2tdy2R>ttheta1ttheta2tdtheta((s0lib/python2.7/site-packages/matplotlib/bezier.pytcheck_if_parallel9s c C`s|d\}}|d\}}|d\}}t||||||||}|dkrtjdt||||\} } | | } } n6t||||\} } t||||\} } t||| | |\} }}}t||| | |\}}}}|dkr`d| |d||}}d||d||}}nNt| || | ||| | \}}t||| | ||| | \}}| |f||f||fg}||f||f||fg}||fS(u Given the quadratic bezier control points *bezier2*, returns control points of quadratic bezier lines roughly parallel to given one separated by *width*. iiiiu8Lines do not intersect. A straight line is used instead.g?(RtwarningstwarnRR*R (tbezier2twidthtc1xtc1ytcmxtcmytc2xtc2yt parallel_testR R RRtc1x_lefttc1y_leftt c1x_rightt c1y_righttc2x_lefttc2y_leftt c2x_rightt c2y_righttcmx_lefttcmy_leftt cmx_rightt cmy_rightt path_leftt path_right((s0lib/python2.7/site-packages/matplotlib/bezier.pyt get_parallelsJs<  $$          cC`sKdd|||}dd|||}||f||f||fgS(u Find control points of the bezier line through c1, mm, c2. We simply assume that c1, mm, c2 which have parametric value 0, 0.5, and 1. g?i((RRtmmxtmmyRRRR((s0lib/python2.7/site-packages/matplotlib/bezier.pytfind_control_pointssg?c%C`s|d\}}|d\}}|d\} } t||||\} } t||| | \} }t||| | ||\}}}}t| | | |||\}}}}||d||d}}|| d|| d}}||d||d}}t||||\}}t||||||\}} }!}"t|||| ||}#t|||!|"||}$|#|$fS(u Being similar to get_parallels, returns control points of two quadrativ bezier lines having a width roughly parallel to given one separated by *width*. iiig?(RR*R(%RRtw1twmtw2RRRRtc3xtc3yR R RRRRRRtc3x_lefttc3y_leftt c3x_rightt c3y_righttc12xtc12ytc23xtc23ytc123xtc123ytcos_t123tsin_t123t c123x_leftt c123y_leftt c123x_rightt c123y_rightRR((s0lib/python2.7/site-packages/matplotlib/bezier.pytmake_wedged_bezier2s&(((    cC`sf|j}|dkr^tj|jjd d}|jtjtj |ds0"       /# >  J 3