UW=@sdZddlmZmZmZmZddlmZddlZ ddl m Z ddl m Z ddlZGdddeZd d Zd d Zd dZddZdddddZGdddeZdddZdddddZddddZdd Zd!d"Zd#d$d%Zd&d'Zd(d)Zdd*dd+d,Z d-d.Z!d/d0Z"dS)1zO A module providing some utility functions regarding bezier path manipulation. )absolute_importdivisionprint_functionunicode_literals)sixN)Path)xorc@seZdZdS)NonIntersectingPathExceptionN)__name__ __module__ __qualname__r r L/s/python-3.5.2/amd64_ubu14/lib/python3.5/site-packages/matplotlib/bezier.pyr s r cs||||}||||} || } } || } } | | | | dkrjtd| | }}| | }}fdd||||gD\}}}}|||| }|||| }||fS)z return a intersecting point between a line through (cx1, cy1) and having angle t1 and a line through (cx2, cy2) and angle t2. gzGiven lines do not intersectcsg|]}|qSr r ).0k)ad_bcr r .s z$get_intersection..) ValueError)Zcx1Zcy1cos_t1sin_t1Zcx2Zcy2cos_t2sin_t2Z line1_rhsZ line2_rhsabcdZa_Zb_c_Zd_xyr )rrget_intersections   1rc Cs|dkr||||fS|| }}| |}}||||||} } ||||||} } | | | | fS)z 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*. gr ) cxcycos_tsin_tlengthrrrrx1y1x2y2r r rget_normal_points6s r)cCs.|ddd||dd|}|S)Nr )betatZ next_betar r r_de_casteljau1Os*r.cCstj|}|g}x3t||}|j|t|dkrPqWdd|D}ddt|D}||fS)zsplit a bezier segment defined by its controlpoints *beta* into two separate segment divided at *t* and return their control points. r*cSsg|]}|dqS)rr )rr,r r rr`s z&split_de_casteljau..cSsg|]}|dqS)r*r+r )rr,r r rras )npasarrayr.appendlenreversed)r,r-Z beta_listZ left_betaZ right_betar r rsplit_de_casteljauTs  r4gg?g{Gz?c Cs||}||}||}||}||krT||krTtdx|d|dd|d|dd|dkr||fSd||} || } || } t|| r| }| }| }qW| }| }| }qWWdS)a$ 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 z4the segment does not seem to intersect with the pathrr*g?N)r r) bezier_point_at_tinside_closedpatht0t1 tolerencestartendZ start_insideZ end_insideZmiddle_tZmiddleZ middle_insider r r*find_bezier_t_intersecting_with_closedpathgs,       !    r=c @s|eZdZdZdejddgdejdddgdejddddgiZdd Zd d Zd S) BezierSegmentz: A simple class of a 2-dimensional bezier segment r*g?r5g@g@cCst|}tj||_tj|d}tj|}|dddf}|dddf}|||_|||_dS)z *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. r*Nr) r2r/arange_ordersr> _binom_coeffr0_px_py)selfZcontrol_points_oZ_coeffZ_control_pointsZxxyyr r r__init__s  zBezierSegment.__init__cCsutjd||jddd}tj||j}||}t||j}t||j}||fS)zevaluate a point at tg?Nr*r+)r/powerrAsumrCrD)rEr-Zone_minus_t_powersZt_powerstt_xZ_yr r r point_at_ts & zBezierSegment.point_at_tN) r r r __doc__r/arrayrBrHrMr r r rr>s ! r>c CsWt|}|j}t||d|\}}t|||d\}}||fS)z bezier : control points of the bezier segment inside_closedpath : a function which returns true if the point is inside the path r:g@)r>rMr=r4) Zbezierr7r:Zbzr6r8r9_left_rightr r r)split_bezier_intersecting_with_closedpaths  rRc sJ|\fdd}t||d|d|d|dS)z 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 : cs||fS)Nr )r)r"r r!r#r r_fsz,find_r_to_boundary_of_closedpath.._fr8r9r:N)r=)r7xyr"r#rminrmaxr:rTr )r"r r!r#r find_r_to_boundary_of_closedpaths   rXFcCs|j}t|\}}||d d}d}|} tj} d} d} xm|D]e\}}| } | t|d7} ||d d|kr| | d d|g}P|} q\W|dkrtdtt|ddd|ddd} t| ||\}}t|dkrWt j g}t j t j g}nt|dkrt j t j g}t j t j t j g}nTt|dkrt j t j t j g}t j t j t j t j g}n t|dd}|dd}|jdkrft | |jd| |g}t | ||j| dg}nt | |jd| |g| |jd| |g}t | ||j| dg| ||j| dg}|r|dkr||}}||fS) zW divide a path into two segment at the point where inside(x, y) becomes False. r5Nrr*z2The path does not seem to intersect with the patchr?FrZrZ)Z iter_segmentsnextr/ concatenater2rlistziprRrLINETOMOVETOZCURVE3ZCURVE4codesvertices)pathZinsider:Z reorder_inoutZ path_iterZ ctl_pointscommandZ begin_insideZ bezier_pathZctl_points_oldconcatZioldibpleftrightZ codes_leftZ codes_rightZ verts_leftZ verts_rightZpath_inZpath_outr r rsplit_path_inoutsV     / ! %("" rjcs&|dfdd}|S)Nr5cs*|\}}|d|dkS)Nr5r )rUrr)r r!r2r rrT6s zinside_circle.._fr )r r!rSrTr )r r!rkr inside_circle3s rlcCsM||||}}||||d}|dkr;dS||||fS)Ng?r)rmrmr )Zx0Zy0r%r&dxdyrr r r get_cos_sin>s  rpgh㈵>cCsotj||}tj||}tj||}||krGdStj|tj|krgdSdSdS)z returns * 1 if two lines are parralel in same direction * -1 if two lines are parralel in opposite direction * 0 otherwise r*FNr+)r/arctan2abspi)Zdx1Zdy1Zdx2Zdy2r:Ztheta1Ztheta2Zdthetar r rcheck_if_parallelGs rtc Cs|d\}}|d\}}|d\}}t||||||||}|dkrtjdt||||\} } | | } } n6t||||\} } t||||\} } t||| | |\} }}}t||| | |\}}}}|dkr`d| |d||}}d||d||}}nNt| || | ||| | \}}t||| | ||| | \}}| |f||f||fg}||f||f||fg}||fS)z Given the quadratic bezier control points *bezier2*, returns control points of quadratic bezier lines roughly parallel to given one separated by *width*. rr*r5z8Lines do not intersect. A straight line is used instead.g?r+)rtwarningswarnrpr)r)bezier2widthc1xc1ycmxcmyc2xc2yZ parallel_testrrrrc1x_leftc1y_left c1x_right c1y_rightZc2x_leftZc2y_leftZ c2x_rightZ c2y_rightZcmx_leftZcmy_leftZ cmx_rightZ cmy_right path_left path_rightr r r get_parallelsXs<  $$          rcCsKdd|||}dd|||}||f||f||fgS)z Find control points of the bezier line throught c1, mm, c2. We simply assume that c1, mm, c2 which have parametric value 0, 0.5, and 1. g?rYr )ryrzZmmxZmmyr}r~r{r|r r rfind_control_pointssrg?c%Cs|d\}}|d\}}|d\} } t||||\} } t||| | \} }t||| | ||\}}}}t| | | |||\}}}}||d||d}}|| d|| d}}||d||d}}t||||\}}t||||||\}} }!}"t|||| ||}#t|||!|"||}$|#|$fS)z Being similar to get_parallels, returns control points of two quadrativ bezier lines having a width roughly parralel to given one separated by *width*. rr*r5g?)rpr)r)%rwrxZw1ZwmZw2ryrzr{r|Zc3xZc3yrrrrrrrrZc3x_leftZc3y_leftZ c3x_rightZ c3y_rightZc12xZc12yZc23xZc23yZc123xZc123yZcos_t123Zsin_t123Z c123x_leftZ c123y_leftZ c123x_rightZ c123y_rightrrr r rmake_wedged_bezier2s&(((    rcCsl|j}|dkrdtj|jjddd}|jtjtj|drRrXrjrlrprtrrrrrr r r rs0"      2*B  J 3