B ]t\7<@sdZddlZddlZddlmZGdddeZddZdd Z d d Z d d Z d.ddZ Gddde Zd/ddZd0ddZd1ddZddZddZd2d!d"Zd#d$Zd%d&Zd3d(d)Zd*d+Zd,d-ZdS)4zO A module providing some utility functions regarding bezier path manipulation. N)Pathc@s eZdZdS)NonIntersectingPathExceptionN)__name__ __module__ __qualname__rr0lib/python3.7/site-packages/matplotlib/bezier.pyr srcs||||}||||} || } } || } } | | | | tdkr^td| | }}| | }}fdd||||gD\}}}}|||| }|||| }||fS)z return a intersecting point between a line through (cx1, cy1) and having angle t1 and a line through (cx2, cy2) and angle t2. g-q=zcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.csg|] }|qSrr).0k)ad_bcrr )sz$get_intersection..)npabs ValueError)Zcx1Zcy1cos_t1sin_t1Zcx2Zcy2cos_t2sin_t2Z line1_rhsZ line2_rhsabcdZa_Zb_Zc_Zd_xyr)r rget_intersections     "rc Csl|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_tlengthrrrrx1y1Zx2Zy2rrrget_normal_points1s   r"cCs(|ddd||dd|}|S)Nr)betatZ next_betarrr_de_casteljau1Js$r'cCs`t|}|g}x&t||}||t|dkrPqWdd|D}ddt|D}||fS)zsplit a bezier segment defined by its controlpoints *beta* into two separate segment divided at *t* and return their control points. r$cSsg|] }|dqS)rr)r r%rrrr [sz&split_de_casteljau..cSsg|] }|dqS)r#r)r r%rrrr \s)r asarrayr'appendlenreversed)r%r&Z beta_listZ left_betaZ right_betarrrsplit_de_casteljauOs    r,?{Gz?c Cs||}||}||}||}||kr8||kr8tdxrt|d|d|d|d|krj||fSd||} || } || } || Ar| }| }| }q:| }| }| }q:WdS)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 inside the path z3Both points are on the same side of the closed pathrr$g?N)rr Zhypot) bezier_point_at_tinside_closedpatht0t1 tolerencestartendZ start_insideZ end_insideZmiddle_tZmiddleZ middle_insiderrr*find_bezier_t_intersecting_with_closedpathbs(( r7c@sPeZdZdZeddgedddgeddddgdZddZdd Zd S) BezierSegmentz: A simple class of a 2-dimensional bezier segment g?g@g@)r$cCsJt|}t||_tj|d}t|j\}}|||_|||_ 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$N) r*r Zarange_ordersr8 _binom_coeffr(T_px_py)selfZcontrol_pointsZ_oZ_coeffZxxZyyrrr__init__s   zBezierSegment.__init__cCsFd||jddd||j}t||j}t||j}||fS)zevaluate a point at tr$Nr#)r;r dotr>r?)r@r&ZttZ_xZ_yrrr point_at_ts"zBezierSegment.point_at_tN) rrr__doc__r Zarrayr<rArCrrrrr8s  r8c Cs>t|}|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 )r4g@)r8rCr7r,) Zbezierr1r4Zbzr0r2r3Z_leftZ_rightrrr)split_bezier_intersecting_with_closedpaths  rEcs0|\fdd}t|||||ddS)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)rrrrrr_fsz,find_r_to_boundary_of_closedpath.._f)r2r3r4N)r7)r1xyrrZrminZrmaxr4rGr)rrrrr find_r_to_boundary_of_closedpaths rIFcCs |}t|\}}||dd}|}tj} d} d} xZ|D]J\}}| } | t|d7} ||dd|kr| |dd|g} P|}q._fr)rrrFrGr)rrrYr inside_circle srZcCsB||||}}||||d}|dkr2dS||||fS)Ng?r)ggr)Zx0Zy0r r!ZdxZdyrrrr get_cos_sin+s r[h㈵>cCsRt||}t||}t||}||kr2dSt|tj|krJdSdSdS)z returns * 1 if two lines are parralel in same direction * -1 if two lines are parralel in opposite direction * 0 otherwise r$r#FN)r Zarctan2rZpi)Zdx1Zdy1Zdx2Zdy2r4Ztheta1Ztheta2Zdthetarrrcheck_if_parallel4s  r]c Csn|d\}}|d\}}|d\}}t||||||||}|dkrrtdt||||\} } | | } } n$t||||\} } t||||\} } t||| | |\} }}}t||| | |\}}}}|dkrd| |d||}}d||d||}}n4t| || | ||| | \}}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$r9r#z8Lines do not intersect. A straight line is used instead.g?)r]warningswarnr[r"r)bezier2widthc1xc1ycmxcmyc2xc2yZ parallel_testrrrrc1x_leftc1y_left c1x_right c1y_rightZc2x_leftZc2y_leftZ c2x_rightZ c2y_rightZcmx_leftZcmy_leftZ cmx_rightZ cmy_right path_left path_rightrrr get_parallelsEs<         rncCs>dd|||}dd|||}||f||f||fgS)z Find control points of the bezier line through c1, mm, c2. We simply assume that c1, mm, c2 which have parametric value 0, 0.5, and 1. g?rKr)rbrcZmmxZmmyrfrgrdrerrrfind_control_pointssro?c%Cs(|d\}}|d\}}|d\} } t||||\} } t||| | \} }t||| | ||\}}}}t| | | |||\}}}}||d||d}}|| d|| d}}||d||d}}t||||\}}t||||||\}} }!}"t|||| ||}#t|||!|"||}$|#|$fS)z Being similar to get_parallels, returns control points of two quadrativ bezier lines having a width roughly parallel to given one separated by *width*. rr$r9g?)r[r"ro)%r`raZw1ZwmZw2rbrcrdreZc3xZc3yrrrrrhrirjrkZc3x_leftZc3y_leftZ c3x_rightZ c3y_rightZc12xZc12yZc23xZc23yZc123xZc123yZcos_t123Zsin_t123Z c123x_leftZ c123y_leftZ c123x_rightZ c123y_rightrlrmrrrmake_wedged_bezier2s&   rqcCsP|j}|dkrHt|jjddd}|tjtj|d<t|j|S|SdS)z$ fill in the codes if None. Nr$rUr) rQr emptyrRshapeZfillrrNrO)prrrrmake_path_regulars   rucCsPg}g}x,|D]$}t|}||j||jqWtt|t|}|S)z7 concatenate list of paths into a single path. )rur)rRrQrr rM)pathsrRrQrt_pathrrrconcatenate_pathss    rx)r-r.r/)r/)r-r.r/)r/F)r\)r.rpr-)rDr^Znumpyr Zmatplotlib.pathrrrrr"r'r,r7objectr8rErIrXrZr[r]rnrorqrurxrrrrs*   /#   >  J 3