o :aI@sdZddlmZddlZddlZddlZddlmZej eddddZ Gd d d e Z d d Z d dZddZddZ d-ddZGdddZ d.ddZd/ddZdd Zd!d"Zd0d$d%Zd&d'Zd(d)Zd1d+d,ZdS)2zO A module providing some utility functions regarding Bezier path manipulation. ) lru_cacheN)_api)maxsizecCsF||krdSt|||}td|d}t|d||tS)Nr)minnparangeZprodZastypeint)nkir3/usr/lib/python3/dist-packages/matplotlib/bezier.py_combs rc@s eZdZdS)NonIntersectingPathExceptionN)__name__ __module__ __qualname__rrrrrsrcs||||}||||} || } } || } } | | | | tdkr.td| | }}| | }}fdd||||fD\}}}}|||| }|||| }||fS)z Return the intersection between the line through (*cx1*, *cy1*) at angle *t1* and the line through (*cx2*, *cy2*) at angle *t2*. g-q=zcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.csg|]}|qSrr).0r Zad_bcrr 9z$get_intersection..)abs ValueError)Zcx1Zcy1cos_t1sin_t1Zcx2Zcy2cos_t2sin_t2Z line1_rhsZ line2_rhsabcdZa_Zb_Zc_Zd_xyrrrget_intersection s      "r%c Csl|dkr ||||fS|| }}| |}}||||||} } ||||||} } | | | | 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) cxcyZcos_tZsin_tlengthrrrrx1y1Zx2Zy2rrrget_normal_pointsAs    r,cCs(|ddd||dd|}|S)Nrr)betatZ next_betarrr_de_casteljau1Zs$r0cCs^t|}|g} t||}||t|dkrnq dd|D}ddt|D}||fS)z Split a Bezier segment defined by its control points *beta* into two separate segments divided at *t* and return their control points. TrcSg|]}|dqS)rrrr.rrrrkrz&split_de_casteljau..cSr1)r-rr2rrrrlr)rasarrayr0appendlenreversed)r.r/Z beta_listZ left_betaZ right_betarrrsplit_de_casteljau_s    r7r&?{Gz?c Cs||}||}||}||}||kr||krtd t|d|d|d|d|kr5||fSd||} || } || } || ArN| }| }| }n| }| }| }q)a Find the intersection of the Bezier 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 Bezier 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 Bezier path parameters. z3Both points are on the same side of the closed pathTrr?)rrZhypot) bezier_point_at_tinside_closedpatht0t1 tolerancestartendZ start_insideZ end_insideZmiddle_tZmiddleZ middle_insiderrr*find_bezier_t_intersecting_with_closedpathqs,&( rBc@s`eZdZdZddZddZddZedd Zed d Z ed d Z eddZ ddZ dS) BezierSegmentz A d-dimensional Bezier segment. Parameters ---------- control_points : (N, d) array Location of the *N* control points. csVt|_jj\__tj_fddtjD}jj |j _ dS)Ncs:g|]}tjdt|tjd|qS)r)mathZ factorial_N)rr selfrrrs z*BezierSegment.__init__..) rr3_cpointsshaperE_dr _ordersrangeT_px)rGcontrol_pointsZcoeffrrFr__init__s  zBezierSegment.__init__cCs>t|}tjd||jdddtj||j|jS)a& Evaluate the Bezier 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*. rNr-)rr3ZpowerZouterrKrNrGr/rrr__call__s zBezierSegment.__call__cCs t||S)zX Evaluate the curve at a single point, returning a tuple of *d* floats. )tuplerQrrr point_at_ts zBezierSegment.point_at_tcC|jS)z The control points of the curve.)rHrFrrrrOzBezierSegment.control_pointscCrU)zThe dimension of the curve.)rJrFrrr dimensionrVzBezierSegment.dimensioncCs |jdS)z@Degree of the polynomial. One less the number of control points.r)rErFrrrdegrees zBezierSegment.degreecCs||j}|dkr tdt|j}t|ddddf}t|ddddf}d||t||}t||||S)a The polynomial coefficients of the Bezier 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 bezier 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!rNr-)rXwarningswarnRuntimeWarningrOrr r)rGr Pjr Z prefactorrrrpolynomial_coefficientssz%BezierSegment.polynomial_coefficientsc Cs|j}|dkrtgtgfS|j}td|ddddf|dd}g}g}t|jD]\}}t|ddd}|||t ||q1t |}t |}t ||dk@|dk@} || t || 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` rNr-r) rXrZarrayr_r enumeraterMrootsr4Z full_like concatenateZisrealreal) rGr ZCjZdCjZdimsrar pirZin_rangerrraxis_aligned_extremas(   z"BezierSegment.axis_aligned_extremaN) rrr__doc__rPrRrTpropertyrOrWrXr_rfrrrrrCs       #rCc Cs>t|}|j}t|||d\}}t|||d\}}||fS)ao Split a Bezier curve into two at the intersection with a closed path. Parameters ---------- bezier : (N, 2) array-like Control points of the Bezier 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 Bezier segments. )r?g@)rCrTrBr7) Zbezierr<r?Zbzr;r=r>Z_leftZ_rightrrr)split_bezier_intersecting_with_closedpath5s riFcCsddlm}|}t|\}}||dd}|} d} d} |D]'\}}| } | t|d7} ||dd|krEt| dd|g} n|} q td| d} t | ||\}}t|dkrj|j g}|j |j g}n2t|d kr|j |j g}|j |j |j g}nt|d kr|j |j |j g}|j |j |j |j g}ntd |dd}|dd}|jdur|t|jd| |g}|t||j| dg}n2|t|jd| |gt|jd| |g}|t||j| dgt||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)r-rlzThis should never be reached)pathrjZ iter_segmentsnextr5rrbrZreshaperiZLINETOZMOVETOZCURVE3ZCURVE4AssertionErrorZcodesZvertices)roZinsider?Z reorder_inoutrjZ path_iterZ ctl_pointsZcommandZ begin_insideZctl_points_oldZioldr Z bezier_pathZbpleftrightZ codes_leftZ codes_rightZ verts_leftZ verts_rightZpath_inZpath_outrrrsplit_path_inoutXsV             rtcs|dfdd}|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 rlcs$|\}}|d|dkS)Nrlr)Zxyr#r$r'r(Zr2rr_fszinside_circle.._fr)r'r(rervrrur inside_circles rwcCsB||||}}||||d}|dkrdS||||fS)Nr:r)r&r&r)Zx0Zy0r*r+ZdxZdyr"rrr get_cos_sins rxh㈵>cCsJt||}t||}t||}||krdSt|tj|kr#dSdS)a Check if two lines are parallel. Parameters ---------- dx1, dy1, dx2, dy2 : float The gradients *dy*/*dx* of the two lines. tolerance : float The angular tolerance in radians up to which the lines are considered parallel. Returns ------- is_parallel - 1 if two lines are parallel in same direction. - -1 if two lines are parallel in opposite direction. - False otherwise. rr-F)rZarctan2rrd)Zdx1Zdy1Zdx2Zdy2r?Ztheta1Ztheta2Zdthetarrrcheck_if_parallels   rzc Csz|d\}}|d\}}|d\}}t||||||||}|dkr9tdt||||\} } | | } } nt||||\} } t||||\} } t||| | |\} }}}t||| | |\}}}}zt| || | ||| | \}}t||| | ||| | \}}Wn#tyd| |d||}}d||d||}}Ynw| |f||f||fg}||f||f||fg}||fS)z Given the quadratic Bezier control points *bezier2*, returns control points of quadratic Bezier lines roughly parallel to given one separated by *width*. rrrlr-z8Lines do not intersect. A straight line is used instead.r:)rzrZ warn_externalrxr,r%r)bezier2widthc1xc1ycmxcmyc2xc2yZ parallel_testrrrrc1x_leftc1y_left c1x_right c1y_rightZc2x_leftZc2y_leftZ c2x_rightZ c2y_rightZcmx_leftZcmy_leftZ cmx_rightZ cmy_right path_left path_rightrrr get_parallelssT         rcCs>dd|||}dd|||}||f||f||fgS)z Find control points of the Bezier curve passing through (*c1x*, *c1y*), (*mmx*, *mmy*), and (*c2x*, *c2y*), at parametric values 0, 0.5, and 1. r:rnr)r}r~ZmmxZmmyrrrrrrrfind_control_pointssrr:c%Cs(|d\}}|d\}}|d\} } t||||\} } t||| | \} }t||| | ||\}}}}t| | | |||\}}}}||d||d}}|| d|| d}}||d||d}}t||||\}}t||||||\}} }!}"t|||| ||}#t|||!|"||}$|#|$fS)z Being similar to get_parallels, returns control points of two quadratic Bezier lines having a width roughly parallel to given one separated by *width*. rrrlr:)rxr,r)%r{r|Zw1ZwmZw2r}r~rrZc3xZc3yrrrrrrrrZc3x_leftZc3y_leftZ c3x_rightZ c3y_rightZc12xZc12yZc23xZc23yZc123xZc123yZcos_t123Zsin_t123Z c123x_leftZ c123y_leftZ c123x_rightZ c123y_rightrrrrrmake_wedged_bezier2#s0      r)r&r8r9)r9)r9F)ry)r8r:r&)rg functoolsrrDrZZnumpyrZ matplotlibrZ vectorizerrrr%r,r0r7rBrCrirtrwrxrzrrrrrrrs6   ! 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