a SicH@sdZddlmZddlZddlZddlZddlmZej eddddZ Gd d d e Z d d Z d dZddZddZd-ddZGdddZd.ddZd/ddZdd Zd!d"Zd0d$d%Zd&d'Zd(d)Zd1d+d,ZdS)2zO A module providing some utility functions regarding Bezier path manipulation. ) lru_cacheN)_api)maxsizecCsF||kr dSt|||}td|d}t|d||tS)Nr)minnparangeprodastypeint)nkirM/var/www/html/django/DPS/env/lib/python3.9/site-packages/matplotlib/bezier.py_combs rc@s eZdZdS)NonIntersectingPathExceptionN)__name__ __module__ __qualname__rrrrrsrcs||||}||||} || } } || } } | | | | tdkr\td| | }}| | }}fdd||||fD\}}}}|||| }|||| }||fS)z Return the intersection between the line through (*cx1*, *cy1*) at angle *t1* and the line through (*cx2*, *cy2*) at angle *t2*. g-q=zcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.csg|] }|qSrr).0rZad_bcrr 9z$get_intersection..)abs ValueError)Zcx1Zcy1cos_t1sin_t1Zcx2Zcy2cos_t2sin_t2Z line1_rhsZ line2_rhsabcdZa_Zb_c_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_tlengthrrrr x1y1x2y2rrrget_normal_pointsAs   r1cCs(|ddd||dd|}|S)Nrr)betat next_betarrr_de_casteljau1Zs$r6cCs\t|}|g}t||}||t|dkrq4qdd|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. rcSsg|] }|dqS)rrrr3rrrrkrz&split_de_casteljau..cSsg|] }|dqS)r2rr7rrrrlr)rasarrayr6appendlenreversed)r3r4Z beta_listZ left_betaZ right_betarrrsplit_de_casteljau_s    r<r)?{Gz?c Cs||}||}||}||}||kr8||kr8tdt|d|d|d|d|krh||fSd||} || } || } || Ar| }| }q8| }| }| }q8dS)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 pathrr?N)rrhypot) bezier_point_at_tinside_closedpatht0t1 tolerancestartendZ start_insideZ end_insideZmiddle_tmiddleZ middle_insiderrr*find_bezier_t_intersecting_with_closedpathqs&&( rIc@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|]2}tjdt|tjd|qS)r)math factorial_N)rrselfrrrsz*BezierSegment.__init__..) rr8_cpointsshaperM_dr _ordersrangeT_px)rOcontrol_pointscoeffrrNr__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*. rNr2)rr8powerouterrSrVrOr4rrr__call__s  zBezierSegment.__call__cCs t||S)zX Evaluate the curve at a single point, returning a tuple of *d* floats. )tupler\rrr point_at_tszBezierSegment.point_at_tcCs|jS)z The control points of the curve.)rPrNrrrrWszBezierSegment.control_pointscCs|jS)zThe dimension of the curve.)rRrNrrr dimensionszBezierSegment.dimensioncCs |jdS)z@Degree of the polynomial. One less the number of control points.r)rMrNrrrdegreeszBezierSegment.degreecCs||j}|dkrtdt|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!rNr2)rawarningswarnRuntimeWarningrWrr r)rOr PjrZ prefactorrrrpolynomial_coefficientssz%BezierSegment.polynomial_coefficientsc Cs|j}|dkr"tgtgfS|j}td|ddddf|dd}g}g}t|jD]8\}}t|ddd}|||t ||qbt |}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` rNr2r) rararrayrhr enumeraterUrootsr9 full_like concatenateisrealreal) rOr ZCjZdCjdimsrkrpirin_rangerrraxis_aligned_extremas(   z"BezierSegment.axis_aligned_extremaN) rrr__doc__rYr]r_propertyrWr`rarhrtrrrrrJs      #rJc 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. )rEg@)rJr_rIr<) bezierrBrEbzrArCrD_left_rightrrr)split_bezier_intersecting_with_closedpath4s r{FcCsddlm}|}t|\}}||dd}|} d} d} |D]N\}}| } | t|d7} ||dd|krt| dd|g} q|} q@td| d} t | ||\}}t|dkr|j g}|j |j g}nft|d kr|j |j g}|j |j |j g}n bool r~cs$|\}}|d|dkS)Nr~r)xyr&r'r*r+Zr2rr_fszinside_circle.._fr)r*r+rrrrrr inside_circles rcCsB||||}}||||d}|dkr2dS||||fS)Nr?r)r)r)r)x0y0r-r.dxdyr$rrr get_cos_sins rh㈵>cCsNt||}t||}t||}||kr0dSt|tj|krFdSdSdS)a Check if two lines are parallel. Parameters ---------- dx1, dy1, dx2, dy2 : float The gradients *dy*/*dx* of the two lines. tolerance : float The angular tolerance in radians up to which the lines are considered parallel. Returns ------- is_parallel - 1 if two lines are parallel in same direction. - -1 if two lines are parallel in opposite direction. - False otherwise. rr2FN)rarctan2rrq)dx1Zdy1dx2Zdy2rEtheta1theta2Zdthetarrrcheck_if_parallels   rc Cs||d\}}|d\}}|d\}}t||||||||}|dkrrtdt||||\} } | | } } n$t||||\} } t||||\} } t||| | |\} }}}t||| | |\}}}}z8t| || | ||| | \}}t||| | ||| | \}}WnHtyFd| |d||}}d||d||}}Yn0| |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*. rrr~r2z8Lines do not intersect. A straight line is used instead.r?)rr warn_externalrr1r(r)bezier2widthc1xc1ycmxcmyc2xc2yZ parallel_testrrrr c1x_leftc1y_left c1x_right c1y_rightZc2x_leftZc2y_leftZ c2x_rightZ c2y_rightZcmx_leftZcmy_leftZ cmx_rightZ cmy_right path_left path_rightrrr get_parallelssR         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?rr)rrZmmxZmmyrrrrrrrfind_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*. rrr~r?)rr1r)%rrw1wmw2rrrrZc3xZc3yrrrr rrrrZc3x_leftZc3y_leftZ c3x_rightZ c3y_rightZc12xZc12yZc23xZc23yZc123xZc123yZcos_t123Zsin_t123Z c123x_leftZ c123y_leftZ c123x_rightZ c123y_rightrrrrrmake_wedged_bezier2"s0      r)r)r=r>)r>)r>F)r)r=r?r))ru functoolsrrKrcnumpyr matplotlibr vectorizerrrr(r1r6r<rIrJr{rrrrrrrrrrrs4   ! 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