o hiJ@sdZddlmZddlZddlZddlZddlmZej eddddZ Gd d d e Z d d Z d dZddZddZ d-ddZGdddZ d.ddZd/ddZdd Zd!d"Zd0d$d%Zd&d'Zd(d)Zd1d+d,ZdS)2uP A module providing some utility functions regarding Bézier path manipulation. ) lru_cacheN)_api)maxsizecCsF||krdSt|||}td|d}t|d||tS)Nr)minnparangeprodastypeint)nkire/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/matplotlib/bezier.py_combs rc@s eZdZdS)NonIntersectingPathExceptionN)__name__ __module__ __qualname__rrrrrsrcs||||}||||} || } } || } } | | | | tdkr.td| | }}| | }}fdd||||fD\}}}}|||| }|||| }||fS)z Return the intersection between the line through (*cx1*, *cy1*) at angle *t1* and the line through (*cx2*, *cy2*) at angle *t2*. g-q=zcGiven lines do not intersect. Please verify that the angles are not equal or differ by 180 degrees.c3s|]}|VqdS)Nr).0rad_bcrr 9sz#get_intersection..)abs ValueError)cx1cy1cos_t1sin_t1cx2cy2cos_t2sin_t2 line1_rhs line2_rhsabcda_b_c_d_xyrrrget_intersection s      "r1c Csl|dkr ||||fS|| }}| |}}||||||} } ||||||} } | | | | fS)z For a line passing through (*cx*, *cy*) and having an angle *t*, return locations of the two points located along its perpendicular line at the distance of *length*. r) cxcycos_tsin_tlengthrr r#r$x1y1x2y2rrrget_normal_pointsAs    r<cCs(|ddd||dd|}|S)Nrr)betat next_betarrr_de_casteljau1Zs$rAcCs^t|}|g} t||}||t|dkrnq dd|D}ddt|D}||fS)u Split a Bézier segment defined by its control points *beta* into two separate segments divided at *t* and return their control points. TrcSg|]}|dqS)rrrr>rrr kz&split_de_casteljau..cSrB)r=rrCrrrrDlrE)rasarrayrAappendlenreversed)r>r? beta_list left_beta right_betarrrsplit_de_casteljau_s    rMr2?{Gz?c Cs||}||}||}||}||kr||krtd t|d|d|d|d|kr5||fSd||} || } || } || ArT| }|| krQ||fS| }n| }|| kr^||fS| }| }q)u Find the intersection of the Bézier 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 Bézier 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 Bézier path parameters. z3Both points are on the same side of the closed pathTrr?)rrhypot) bezier_point_at_tinside_closedpatht0t1 tolerancestartend start_inside end_insidemiddle_tmiddle middle_insiderrr*find_bezier_t_intersecting_with_closedpathqs2&( r^c@s`eZdZdZddZddZddZedd Zed d Z ed d Z eddZ ddZ dS) BezierSegmentu A d-dimensional Bézier 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)math factorial_N)rrselfrrrDs z*BezierSegment.__init__..) rrF_cpointsshaperb_dr _ordersrangeT_px)rdcontrol_pointscoeffrrcr__init__s  zBezierSegment.__init__cCs>t|}tjd||jdddtj||j|jS)u) Evaluate the Bézier 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=)rrFpowerouterrhrkrdr?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.)rercrrrrlzBezierSegment.control_pointscCru)zThe dimension of the curve.)rgrcrrr dimensionrvzBezierSegment.dimensioncCs |jdS)z@Degree of the polynomial. One less the number of control points.r)rbrcrrrdegrees zBezierSegment.degreecCs||j}|dkr tdt|j}t|ddddf}t|ddddf}d||t||}t||||S)u The polynomial coefficients of the Bézier 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 Bézier 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=)rxwarningswarnRuntimeWarningrlrr r)rdr Pjr 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) rxrarrayrr enumeraterjrootsrG full_like concatenateisrealreal) rdr CjdCjdimsrrpirin_rangerrraxis_aligned_extremas(   z"BezierSegment.axis_aligned_extremaN) rrr__doc__rnrrrtpropertyrlrwrxrrrrrrr_s       #r_c Cs>t|}|j}t|||d\}}t|||d\}}||fS)ur Split a Bézier curve into two at the intersection with a closed path. Parameters ---------- bezier : (N, 2) array-like Control points of the Bézier 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 Bézier segments. )rVg@)r_rtr^rM) bezierrSrVbzrRrTrU_left_rightrrr)split_bezier_intersecting_with_closedpath<s rFcCsddlm}|}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=rzThis should never be reached)pathr iter_segmentsnextrHrrrreshaperLINETOMOVETOCURVE3CURVE4AssertionErrorcodesvertices)rinsiderV reorder_inoutr path_iter ctl_pointscommand begin_insidectl_points_oldioldr bezier_pathbpleftright codes_left codes_right verts_left verts_rightpath_inpath_outrrrsplit_path_inout_sV             rcs|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 rcs$|\}}|d|dkS)Nrr)xyr/r0r3r4r2rr_fszinside_circle.._fr)r3r4rrrrr inside_circles rcCsB||||}}||||d}|dkrdS||||fS)NrPr)r2r2r)x0y0r8r9dxdyr*rrr get_cos_sins rh㈵>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)rarctan2rr)dx1dy1dx2dy2rVtheta1theta2dthetarrrcheck_if_parallels   rc 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)u Given the quadratic Bézier control points *bezier2*, returns control points of quadratic Bézier lines roughly parallel to given one separated by *width*. rrrr=z8Lines do not intersect. A straight line is used instead.rP)rr warn_externalrr<r1r)bezier2widthc1xc1ycmxcmyc2xc2y parallel_testrr r#r$c1x_leftc1y_left c1x_right c1y_rightc2x_leftc2y_left c2x_right c2y_rightcmx_leftcmy_left cmx_right cmy_right path_left path_rightrrr get_parallelssT         rcCs>dd|||}dd|||}||f||f||fgS)u Find control points of the Bézier curve passing through (*c1x*, *c1y*), (*mmx*, *mmy*), and (*c2x*, *c2y*), at parametric values 0, 0.5, and 1. rPrr)rrmmxmmyrrrrrrrfind_control_points srrPc%Cs(|d\}}|d\}}|d\} } t||||\} } t||| | \} }t||| | ||\}}}}t| | | |||\}}}}||d||d}}|| d|| d}}||d||d}}t||||\}}t||||||\}} }!}"t|||| ||}#t|||!|"||}$|#|$fS)u Being similar to `get_parallels`, returns control points of two quadratic Bézier lines having a width roughly parallel to given one separated by *width*. rrrrP)rr<r)%rrw1wmw2rrrrc3xc3yrr r#r$rrrrc3x_leftc3y_left c3x_right c3y_rightc12xc12yc23xc23yc123xc123ycos_t123sin_t123 c123x_left c123y_left c123x_right c123y_rightrrrrrmake_wedged_bezier2*s0      r)r2rNrO)rO)rOF)r)rNrPr2)r functoolsrr`rznumpyr matplotlibr vectorizerrrr1r<rArMr^r_rrrrrrrrrrrrs6   ! 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