{:iiJSrSSKJr SSKrSSKrSSKrSSKJr \R\"SS9S55r "SS \ 5r S r S rS rS rSSjr"SS5rSSjrSSjrSrSrSSjrSrSrSSjrg)uP A module providing some utility functions regarding Bézier path manipulation. ) lru_cacheN)_api)maxsizecX:ag[XU- 5n[R"SUS-5n[R"US-U- U- 5R [ 5$)Nr)minnparangeprodastypeint)nkis T/srv/projetos/modelo_ml_acdoc/venv/lib/python3.13/site-packages/matplotlib/bezier.py_combrsS u A1u A !QUA 77AEAIq= ! ( ( --c\rSrSrSrg)NonIntersectingPathExceptionN)__name__ __module__ __qualname____firstlineno____static_attributes__rrrrrsrrc^X0-X!-- nXt-Xe-- n X2*pXv*pX-X-- m[T5S:a [S5eX*pU *U nnU4SjXUU45upnnX-X--nUU-UU --nUU4$)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.c3,># UH oT- v M g7f)Nr).0rad_bcs r #get_intersection..9s:)9A%i)9s)abs ValueError)cx1cy1cos_t1sin_t1cx2cy2cos_t2sin_t2 line1_rhs line2_rhsabcda_b_c_d_xyr!s @rget_intersectionr: s v|+I v|+I 7q 7q EAEME 5zENO ORB:""b)9:NBB 'A Yi'A a4Krc`US:XaXX4$X2*peU*UpXE-U-XF-U-pXG-U-XH-U-pXX4$)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_tlengthr(r)r,r-x1y1x2y2s rget_normal_pointsrFAsY|r~FFVUF _r !6?R#7 _r !6?R#7 2>rc.USSSU- -USSU--nU$)Nrr)betat next_betas r_de_casteljau1rLZs+Sb QU#d12hl2I rc[R"U5nU/n[X5nURU5 [ U5S:XaOM.UVs/sHoSPM nn[ U5Vs/sHoSPM nnX44$s snfs snf)u Split a Bézier segment defined by its control points *beta* into two separate segments divided at *t* and return their control points. rrrH)r asarrayrLappendlenreversed)rIrJ beta_list left_beta right_betas rsplit_de_casteljaurU_s ::d DI d& t9>   &//YTaYI/'/ ':;':tr(':J;   0;s A=*BcHU"U5nU"U5nU"U5nU"U5nXx:XaXV:wa [S5e[R"USUS- USUS- 5U:aX#4$SX#--n U"U 5n U"U 5n X{- (a U nXj:XaX#4$U nOU nXZ:XaX#4$U nU nMm)u$ 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 pathrr?)rr hypot) bezier_point_at_tinside_closedpatht0t1 tolerancestartend start_inside end_insidemiddle_tmiddle middle_insides r*find_bezier_t_intersecting_with_closedpathreqsL b !E B C$U+L"3'J!el* AC C  88E!Hs1v%uQx#a&'8 9I E6M"'?"8,)&1  'B}v CBv E(L3 rcp\rSrSrSrSrSrSr\S5r \S5r \S5r \S 5r S r S rg ) BezierSegmentu A d-dimensional Bézier segment. Parameters ---------- control_points : (N, d) array Location of the *N* control points. c ,[R"U5UlURRuUlUl[R "UR5Ul[UR5Vs/sHdn[R"URS- 5[R"U5[R"URS- U- 5--PMf nnURRU-RUl gs snf)Nr) r rN_cpointsshape_N_dr _ordersrangemath factorialT_px)selfcontrol_pointsrcoeffs r__init__BezierSegment.__init__s >2 ==..yy)  .*(Q! ,^^A&! a)HHJ( *MMOOe+..*s;A+Dc[R"U5n[RRSU- URSSS25[RRXR5-UR -$)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*. rNrH)r rNpowerouterrnrsrtrJs r__call__BezierSegment.__call__s^ JJqMq1udll4R4&89((..LL1259XX> >rc$[U"U55$)zH Evaluate the curve at a single point, returning a tuple of *d* floats. )tupler|s r point_at_tBezierSegment.point_at_tsT!W~rcUR$)z The control points of the curve.)rjrts rruBezierSegment.control_pointss}}rcUR$)zThe dimension of the curve.)rmrs r dimensionBezierSegment.dimensions wwrc URS- $)z@Degree of the polynomial. One less the number of control points.r)rlrs rdegreeBezierSegment.degreesww{rc<URnUS:a[R"S[5 URn[ R "US-5SS2S4n[ R "US-5SSS24nSXC--[X45-n[X5U-U-$)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!rNrH)rwarningswarnRuntimeWarningrur r r)rtrPjr prefactors rpolynomial_coefficients%BezierSegment.polynomial_coefficientss2 KK r6 MM12@ B    IIacN1d7 # IIacN47 #15ME!K/ Q{Y&**rcURnUS::a,[R"/5[R"/54$URn[R"SUS-5SS2S4USS-n/n/n[ UR 5HWupg[R"USSS25nURU5 UR[R"X55 MY [R"U5n[R"U5n[R"U5US:-US:*-n XI[R"U5U 4$)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` rNrHr) rr arrayrr enumeraterrrootsrO full_like concatenateisrealreal) rtrCjdCjdimsrrpirin_ranges raxis_aligned_extrema"BezierSegment.axis_aligned_extremas KK 688B<"- -  ) )ii1Q34(2ab61suu%EADbD"A LLO KK Q* +&u%~~d#99U#uz2eqjA~rwwu~h777r)rlrjrmrnrsN)rrrr__doc__rwr}rpropertyrurrrrrrrrrgrgsl/>$ !+!+F8rrgct[U5nURn[XAUS9upV[XU-S- 5upxXx4$)u2 Split a Bézier curve into two at the intersection with a closed path. Parameters ---------- bezier : (N, 2) array-like Control points of the Bézier segment. See `.BezierSegment`. inside_closedpath : callable A function returning True if a given point (x, y) is inside the closed path. See also `.find_bezier_t_intersecting_with_closedpath`. tolerance : float The tolerance for the intersection. See also `.find_bezier_t_intersecting_with_closedpath`. Returns ------- left, right Lists of control points for the two Bézier segments. )r]g@)rgrrerU) bezierrZr]bzrYr[r\_left_rights r)split_bezier_intersecting_with_closedpathr<sH, v B  7 CFB'vR2~>ME =rc rSSKJn UR5n[U5upgU"USS5nUn Sn Sn UHFupgU n U [ U5S-- n U"USS5U:wa[ R "U SSU/5n OUn MH [S5eU RS5n [XU5up[ U5S:Xa&UR/nURUR/nO[ U5S :Xa<URUR/nURURUR/nOl[ U5S :XaRURURUR/nURURURUR/nO [S 5eUSSnUSSnURcWU"[ R "UR SU U/55nU"[ R "UUR U S/55nOU"[ R "UR SU U/5[ R "URSU U/55nU"[ R "UUR U S/5[ R "UURU S/55nU(a U(dUUnnUU4$) zT 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)rHrzThis should never be reached)pathr iter_segmentsnextrPr rr%reshaperLINETOMOVETOCURVE3CURVE4AssertionErrorcodesvertices)rinsider] reorder_inoutr path_iter ctl_pointscommand begin_insidectl_points_oldioldr bezier_pathbpleftright codes_left codes_right verts_left verts_rightpath_inpath_outs rsplit_path_inoutr_sy ""$Iy/J*RS/*LN D A(  S_ !! *RS/ "l 2...*=z)JKK # )EFF   W %B; IKD 4yA~kk] {{DKK0 Takk4;;/ {{DKK= Takk4;; < {{DKKdkkJ ;<<abJ(K zzr~~t}}Ra'8*&EFG T]]125F'GHIr~~t}}Ud';Z&HI~~tzz%4'8*&EFH T]]125F'GH TZZ^'DEG\$g H rc&^^^US-mUUU4SjnU$)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 rc4>UupUT- S-UT- S--T:$)Nrr)xyr8r9r=r>r2s r_finside_circle.._fs*B1}B1},r11rr)r=r>rrrs`` @r inside_circlers aB2 IrcFX - X1- pTXD-XU--S-nUS:XagXF- XV- 4$)NrWr)r<r<r)x0y0rBrCdxdyr3s r get_cos_sinrs8 Wbg 27 r!AAv 626>rc[R"X5n[R"X#5n[XV- 5nXt:ag[U[R- 5U:agg)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. rrHF)r arctan2r$r)dx1dy1dx2dy2r]theta1theta2dthetas rcheck_if_parallelrsP&ZZ !F ZZ !F  !F  Vbee^ y (rc USup#USupEUSupg[X$- X5- XF- XW- 5nUS:Xa'[R"S5 [X#Xg5upXpO[X#XE5up[XEXg5up[ X#XU5upnn[ XgXU5unnnn[ XU U UUX5unn[ UUU U UUX5unnX4UU4UU4/nUU4UU4UU4/nUU4$![ a# SU U--SUU--nnSUU--SUU--nnNEf=f)u Given the quadratic Bézier control points *bezier2*, returns control points of quadratic Bézier lines roughly parallel to given one separated by *width*. rrrrHz8Lines do not intersect. A straight line is used instead.rW)rr warn_externalrrFr:r%)bezier2widthc1xc1ycmxcmyc2xc2y parallel_testr(r)r,r-c1x_leftc1y_left c1x_right c1y_rightc2x_leftc2y_left c2x_right c2y_rightcmx_leftcmy_left cmx_right cmy_right path_left path_rights r get_parallelsrsqzHCqzHCqzHC%ci&)i( 0 9f06 906 @ 9 %H%H%'Ii(i(i(*J j  )   8h& '80C)D 9y( )3)i2G+H 9  s'C*DDcFSSU-X-- -nSSU-X-- -nX4Xg4XE4/$)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. rWrr)rrmmxmmyrrrrs rfind_control_pointsr sA C39% &C C39% &C J SJ //rcUSupVUSupxUSup[XVXx5up[XxX5up[XVXX-5unnnn[XXX-5unnnnXW-S-Xh-S-nnXy-S-X-S-nnUU-S-UU-S-nn[UUUU5unn[UUUUX-5unn n!n"[UUUU UU5n#[UUU!U"UU5n$U#U$4$)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*. rrrrW)rrFr)%rrw1wmw2rrrrc3xc3yr(r)r,r-rrrrc3x_leftc3y_left c3x_right c3y_rightc12xc12yc23xc23yc123xc123ycos_t123sin_t123 c123x_left c123y_left c123x_right c123y_rightrrs% rmake_wedged_bezier2r*sAqzHCqzHCqzHC!34NF 34NF #FEJ?-Hh 9 #FEJ?-Hh 9 )r!CI#3$D)r!CI#3$D4K2%t r'95E%T4t<Hh %(EJG5J K$Hh$. $,h8I%Y %0+%. ;J j  r)r<?{Gz?)r)rF)gh㈵>)rrWr<)r functoolsrrprnumpyr matplotlibr vectorizerr%rr:rFrLrUrergrrrrrrrrrrrr$s  3.. : B2 !&GKI)X|8|8@.2F:z&