h+SSKJr SSKJrJr SSKJr SSKrSSKr SSK Jr SSK J r JrJrJrJrJrJr Sr\R*S- r\R*r\S-rS\R*-r/S QrSS jrSS jrS S jrS!S jrS"SjrS\4Sjr S\4S#Sjjr!\4S$Sjjr"S%S#Sjjr#S&Sjr$S'Sjr%S(Sjr&S)Sjr'S*Sjr(SSS.S+Sjjr)S,Sjr*g)-) annotations)IterableSequence)partialN)Vec3Vec2UVecMatrix44X_AXISY_AXISarc_angle_span_radg|=@g@) closest_pointconvex_hull_2ddistance_point_line_2dis_convex_polygon_2dis_axes_aligned_rectangle_2dis_point_on_line_2dis_point_left_of_linepoint_to_line_relationenclosing_anglessignareanp_areacircle_radius_3p TOLERANCEhas_matrix_2d_stretching decdeg2dmsellipse_param_spancUS:aS$S$)z2Return sign of float `f` as -1 or +1, 0 returns +1gg?)fs H/var/www/html/env/lib/python3.13/site-packages/ezdxf/math/construct2d.pyrr0ss74$$cH[US-S5up[US5up1X1U4$)z[[U5[U55$)uReturns the counter-clockwise params span of an elliptic arc from start- to end param. Returns the param span in the range [0, 2π], 2π is a full ellipse. Full ellipse handling is a special case, because normalization of params which describe a full ellipse would return 0 if treated as regular params. e.g. (0, 2π) → 2π, (0, -2π) → 2π, (π, -π) → 2π. Input params with the same value always return 0 by definition: (0, 0) → 0, (-π, -π) → 0, (2π, 2π) → 0. Alias to function: :func:`ezdxf.math.arc_angle_span_rad` )r float) start_param end_params r$rr<s eK0% 2B CCr%c[U5nSnSnUH-n[U5nURU5nUbXb:dM)UnUnM/ U$)zReturns the closest point to a give `base` point. Args: base: base point as :class:`Vec3` compatible object points: iterable of points as :class:`Vec3` compatible object N)rdistance)basepointsmin_distfoundpointpdists r$rrMsS :D!HE K}}Q  $/HE  Lr%cS Sjn[R"[U55nUR5 [ U5S:a [ S5e[ U5n[5/SU--nSn[ U5HUnUS:aAU"XES- XES- X&5S::a'US-nUS:aU"XES- XES- X&5S::aM'X&XE'US- nMW US-n[ US- SS5HSnXW:a@U"XES- XES- X&5S::a&US-nXW:aU"XES- XES- X&5S::aM&X&XE'US- nMU US U$) zReturns the 2D convex hull of given `points`. Returns a closed polyline, first vertex is equal to the last vertex. Args: points: iterable of points, z-axis is ignored c,X- RX - 5$N)det)oabs r$crossconvex_hull_2d..crossls{{15!!r%z9Convex hull calculation requires 3 or more unique points.rr!N)r=rr>rr?rreturnr-)rlistsetsortlen ValueErrorrange)r3r@verticesnhullkits r$rrasc"yyV%H MMO 8}qTUU ]Ax1q5)D A 1X1ftE{DQKEL FA1ftE{DQKEL+ Q  UA 1q5"b !ftE{DQKEL FAftE{DQKEL+ Q " 8Or%TcT[[RUS9nU[R-nU[R-nU[R-nU"Xg5(aU"Xh5$Xg:aXhs=:=(a U:Os n OXxs=:=(a U:Os (+n U(aU $U (+$)N)abs_tol)rmathisclosetau) angle start_angle end_angleccwrTrVser>rs r$rrsdllG4GdhhADHHA Aq}}q}u IIAIO1Qr%c UupVUupxUup[R"X- U-X- U-- X-X-- -5U:*n U (aU(aU $Xy:aXpXt- Us=::a X-::dg gX:aXpX- Us=::a X-::dg gg)a`Returns ``True`` if `point` is on `line`. Args: point: 2D point to test as :class:`Vec2` start: line definition point as :class:`Vec2` end: line definition point as :class:`Vec2` ray: if ``True`` point has to be on the infinite ray, if ``False`` point has to be on the line segment abs_tol: tolerance for on the line test FT)rUfabs) r6startendrayrTpoint_xpoint_ystart_xstart_yend_xend_yon_lines r$rrsGGLE _ '') *0 2     c ?"U!W??@ ?"U!W??@r%cURUR- URUR- -URUR- URUR- -- n[U5U::agUS:agg)aReturns ``-1`` if `point` is left `line`, ``+1`` if `point` is right of `line` and ``0`` if `point` is on the `line`. The `line` is defined by two vertices given as arguments `start` and `end`. Args: point: 2D point to test as :class:`Vec2` start: line definition point as :class:`Vec2` end: line definition point as :class:`Vec2` abs_tol: tolerance for minimum distance to line rrDrE)xyabs)r6rarbrTrels r$rrsm 55577?uww0 1SUUUWW_ %''5 C 3x7 qr%Fc<[XU5nU(aUS:$US:$)axReturns ``True`` if `point` is "left of line" defined by `start-` and `end` point, a colinear point is also "left of line" if argument `colinear` is ``True``. Args: point: 2D point to test as :class:`Vec2` start: line definition point as :class:`Vec2` end: line definition point as :class:`Vec2` colinear: a colinear point is also "left of line" if ``True`` rDr)r)r6rarbcolinearros r$rrs% !s 3CQwQwr%cURU5(a [S5e[R"X- R X - 55X!- R - $)zYReturns the normal distance from `point` to 2D line defined by `start-` and `end` point. z Not a line.)rVZeroDivisionErrorrUr`r< magnitude)r6rarbs r$rrsI  }}S .. 99em((5 6#+9P9P PPr%cX- nX - nX!- nURUR-UR-nURU5RS-nXg- $)Nr)rtr@)r>r?cbacacbupperlowers r$rrsR B B B LL2<< '",, 6E HHRL " "S (E =r%c \[R"U5n[U5S:agUSRUS5(dUR US5 [ [ R"UVs/sHo"RUR4PM sn[ RS95$s snf)zwReturns the area of a polygon. Returns the projected area in the xy-plane for any vertices (z-axis will be ignored). rBr!rrE)dtype) rrGrJrVappendrnparrayrlrmfloat64)rMvec2svs r$rrs IIh E 5zA~ 8  E"I & & U1X 2887Acc133Z7rzzJ KK7s0!B) cUSS2S4nUSS2S4nUSS2S4nUSS2S4n[R"[R"X-X2-- 55S-$)aReturns the area of a polygon. Returns the projected area in the xy-plane, the z-axis will be ignored. The polygon has to be closed (first vertex == last vertex) and should have 3 or more corner vertices to return a valid result. Args: vertices: numpy array [:, n], n > 1 NrErrDg?)rrnsum)rMp1xp2xp1yp2ys r$rrsl 3B36 C 12q5/C 3B36 C 12q5/C 66"&&SY./ 03 66r%cUR[5nUR[5n[R"UR UR 5(+$)aReturns ``True`` if matrix `m` performs a non-uniform xy-scaling. Uniform scaling is not stretching in this context. Does not check if the target system is a cartesian coordinate system, use the :class:`~ezdxf.math.Matrix44` property :attr:`~ezdxf.math.Matrix44.is_cartesian` for that. )transform_directionr r rUrVmagnitude_square)muxuys r$rr sD  v &B  v &B||B//1D1DE EEr%gư>)strictepsilonc.[U5S:agSnSnUSnUSnUHgnURU5(aMXW- RXe- 5n[U5U:aUS:aSOSnU(dUnX4:wa gO U(a gUnUnMi [ U5$)apReturns ``True`` if the 2D `polygon` is convex. This function supports open and closed polygons with clockwise or counter-clockwise vertex orientation. Coincident vertices will always be skipped and if argument `strict` is ``True``, polygons with collinear vertices are not considered as convex. This solution works only for simple non-self-intersecting polygons! rBFrrEr!rD)rJrVr<rnbool) polygonrr global_sign current_signprev prev_prevvertexr<s r$rr-s 7|aKL 2;D I >>$   }!!)"23 s8w !$s2L* *+  !"  r%c\S SjnS Sjn[U5nUSRUS5(aUS-nUS:wagUtpEpgnU"XE5(a(U"XV5(aU"Xg5(aU"Xt5(agU"XV5(a(U"Xg5(aU"Xt5(aU"XE5(agg) aReturns ``True`` if the given points represent a rectangle aligned with the coordinate system axes. The sides of the rectangle must be parallel to the x- and y-axes of the coordinate system. The rectangle can be open or closed (first point == last point) and oriented clockwise or counter-clockwise. Only works with 4 or 5 vertices, rectangles that have sides with collinear edges are not considered rectangles. .. versionadded:: 1.2.0 cX[R"URUR5$r;)rUrVrmr>r?s r$ is_horizontal3is_axes_aligned_rectangle_2d..is_horizontalb||ACC%%r%cX[R"URUR5$r;)rUrVrlrs r$ is_vertical1is_axes_aligned_rectangle_2d..is_verticalerr%rrErDFT)r>rr?rrFr)r>rr?r)rJrV) r3rrcountp0p1p2p3_s r$rrUs&& KE ay$$   zBBQb    " ! !   b    " ! !    r%)r#r-rFr-)r(r-rFztuple[float, float, float])r.r-r/r-rFr-)r2r r3Iterable[UVec]rFz Vec3 | None)r3rrF list[Vec2])r6rrarrbrrFr)r6rrarrbrrFint)F)r6rrarrbrrFr-)r>rr?rrvrrFr-)rMrrFr-)rMz npt.NDArrayrFr-)rr rFr)rrrFr)r3rrFr)+ __future__rtypingrr functoolsrrUnumpyr numpy.typingnpt ezdxf.mathrrr r r r r rpi RADIANS_90 RADIANS_180 RADIANS_270 RADIANS_360__all__rrrrrrrrrrrrrrrrr"r%r$rs#%   WWs] gg 3 DGGm  *% D"("J9=i ".29$ $$#'$ $P2; #'2&QL$7$ F9>t%P'r%