hb-ddlmZddlmZmZddlmZddlZddlZ ddl mZ ddl m Z mZmZmZmZmZmZdZej*dz Zej*ZedzZdej*zZgd Zdd Zdd Zd d Zd!d Zd"dZdefdZ def d#dZ!ef d$dZ"d%d#dZ#d&dZ$d'dZ%d(dZ&d)dZ'd*dZ(dddd+dZ)d,dZ*y)-) 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_spanc|dkrdSdS)z2Return sign of float `f` as -1 or +1, 0 returns +1gg?)fs 6lib/python3.12/site-packages/ezdxf/math/construct2d.pyrr0ss74$$cNt|dzd\}}t|d\}}|||fS)ztt|t|S)u?Returns 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%ct|}d}d}|D]*}t|}|j|}|||ks'|}|},|S)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$rrMsU :D!HE K}}Q  $/HE  Lr%cd d}tjt|}|jt |dkr t dt |}tgd|zz}d}t |D]W}|dk\rC|||dz ||dz ||dkr'|dz}|dk\r|||dz ||dz ||dkr'||||<|dz }Y|dz}t |dz ddD]W}||k\rC|||dz ||dz ||dkr'|dz}||k\r|||dz ||dz ||dkr'||||<|dz }Y|d |S) 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 c0||z j||z SN)det)oabs r$crosszconvex_hull_2d..crosslsA{{1q5!!r%z9Convex hull calculation requires 3 or more unique points.rr!N)r=rr>rr?rreturnr-)rlistsetsortlen ValueErrorrange)r3r@verticesnhullkits r$rras"yyV%H MMO 8}qTUU ]Ax1q5)D A 1X1ftAE{DQK!EL FA1ftAE{DQK!EL1+Q Q  UA 1q5"b !1ftAE{DQK!EL FA1ftAE{DQK!EL1+Q Q " 8Or%Tc*ttj|}|tjz}|tjz}|tjz}|||r |||S||kr||cxkxr|knc} n||cxkxr|knc } |r| S| S)N)abs_tol)rmathisclosetau) angle start_angle end_angleccwrSrUser>rs r$rrsdllG4GdhhADHHA Aq!}q!}1u IAIQO1Qr%c|\}}|\}}|\} } tj| |z |z| |z |zz | |z| |zz z|k} | r|r| S|| kDr| |} }||z |cxkr| |zksyy|| kDr| |} }||z |cxkr| |zksyyy)aReturns ``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)rTfabs) r6startendrayrSpoint_xpoint_ystart_xstart_yend_xend_yon_lines r$rrsGWGWLE5 W_ 'w') *w0 2     c U?"GUG'!W??@ U?"GUG'!W??@r%c|j|jz |j|jz z|j|jz |j|jz zz }t||kry|dkryy)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 rrCrD)xyabs)r6r`rarSrels r$rrsm 55577?uww0 1SUUUWW_ %''5 C 3x7 qr%Fc4t|||}|r|dkS|dkS)aReturns ``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`` rCr)r)r6r`racolinearrns r$rrs' !s 3CQwQwr%c|j|r tdtj||z j ||z ||z j z S)zaReturns the normal distance from `point` to 2D line defined by `start-` and `end` point. z Not a line.)rUZeroDivisionErrorrTr_r< magnitude)r6r`ras r$rrsL  }}S .. 99eem((u5 6#+9P9P PPr%c||z }||z }||z }|j|jz|jz}|j|jdz}||z S)Nr)rsr@)r>r?cbacacbupperlowers r$rrsZ QB QB QB LL2<< '",, 6E HHRL " "S (E 5=r%c Ntj|}t|dkry|dj|ds|j |dt t j|Dcgc]}|j|jfc}t jScc}w)zReturns the area of a polygon. Returns the projected area in the xy-plane for any vertices (z-axis will be ignored). rAr!rrD)dtype) rrFrIrUappendrnparrayrkrlfloat64)rLvec2svs r$rrs IIh E 5zA~ 8  E"I & U1X 2887Aacc133Z7rzzJ KK7s(B" c|dddf}|dddf}|dddf}|dddf}tjtj||z||zz dzS)a/Returns 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 NrDrrCg?)r~rmsum)rLp1xp2xp1yp2ys r$rrsp 3B36 C 12q5/C 3B36 C 12q5/C 66"&&sS3Y./ 03 66r%c|jt}|jt}tj|j |j  S)a3Returns ``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 rTrUmagnitude_square)muxuys r$rr sD  v &B  v &B||B//1D1DE EEr%gư>)strictepsilonct|dkryd}d}|d}|d}|D]U}|j|r||z j||z }t||k\r|dkrdnd}|s|}||k7ry|ry|}|}Wt |S)aReturns ``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! rAFrrDr!rC)rIrUr<rmbool) polygonrr global_sign current_signprev prev_prevvertexr<s r$rr-s 7|aKL 2;D I >>$  f}!!)d"23 s8w !$s2L* l*  !"  r%cd d}d d}t|}|dj|dr|dz}|dk7ry|^}}}}}|||r|||r|||r |||ry|||r|||r|||r |||ryy) 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 cVtj|j|jSr;)rTrUrlr>r?s r$ is_horizontalz3is_axes_aligned_rectangle_2d..is_horizontalb||ACC%%r%cVtj|j|jSr;)rTrUrkrs r$ is_verticalz1is_axes_aligned_rectangle_2d..is_verticalerr%rrDrCFT)r>rr?rrEr)r>rr?r)rIrU) r3rrcountp0p1p2p3_s r$rrUs&& KE ay$   zBBQb" B  "b ! B b" B  "b ! B  r%)r#r-rEr-)r(r-rEztuple[float, float, float])r.r-r/r-rEr-)r2r r3Iterable[UVec]rEz Vec3 | None)r3rrE list[Vec2])r6rr`rrarrEr)r6rr`rrarrEint)F)r6rr`rrarrEr-)r>rr?rrurrEr-)rLrrEr-)rLz npt.NDArrayrEr-)rr rEr)rrrEr)r3rrEr)+ __future__rtypingrr functoolsrrTnumpyr~ 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%