'jjddlmZddlmZddlmZddlmZmZdgZ dd Z ddZ GddZ dS)) annotations)Iterable)Vec3)global_bspline_interpolationBSpline EulerSpiralbasefloatcountintreturn list[float]c|dks Jdd|g}|}t|dz D]}||z}|||S)Nzrequires count > 2?)rangeappend)r r values next_value_s P/DATA/AppData/hermes/venv/lib/python3.11/site-packages/ezdxf/math/eulerspiral.pypowersr sc 1999*9994[FJ 519  ""d  j!!!! MlengthsegmentsIterable[float]c#Kt|t|z }td|dzD] }||zV dS)Nr)r r)rrdelta_lindexs r_paramsr!sVFmmeHoo-Gq(Q,''orc\eZdZdZdddZddZd d Zd!d Zd d Zd"dZ d dZ d#d$dZ dS)%rz This class represents an euler spiral (clothoid) for `curvature` (Radius of curvature). This is a parametric curve, which always starts at the origin = ``(0, 0)``. Args: curvature: radius of curvature r curvaturer cjt|}||_t|d|_i|_dS)N)r r#rcurvature_powers_cache)selfr#s r__init__zEulerSpiral.__init__'s3)$$ "-3Ir-B-B)+ rtr c2|dkr|jd|z SdS)z%Get radius of circle at distance `t`.grr&)r(r*s rradiuszEulerSpiral.radius-s# s77(+a/ /3rrcV|dzd|jdzz }tj|S)z4Get tangent at distance `t` as :class:`Vec3` object.rg@)r&r from_angle)r(r*angles rtangentzEulerSpiral.tangent4s-Q# 5a 889u%%%rr-c<|jdt|z S)z(Get distance L from origin for `radius`.r)r&r )r(r-s rdistancezEulerSpiral.distance9s$Q'%--77rclfd}jvr|ddd|dddz |dd d z|d d d z |dddz}|dddz |dddz|dddz |dddz}t||j<jS)z+Get point at distance `t` as :class:`Vec3`.c0|z|j|zz S)Nr,) length_powercurvature_powerconstr(r*s rtermzEulerSpiral.point..term@s% $-o>> rrg@gu@ g@gubAr%g MAgD@ g@ gH"AgA)r'r)r(r*r9yxs`` rpointzEulerSpiral.point=s(       DK  Q3$q!U##$$r2w''($r2y))*$r2|,, - $q!T""#$q!V$$%$r2x(()$r2{++ , "!QZZDKN{1~rrrr Iterable[Vec3]c#^Kt||D]}||VdS)zyApproximate curve of length with line segments. Generates segments+1 vertices as :class:`Vec3` objects. N)r!rL)r(rrr*s r approximatezEulerSpiral.approximateWsD **  A**Q--      rc||}||}||||zS)z"Get circle center at distance `t`.)rLr-r1 normalize orthogonal)r(r*prs r circle_centerzEulerSpiral.circle_center_sO JJqMM KKNN4<<??,,Q//::<<<r:uniformdegreemethodstrrc>tt|}fdt|D}t ||||}t |j|jfd|DS)a?Approximate euler spiral as B-spline. Args: length: length of euler spiral segments: count of fit points for B-spline calculation degree: degree of BSpline method: calculation method for parameter vector t Returns: :class:`BSpline` )rc`g|]*}|+S)r1rQ).0r*rr(s r z'EulerSpiral.bspline..zsC    LLOO % %f - -   r)rXtangentscg|]}|zSr\r\)r]vrs rr^z'EulerSpiral.bspline..s 0 0 0AQZ 0 0 0r) r listrOr!rrcontrol_pointsorderknots)r(rrrWrX fit_points derivativessplines`` rbsplinezEulerSpiral.bsplinees&v$**6H*EEFF      VX..    . v      ! L 0 0 0 0 0 0 0    rN)r)r#r )r*r r r )r*r r r)r-r r r )rr rr r rM)r>r:rV) rr rr rWr rXrYr r) __name__ __module__ __qualname____doc__r)r-r1r3rLrOrUrir\rrrrs  ,,,,, &&&& 88884    ==== # # # # # # # rN)r r r r r r)rr rr r r) __future__rtypingr ezdxf.mathrezdxf.math.bsplinerr__all__rr!rr\rrrss#"""""DDDDDDDD / m m m m m m m m m m r