a Эм>> from sympy import Curve, sin, cos, interpolate >>> from sympy.abc import t, a >>> C = Curve((sin(t), cos(t)), (t, 0, 2)) >>> C.functions (sin(t), cos(t)) >>> C.limits (t, 0, 2) >>> C.parameter t >>> C = Curve((t, interpolate([1, 4, 9, 16], t)), (t, 0, 1)); C Curve((t, t**2), (t, 0, 1)) >>> C.subs(t, 4) Point2D(4, 16) >>> C.arbitrary_point(a) Point2D(a, a**2) See Also ======== sympy.core.function.Function sympy.polys.polyfuncs.interpolate cCsft|Г}t|Гrt|Гdkr,tdt|ГГВt|Гr@t|ГdkrPtdt|ГГВtа|t|Оt|ОбS)Nщz3Function argument should be (x(t), y(t)) but got %sщz3Limit argument should be (t, tmin, tmax) but got %s)rr┌len┌ ValueError┌strr┌__new__r)┌cls┌function┌limitsZfunйr·d/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/geometry/curve.pyrKs z Curve.__new__cCs|а|j|бSйN)┌subs┌ parameter)┌self┌frrr┌__call__VszCurve.__call__cs(И|jkr$tЗЗfddД|jDГОSdS)Ncsg|]}|аИИбСqSrйrй┌.0rй┌new┌oldrr┌ [єz$Curve._eval_subs..)rr ┌ functions)rr$r#rr"r┌ _eval_subsYs zCurve._eval_subsщcs^|j\}\}}}t|ГЙtЗЗfddД|DГГ}ЗЗfddД||fDГ\}}|а||||fбS)Ncs g|]}|jfdИiИдОСqSй┌nйZevalfйr!┌iйZdps┌optionsrrr%`r&z%Curve._eval_evalf..cs g|]}|jfdИiИдОСqSr*r,r-r/rrr%ar&)┌argsr┌tuple┌func)r┌precr0r┌t┌a┌brr/r┌_eval_evalf]s zCurve._eval_evalfr5csr|durt|jОSt||jddНЙ|jЙИjИjkrXИjddД|jDГvrXtdИjГВtЗЗfddД|jDГОS) aуA parameterized point on the curve. Parameters ========== parameter : str or Symbol, optional Default value is 't'. The Curve's parameter is selected with None or self.parameter otherwise the provided symbol is used. Returns ======= Point : Returns a point in parametric form. Raises ====== ValueError When `parameter` already appears in the functions. Examples ======== >>> from sympy import Curve, Symbol >>> from sympy.abc import s >>> C = Curve([2*s, s**2], (s, 0, 2)) >>> C.arbitrary_point() Point2D(2*t, t**2) >>> C.arbitrary_point(C.parameter) Point2D(2*s, s**2) >>> C.arbitrary_point(None) Point2D(2*s, s**2) >>> C.arbitrary_point(Symbol('a')) Point2D(2*a, a**2) See Also ======== sympy.geometry.point.Point NTй┌realcss|]}|jVqdSr)┌namer rrr┌ Цr&z(Curve.arbitrary_point..zFSymbol %s already appears in object and cannot be used as a parameter.csg|]}|аИИбСqSrr)r!┌wйr5Ztnewrrr%Щr&z)Curve.arbitrary_point..)r r'rrr;┌free_symbolsr)rrrr>r┌arbitrary_pointds, zCurve.arbitrary_pointcCs<tГ}|j|jddЕD]}||jO}q|а|jhб}|S)a─Return a set of symbols other than the bound symbols used to parametrically define the Curve. Returns ======= set : Set of all non-parameterized symbols. Examples ======== >>> from sympy.abc import t, a >>> from sympy import Curve >>> Curve((t, t**2), (t, 0, 2)).free_symbols set() >>> Curve((t, t**2), (t, a, 2)).free_symbols {a} щN)┌setr'rr?┌ differencer)r┌freer6rrrr?Ыs zCurve.free_symbolscCst|jdГS)a;The dimension of the curve. Returns ======= int : the dimension of curve. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve((t, t**2), (t, 0, 2)) >>> C.ambient_dimension 2 r)rr1йrrrr┌ambient_dimension╖szCurve.ambient_dimensioncCs |jdS)aУThe functions specifying the curve. Returns ======= functions : list of parameterized coordinate functions. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve((t, t**2), (t, 0, 2)) >>> C.functions (t, t**2) See Also ======== parameter rйr1rErrrr'╬szCurve.functionscCs |jdS)aТThe limits for the curve. Returns ======= limits : tuple Contains parameter and lower and upper limits. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve([t, t**3], (t, -2, 2)) >>> C.limits (t, -2, 2) See Also ======== plot_interval rArGrErrrrщszCurve.limitscCs|jddS)amThe curve function variable. Returns ======= Symbol : returns a bound symbol. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve([t, t**2], (t, 0, 2)) >>> C.parameter t See Also ======== functions rArrGrErrrrszCurve.parametercs(ttЗfddДИjDГГГ}t|ИjГS)z├The curve length. Examples ======== >>> from sympy import Curve >>> from sympy.abc import t >>> Curve((t, t), (t, 0, 1)).length sqrt(2) c3s"|]}t|ИjdГdVqdS)rrN)rr)r!r3rErrr<,r&zCurve.length..)r┌sumr'r r)rZ integrandrrEr┌lengths zCurve.lengthcCs(t||jddН}|gt|jddЕГS)aыThe plot interval for the default geometric plot of the curve. Parameters ========== parameter : str or Symbol, optional Default value is 't'; otherwise the provided symbol is used. Returns ======= List : the plot interval as below: [parameter, lower_bound, upper_bound] Examples ======== >>> from sympy import Curve, sin >>> from sympy.abc import x, s >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval() [t, 1, 2] >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval(s) [s, 1, 2] See Also ======== limits : Returns limits of the parameter interval Tr9rAN)rr┌listr)rrr5rrr┌ plot_interval/s!zCurve.plot_intervalrNcCsЪddlm}m}|r$t|ddН}n tddГ}|j|jО}t|jГ}|аdб|dd|Г}|||Г9}|а |dddЕfа бd|jб}|}|j|jОS)a■This function is used to rotate a curve along given point ``pt`` at given angle(in radian). Parameters ========== angle : the angle at which the curve will be rotated(in radian) in counterclockwise direction. default value of angle is 0. pt : Point the point along which the curve will be rotated. If no point given, the curve will be rotated around origin. Returns ======= Curve : returns a curve rotated at given angle along given point. Examples ======== >>> from sympy import Curve, pi >>> from sympy.abc import x >>> Curve((x, x), (x, 0, 1)).rotate(pi/2) Curve((-x, x), (x, 0, 1)) r)┌Matrix┌ rot_axis3rйZdimrArN)Zsympy.matricesrLrMr ┌ translater1rJr'┌appendr3┌tolistr)rZangle┌ptrLrM┌rvrrrr┌rotateSs "zCurve.rotaterAcCsR|r.t|ddН}|j|jОа||бj|jОS|j\}}|а||||f|jбS)a^Override GeometryEntity.scale since Curve is not made up of Points. Returns ======= Curve : returns scaled curve. Examples ======== >>> from sympy import Curve >>> from sympy.abc import x >>> Curve((x, x), (x, 0, 1)).scale(2) Curve((2*x, x), (x, 0, 1)) rrN)r rOr1┌scaler'r3r)r┌x┌yrR┌fx┌fyrrrrU~s zCurve.scalecCs$|j\}}|а||||f|jбS)aLTranslate the Curve by (x, y). Returns ======= Curve : returns a translated curve. Examples ======== >>> from sympy import Curve >>> from sympy.abc import x >>> Curve((x, x), (x, 0, 1)).translate(1, 2) Curve((x + 1, x + 2), (x, 0, 1)) )r'r3r)rrVrWrXrYrrrrOЦs zCurve.translate)r))r5)r5)rN)rArAN)rr)┌__name__┌ __module__┌__qualname__┌__doc__rrr(r8r@┌propertyr?rFr'rrrIrKrTrUrOrrrrr s,5 7 $ + r N)r]Z(sympy.functions.elementary.miscellaneousrZ sympy.corerrZsympy.core.containersrZsympy.core.symbolrZsympy.geometry.entityrrZsympy.geometry.pointr Zsympy.integralsr Zsympy.utilities.iterablesrZmpmath.libmp.libmpfrr rrrr┌s