a RG5d'@sdZddlmZddlmZddlmZddlmZddl m Z m Z ddl m Z ddlmZdd lmZmZdd lmZdd lmZGd d d e ZdS)zCCurves in 2-dimensional Euclidean space. Contains ======== Curve )sqrt)diff)Tuple)_symbol)GeometryEntity GeometrySet)Point) integrate)Matrix rot_axis3) is_sequence) prec_to_dpsc@seZdZdZddZddZddZd%d d Zd&d d Ze ddZ e ddZ e ddZ e ddZ e ddZe ddZd'ddZd(ddZd)d!d"Zd*d#d$ZdS)+Curvea,A curve in space. A curve is defined by parametric functions for the coordinates, a parameter and the lower and upper bounds for the parameter value. Parameters ========== function : list of functions limits : 3-tuple Function parameter and lower and upper bounds. Attributes ========== functions parameter limits Raises ====== ValueError When `functions` are specified incorrectly. When `limits` are specified incorrectly. Examples ======== >>> from sympy import Curve, sin, cos, interpolate >>> from sympy.abc import t, a >>> C = Curve((sin(t), cos(t)), (t, 0, 2)) >>> C.functions (sin(t), cos(t)) >>> C.limits (t, 0, 2) >>> C.parameter t >>> C = Curve((t, interpolate([1, 4, 9, 16], t)), (t, 0, 1)); C Curve((t, t**2), (t, 0, 1)) >>> C.subs(t, 4) Point2D(4, 16) >>> C.arbitrary_point(a) Point2D(a, a**2) See Also ======== sympy.core.function.Function sympy.polys.polyfuncs.interpolate cCs^t|rt|dkr$tdt|t|r8t|dkrHtdt|t|t|t|S)Nz3Function argument should be (x(t), y(t)) but got %sz3Limit argument should be (t, tmin, tmax) but got %s)r len ValueErrorstrr__new__r)clsfunctionlimitsrP/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/geometry/curve.pyrLsz Curve.__new__cCs||j|SN)subs parameter)selffrrr__call__VszCurve.__call__cs(|jkr$tfdd|jDSdS)Ncsg|]}|qSrr.0rnewoldrr [z$Curve._eval_subs..)rr functions)rr%r$rr#r _eval_subsYs zCurve._eval_subsc s^|j\}\}}}t|tfdd|D}fdd||fD\}}|||||fS)Ncs g|]}|jfdiqSnevalfr"idpsoptionsrrr&`r'z%Curve._eval_evalf..cs g|]}|jfdiqSr+r-r/r1rrr&ar')argsr tuplefunc)rprecr3rtabrr1r _eval_evalf]s zCurve._eval_evalfr8csr|durt|jSt||jdd|jjjkrXjdd|jDvrXtdjtfdd|jDS) aA 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 NTrealcss|] }|jVqdSr)namer!rrr r'z(Curve.arbitrary_point..zFSymbol %s already appears in object and cannot be used as a parameter.csg|]}|qSrr )r"wr8tnewrrr&r'z)Curve.arbitrary_point..)rr(rrr> free_symbolsr)rrrrArarbitrary_pointds,  zCurve.arbitrary_pointcCs<t}|j|jddD]}||jO}q||jh}|S)aReturn 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} N)setr(rrC differencer)rfreer9rrrrCs  zCurve.free_symbolscCst|jdS)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)rr4rrrrambient_dimensionszCurve.ambient_dimensioncCs |jdS)aThe 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 rr4rIrrrr(szCurve.functionscCs |jdS)aThe 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 rErKrIrrrrsz Curve.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 rErrKrIrrrrszCurve.parametercs(ttfddjD}t|jS)zThe curve length. Examples ======== >>> from sympy import Curve >>> from sympy.abc import t >>> Curve((t, t), (t, 0, 1)).length sqrt(2) c3s"|]}t|jddVqdS)rrN)rr)r"r6rIrrr?,r'zCurve.length..)rsumr(r r)r integrandrrIrlengths z Curve.lengthcCs(t||jdd}|gt|jddS)aThe 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 Tr<rEN)rrlistr)rrr8rrr plot_interval/s!zCurve.plot_intervalrNcCs|rt|dd }n tdd}|j|j}t|j}|dtdd|}|t|9}||dddf d|j }| }|j|jS)aThis 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)) rdimrrErN) r translater4rOr(appendr r r6tolistr)rangleptrvrrrrrotateSs      "z Curve.rotaterEcCsR|r.t|dd}|j| j||j|jS|j\}}|||||f|jS)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)) rrQ)rrSr4scaler(r6r)rxyrWfxfyrrrrZ}s   z Curve.scalecCs$|j\}}|||||f|jS)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(r6r)rr[r\r]r^rrrrSs zCurve.translate)r*)r8)r8)rN)rErEN)rr)__name__ __module__ __qualname____doc__rrr)r;rDpropertyrCrJr(rrrNrPrYrZrSrrrrrs,5   7       $ * rN)rb(sympy.functions.elementary.miscellaneousr sympy.corersympy.core.containersrsympy.core.symbolrZsympy.geometry.entityrrsympy.geometry.pointrsympy.integralsr sympy.matricesr r sympy.utilities.iterablesr mpmath.libmp.libmpfr rrrrrs