Ed'dZddlmZddlmZddlmZddlmZddl m Z m Z ddl m Z ddlmZdd lmZmZdd lmZdd lmZGd 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_dpsceZdZdZdZdZdZddZddZe d Z e d Z e d Z e d Z e d Ze dZddZddZddZddZdS)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 cNt|rt|dkrtdt|zt|rt|dkrtdt|zt j|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)clsfunctionlimitss 4lib/python3.11/site-packages/sympy/geometry/curve.pyrz Curve.__new__Ls8$$ .H (: ."8}}-.. .6"" ,c&kkQ&6 ,"6{{+,, ,%c5(+;UF^LLLc8||j|SN)subs parameter)selffs r__call__zCurve.__call__Vsyy+++rcV|jkrtfd|jDSdS)Nc<g|]}|Sr).0r"newolds r z$Curve._eval_subs..[s'DDD166#s++DDDr)r r functions)r!r*r)s ``r _eval_subszCurve._eval_subsYsE $.  FDDDDDT^DDDE E F Frc |j\}\}}}t|tfd|D}fd||fD\}}|||||fS)Nc.g|]}|jddiSnr&evalfr(idpsoptionss rr+z%Curve._eval_evalf..`s0888717,,S,G,,888rc.g|]}|jddiSr1r3r5s rr+z%Curve._eval_evalf..as0:::a))#))):::r)argsrtuplefunc)r!precr8r"tabr7s ` @r _eval_evalfzCurve._eval_evalf]sy 9Aq!$ 88888a888 9 9:::::Aq6:::1yyQ1I&&&rr>c|t|jSt||jd|jjjkr/jd|jDvrt djztfd|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 NTrealc3$K|] }|jV dSr)name)r(r"s r z(Curve.arbitrary_point..s$@@af@@@@@@rzFSymbol %s already appears in object and cannot be used as a parameter.c<g|]}|Sr&r')r(wr>tnews rr+z)Curve.arbitrary_point..s%???1qvva???r)r r,rr rF free_symbolsr)r!r r>rJs @@rarbitrary_pointzCurve.arbitrary_pointdsX  *$.) )y$.t<<< N I  B @@d.?@@@@ B57;yABB B????????@@rct}|j|jddzD] }||jz} ||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,rrK differencer )r!freer?s rrKzCurve.free_symbolssV,uu$+abb/1 # #A AN "DD/00 rc6t|jdS)a;The dimension of the curve. Returns ======= int : the dimension of curve. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve((t, t**2), (t, 0, 2)) >>> C.ambient_dimension 2 r)rr:r!s rambient_dimensionzCurve.ambient_dimensions*49Q<   rc|jdS)aThe functions specifying the curve. Returns ======= functions : list of parameterized coordinate functions. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve((t, t**2), (t, 0, 2)) >>> C.functions (t, t**2) See Also ======== parameter rr:rSs rr,zCurve.functions2y|rc|jdS)aThe limits for the curve. Returns ======= limits : tuple Contains parameter and lower and upper limits. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve([t, t**3], (t, -2, 2)) >>> C.limits (t, -2, 2) See Also ======== plot_interval rNrVrSs rrz Curve.limitsrWrc(|jddS)amThe curve function variable. Returns ======= Symbol : returns a bound symbol. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve([t, t**2], (t, 0, 2)) >>> C.parameter t See Also ======== functions rNrrVrSs rr zCurve.parameters2y|ArcttfdjD}t|jS)zThe curve length. Examples ======== >>> from sympy import Curve >>> from sympy.abc import t >>> Curve((t, t), (t, 0, 1)).length sqrt(2) c3TK|]"}t|jddzV#dS)rrN)rr)r(r<r!s rrGzCurve.length..,s8VVtT$ A77:VVVVVVr)rsumr,r r)r! integrands` rlengthz Curve.lengthsCVVVVt~VVVVVWW DK000rcpt||jd}|gt|jddzS)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 TrCrNN)rr listr)r!r r>s r plot_intervalzCurve.plot_interval/s:B It~D 9 9 9sT$+abb/****rrNc|rt|d }ntdd}|j|j}t|j}|dt dd|}|t|z}||dddf d|j }| }|j|jS)aThis function is used to rotate a curve along given point ``pt`` at given angle(in radian). Parameters ========== angle : the angle at which the curve will be rotated(in radian) in counterclockwise direction. default value of angle is 0. pt : Point the point along which the curve will be rotated. If no point given, the curve will be rotated around origin. Returns ======= Curve : returns a curve rotated at given angle along given point. Examples ======== >>> from sympy import Curve, pi >>> from sympy.abc import x >>> Curve((x, x), (x, 0, 1)).rotate(pi/2) Curve((-x, x), (x, 0, 1)) rdimrrNrN) r translater:r`r,appendr r r<tolistr)r!angleptrvr"s rrotatez Curve.rotateSs:  """"BBqB T^RW %     1aOO Yu   YYqBQBx((+T[ 9 9Sr|RW%%rrNc|rBt|d}|j| j||j|jS|j\}}|||z||zf|jS)a^Override GeometryEntity.scale since Curve is not made up of Points. Returns ======= Curve : returns scaled curve. Examples ======== >>> from sympy import Curve >>> from sympy.abc import x >>> Curve((x, x), (x, 0, 1)).scale(2) Curve((2*x, x), (x, 0, 1)) rrc)r rer:scaler,r<r)r!xyrifxfys rrmz Curve.scale}s{$  Orq!!!BD>4>RC:.44Q::DbgN NByy"Q$1t{333rc\|j\}}|||z||zf|jS)aLTranslate the Curve by (x, y). Returns ======= Curve : returns a translated curve. Examples ======== >>> from sympy import Curve >>> from sympy.abc import x >>> Curve((x, x), (x, 0, 1)).translate(1, 2) Curve((x + 1, x + 2), (x, 0, 1)) )r,r<r)r!rnrorprqs rrezCurve.translates2$Byy"q&"q&)4;777r)r.)r>)rN)rNrNN)rr)__name__ __module__ __qualname____doc__rr#r-rArLpropertyrKrTr,rr r^rarkrmrer&rrrrss33jMMM,,,FFF''''5A5A5A5AnX6!!X!,X4X4X4 1 1X 1"+"+"+"+H(&(&(&(&T44440888888rrN)rv(sympy.functions.elementary.miscellaneousr sympy.corersympy.core.containersrsympy.core.symbolrsympy.geometry.entityrrsympy.geometry.pointr sympy.integralsr sympy.matricesr r sympy.utilities.iterablesr mpmath.libmp.libmpfrrr&rrrs:99999''''''%%%%%%========&&&&&&%%%%%%,,,,,,,,111111++++++R8R8R8R8R8KR8R8R8R8R8r