\h'SrSSKJr SSKJr SSKJr SSKJr SSK J r J r SSK J r SSKJr SS KJrJr SS KJr SS KJr "S S \ 5rg)zCCurves in 2-dimensional Euclidean space. Contains ======== Curve )sqrt)diff)Tuple)_symbol)GeometryEntity GeometrySet)Point) integrate)Matrix rot_axis3) is_sequence) prec_to_dpsc\rSrSrSrSrSrSrSSjrSSjr \ S5r \ S 5r \ S 5r \ S 5r\ S 5r\ S 5rSSjrSSjrSSjrSSjrSrg)CurveaA 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 c"[U5(a[U5S:wa[S[U5-5e[U5(a[U5S:wa[S[U5-5e[R "U[ U6[ U65$)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 L/var/www/auris/envauris/lib/python3.13/site-packages/sympy/geometry/curve.pyr Curve.__new__Ls8$$H (:"8}-. .6""c&kQ&6"6{+, ,%%c5(+;UF^LLc:URURU5$N)subs parameter)selffs r__call__Curve.__call__Vsyy++rc XR:Xa1[URVs/sHo3RX5PM sn6$gs snfr )r"r functionsr!)r#oldnewr$s r _eval_subsCurve._eval_subsYs9 .. T^^D^66#+^DE E !DsAc URunupEn[U5n[UVs/sHoR"SSU0UD6PM sn5nXV4Vs/sHoR"SSU0UD6PM snupVUR X4XV45$s snfs snf)Nn)argsrtupleevalffunc) r#precoptionsr$tabdpsis r _eval_evalfCurve._eval_evalf]syy 9A!$ a8a77,S,G,a8 9456:6a)#))6:yyI&&9:s BB c ~Uc[UR6$[XRSS9nURnURUR:wa9URSUR 5;a[ SUR-5e[URVs/sHoDRX25PM sn6$s snf)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 Trealc38# UHoRv M g7fr )name).0r$s r (Curve.arbitrary_point..s@.?ff.?szFSymbol %s already appears in object and cannot be used as a parameter.)r r(rr"rA free_symbolsrr!)r#r"tnewr6ws rarbitrary_pointCurve.arbitrary_pointdsX  $..) )y..t< NN II  @d.?.?@@57;yyAB B?1vva?@@?sB:c[5nURURSS-HnXR-nM UR UR 15nU$)aTReturn 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(rrE differencer")r#freer7s rrECurve.free_symbolssN,u$++ab/1A NN "D2/0 rc2[URS5$)zThe 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)rr0r#s rambient_dimensionCurve.ambient_dimensions*499Q<  rc URS$)aThe functions specifying the curve. Returns ======= functions : list of parameterized coordinate functions. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve((t, t**2), (t, 0, 2)) >>> C.functions (t, t**2) See Also ======== parameter rr0rQs rr(Curve.functions2yy|rc URS$)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 rKrUrQs rr Curve.limitsrWrc&URSS$)zThe curve function variable. Returns ======= Symbol : returns a bound symbol. Examples ======== >>> from sympy.abc import t >>> from sympy import Curve >>> C = Curve([t, t**2], (t, 0, 2)) >>> C.parameter t See Also ======== functions rKrrUrQs rr"Curve.parameters2yy|Arc^[[U4SjTR555n[UTR5$)zThe curve length. Examples ======== >>> from sympy import Curve >>> from sympy.abc import t >>> Curve((t, t), (t, 0, 1)).length sqrt(2) c3\># UH!n[UTRS5S-v M# g7f)rrN)rr)rBr3r#s rrCCurve.length..,s%V~tT$ A7:~s),)rsumr(r r)r# integrands` rlength Curve.lengths/Vt~~VVW DKK00rcb[XRSS9nU/[URSS5-$)a;The plot interval for the default geometric plot of the curve. Parameters ========== parameter : str or Symbol, optional Default value is 't'; otherwise the provided symbol is used. Returns ======= List : the plot interval as below: [parameter, lower_bound, upper_bound] Examples ======== >>> from sympy import Curve, sin >>> from sympy.abc import x, s >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval() [t, 1, 2] >>> Curve((x, sin(x)), (x, 1, 2)).plot_interval(s) [s, 1, 2] See Also ======== limits : Returns limits of the parameter interval Tr>rKN)rr"listr)r#r"r6s r plot_intervalCurve.plot_interval/s1B I~~D 9sT$++ab/***rNcU(a [USS9*nO [SS5nUR"UR6n[UR5nUR S5 [ SSU5nU[U5-nURUSSS24R5SUR5nU*nUR"UR6$)afThis function is used to rotate a curve along given point ``pt`` at given angle(in radian). Parameters ========== angle : the angle at which the curve will be rotated(in radian) in counterclockwise direction. default value of angle is 0. pt : Point the point along which the curve will be rotated. If no point given, the curve will be rotated around origin. Returns ======= Curve : returns a curve rotated at given angle along given point. Examples ======== >>> from sympy import Curve, pi >>> from sympy.abc import x >>> Curve((x, x), (x, 0, 1)).rotate(pi/2) Curve((-x, x), (x, 0, 1)) rdimrrKrN) r translater0rdr(appendr r r3tolistr)r#angleptrvr$s rrotate Curve.rotateSs: ""BqB ^^RWW %    1aO Yu  YYqBQBx(+T[[ 9S||RWW%%rcU(aJ[USS9nUR"U*R6RX5R"UR6$URupEUR XA-XR-4UR 5$)aOverride 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)) rrh)r rjr0scaler(r3r)r#xyrnfxfys rrs Curve.scale}sj$ rq!B>>RC::.44Q:DDbggN Nyy"$t{{33rcbURup4URX1-XB-4UR5$)zTranslate 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)r#rtrurvrws rrjCurve.translates-$yy"&"&)4;;77rr/))r6)rN)rKrKN)rr)__name__ __module__ __qualname____firstlineno____doc__rr%r+r;rHpropertyrErRr(rr"rarerprsrj__static_attributes__r/rrrrs3jM,F'5An6!!,444 1 1"+H(&T408rrN)r(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/rrrs8:'%=&%,1+R8KR8r