class_docstr: 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
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docstr: A 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
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code: def arbitrary_point(self, parameter="t"):
      """A 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
  
      """
      if parameter is None:
          return Point(*self.functions)
  
      tnew = _symbol(parameter, self.parameter, real=True)
      t = self.parameter
      if tnew.name != t.name and tnew.name in (
          f.name for f in self.free_symbols
      ):
          raise ValueError(
              "Symbol %s already appears in object "
              "and cannot be used as a parameter." % tnew.name
          )
      return Point(*[w.subs(t, tnew) for w in self.functions])
  
imports: from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.core import diff
  from sympy.core.containers import Tuple
  from sympy.core.symbol import _symbol
  from sympy.geometry.entity import GeometryEntity, GeometrySet
  from sympy.geometry.point import Point
  from sympy.integrals import integrate
  from sympy.matrices import Matrix, rot_axis3
  from sympy.utilities.iterables import is_sequence
  from mpmath.libmp.libmpf import prec_to_dps
label_desc: Use image node_id 5 for calling the Curve obj's underlying member method code with example usage: obj.arbitrary_point(parameter) and returns: Point, Point