maths.line_length
=================

.. py:module:: maths.line_length


Functions
---------

.. autoapisummary::

   maths.line_length.f
   maths.line_length.line_length


Module Contents
---------------

.. py:function:: f(x)

.. py:function:: line_length(fnc: collections.abc.Callable[[float], float], x_start: float, x_end: float, steps: int = 100) -> float

   Approximates the arc length of a line segment by treating the curve as a
   sequence of linear lines and summing their lengths
   :param fnc: a function which defines a curve
   :param x_start: left end point to indicate the start of line segment
   :param x_end: right end point to indicate end of line segment
   :param steps: an accuracy gauge; more steps increases accuracy
   :return: a float representing the length of the curve

   >>> def f(x):
   ...    return x
   >>> f"{line_length(f, 0, 1, 10):.6f}"
   '1.414214'

   >>> def f(x):
   ...    return 1
   >>> f"{line_length(f, -5.5, 4.5):.6f}"
   '10.000000'

   >>> def f(x):
   ...    return math.sin(5 * x) + math.cos(10 * x) + x * x/10
   >>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
   '69.534930'