Python/maths/line_length.py
Sharan Krishnan e25d4248a3 Added an algorithm that approximates line lengths (#1692)
* A recursive insertion sort

* added doctests and typehints

* Added arc length and numerical integration calculators

* fixed doc test

* Fixed some conversion errors

* Fixed some commenting

* Deleted numerical integration to allow 1 file per push

* Changed string formatting method
2020-01-19 01:25:27 +08:00

62 lines
1.7 KiB
Python

from typing import Callable, Union
import math as m
def line_length(fnc: Callable[[Union[int, float]], Union[int, float]],
x_start: Union[int, float],
x_end: Union[int, 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 m.sin(5 * x) + m.cos(10 * x) + x * x/10
>>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
'69.534930'
"""
x1 = x_start
fx1 = fnc(x_start)
length = 0.0
for i in range(steps):
# Approximates curve as a sequence of linear lines and sums their length
x2 = (x_end - x_start) / steps + x1
fx2 = fnc(x2)
length += m.hypot(x2 - x1, fx2 - fx1)
# Increment step
x1 = x2
fx1 = fx2
return length
if __name__ == "__main__":
def f(x):
return m.sin(10*x)
print("f(x) = sin(10 * x)")
print("The length of the curve from x = -10 to x = 10 is:")
i = 10
while i <= 100000:
print(f"With {i} steps: {line_length(f, -10, 10, i)}")
i *= 10