mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 23:11:09 +00:00
cecf43d648
* Pyupgrade to Python 3.9
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
68 lines
1.6 KiB
Python
68 lines
1.6 KiB
Python
from __future__ import annotations
|
|
|
|
import math
|
|
from typing import Callable
|
|
|
|
|
|
def line_length(
|
|
fnc: Callable[[int | float], int | float],
|
|
x_start: int | float,
|
|
x_end: 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 math.sin(5 * x) + math.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 += math.hypot(x2 - x1, fx2 - fx1)
|
|
|
|
# Increment step
|
|
x1 = x2
|
|
fx1 = fx2
|
|
|
|
return length
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
|
def f(x):
|
|
return math.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
|