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66 lines
1.6 KiB
Python
66 lines
1.6 KiB
Python
import math as m
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from typing import Callable, Union
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def line_length(
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fnc: Callable[[Union[int, float]], Union[int, float]],
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x_start: Union[int, float],
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x_end: Union[int, float],
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steps: int = 100,
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) -> float:
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"""
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Approximates the arc length of a line segment by treating the curve as a
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sequence of linear lines and summing their lengths
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:param fnc: a function which defines a curve
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:param x_start: left end point to indicate the start of line segment
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:param x_end: right end point to indicate end of line segment
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:param steps: an accuracy gauge; more steps increases accuracy
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:return: a float representing the length of the curve
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>>> def f(x):
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... return x
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>>> f"{line_length(f, 0, 1, 10):.6f}"
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'1.414214'
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>>> def f(x):
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... return 1
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>>> f"{line_length(f, -5.5, 4.5):.6f}"
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'10.000000'
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>>> def f(x):
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... return m.sin(5 * x) + m.cos(10 * x) + x * x/10
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>>> f"{line_length(f, 0.0, 10.0, 10000):.6f}"
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'69.534930'
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"""
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x1 = x_start
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fx1 = fnc(x_start)
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length = 0.0
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for i in range(steps):
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# Approximates curve as a sequence of linear lines and sums their length
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x2 = (x_end - x_start) / steps + x1
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fx2 = fnc(x2)
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length += m.hypot(x2 - x1, fx2 - fx1)
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# Increment step
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x1 = x2
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fx1 = fx2
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return length
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if __name__ == "__main__":
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def f(x):
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return m.sin(10 * x)
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print("f(x) = sin(10 * x)")
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print("The length of the curve from x = -10 to x = 10 is:")
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i = 10
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while i <= 100000:
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print(f"With {i} steps: {line_length(f, -10, 10, i)}")
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i *= 10
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