How Can You Measure an Irregularly Shaped Tunnel's Area Over Time?

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In summary, the individual is seeking a way to measure the changing area of a tunnel which does not have a defined shape. They can provide the distance between any two points and the width at various points along the length. They are considering using statistical methods such as monte carlo simulation to approximate the area. They are open to ideas for a practical measure.
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Yankel
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Hello all

I have a tricky problem, maybe you can give me some ideas.

In the attached picture, there is a drawing of a shape, it is some sort of a tunnel, or channel.

This tunnel's area is varying in time, and I am looking for a way to measure it's area, so I can analyze the change over time. The problem is, it does not have a defined shape, not a geometric one, for area formulas, and not a functional one for the use of integrals or numerical evaluation of them.

What I CAN provide, is the distance between any two points in the tunnel. For instance, I can measure the length of the tunnel, approximately (!). I can also measure the width at any point, so basically I can measure the width at varying points, along the length (see arrows).

View attachment 1487

I am looking for a way to approximate the area of the tunnel, so I can know if it's "shrinking" or not. I was thinking maybe about statistical ways, like monte carlo simulation, but I am not sure I am even on the right direction here. Maybe you can give me some ideas for a practical measure ?

Thanks !
 

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If you know the width at any point, or set of discrete places, then you can use any of the approximation methods for definite integrals.
 

FAQ: How Can You Measure an Irregularly Shaped Tunnel's Area Over Time?

1. What is "approximating irregular area"?

"Approximating irregular area" refers to the process of estimating the total surface area of a shape or object that does not have a regular, easily calculable shape. This can include complex shapes, curved edges, and irregular boundaries.

2. Why is approximating irregular area important?

Approximating irregular area is important in many scientific fields, such as engineering, architecture, and environmental science. It allows for accurate measurements of objects and landscapes, which can be used for planning, design, and analysis purposes.

3. What are some methods for approximating irregular area?

There are several methods for approximating irregular area, including the trapezoidal rule, Simpson's rule, and the Monte Carlo method. These methods use different mathematical formulas and algorithms to estimate the area based on known data points or randomly generated points within the shape.

4. How accurate are these methods for approximating irregular area?

The accuracy of these methods can vary depending on the complexity of the shape and the number of data points used. Generally, the more data points that are used, the more accurate the approximation will be. Some methods, such as the Monte Carlo method, can provide a more precise estimate but may require more computational power.

5. Are there any limitations to approximating irregular area?

Yes, there are limitations to approximating irregular area. These methods are based on estimations and assumptions, so they may not provide an exact measurement of the area. Additionally, the accuracy of the approximation can be affected by factors such as the shape's complexity, the quality of data points, and the chosen method.

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