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

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SUMMARY

The discussion focuses on measuring the area of an irregularly shaped tunnel that changes over time. The user seeks methods to approximate the area using available measurements of width at various points along the tunnel's length. Suggestions include utilizing approximation methods for definite integrals and considering Monte Carlo simulations for statistical analysis. The conversation emphasizes the need for practical measurement techniques to determine if the tunnel's area is decreasing.

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  • Understanding of definite integrals and approximation methods
  • Familiarity with Monte Carlo simulation techniques
  • Basic knowledge of statistical analysis
  • Ability to perform measurements of length and width in irregular shapes
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  • Research approximation methods for definite integrals
  • Learn about Monte Carlo simulation applications in area estimation
  • Explore statistical techniques for analyzing area changes over time
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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.
 

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