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

[Yankel]

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 !

 

[MarkFL]

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.