[SciPy-user] Approximate volume of an irregular triangular mesh.

Nathan Bell wnbell@gmail....
Tue Feb 17 12:59:41 CST 2009

On Tue, Feb 17, 2009 at 10:48 AM, Dharhas Pothina
<Dharhas.Pothina@twdb.state.tx.us> wrote:
> I want to calculate the approximate volume of this mesh. The brute force way
> is to cycle through each triangular element and calculate the area of each
> triangle and multiply it by the average depth of the three nodes of the element.
> I was wondering if there was a simpler way maybe by just using the surface
> defined by the nodes and ignoring the connectivity.

Look at "Subject 2.01: How do I find the area of a polygon?" here:

This requires that the edges are consistently oriented (e.g. counter
clockwise around the perimeter)

Interestingly, you can apply a similar trick in higher dimensions, and
even compute things like the center of mass and inertia tensor.

Ultimately, it boils down to the fact that you can replace volume
integrals with a surface integrals using the divergence theorem.

Nathan Bell wnbell@gmail.com

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