biVector forum

Volume of Triangle Meshes

Hello there!

I’ve tried to implemented the formulas for area and volume of triangle meshes, by testing them on a cube with side length 2. While the area is correct, the volume is twice as much as it should be:

https://enkimute.github.io/ganja.js/examples/coffeeshop.html#yitRh6KYI

Is there an error in the formula or in the implementation of it? It seems straightforward enough so that I should not have an error in the implementation?!

Cheers

The volume of a simplex with homogeneous point vertices v_1,\dots,v_n is computed as the formula \frac1{(n-1)!}\bigwedge_1^n v_i. In Grassmann.jl this formula works well for computing the volume of a simplex in any dimension. Given a mesh, it is computed by simply calling the detsimplex method.

@phew: You’re right, the volume formula on the 3D PGA cheat sheet should have the factor \frac16=\frac{1}{3!} instead of \frac13. That will be corrected soon. Thanks for pointing that out!

1 Like

Thanks for the quick reply! Looking forward to the fixed cheat sheet!

Cheat sheets have been updated. (I also included the norm-of-line-fix)

:+1:

2 Likes