[vtkusers] Re: Volume of a tetrahedron

[Pearu Peterson]

On Wed, 6 Jun 2001 anast.jm at pg.com wrote:

> 
> The definition I have (CRC Standard Math Tables and Formulae) states volume of a
> tetrahedron
>  with one vertex at the origin and the other vertices at        x1y1z1    x2y2z2
> x3y3z3
> 
>         | x1 y1 z1 |
> v= 1/6  | x2 y2 z2 |
>         | x3 y3 z3 |
> 
> so it seems to me the W matrix in Peter's simplified equation below should be
> 
> W=[p2-p1, p3-p1, p4-p1] so as to translate all points relative to p1 as the
> origin.
> 
> I'm a little rusty so perhaps I missed something???

You are right, of course. I don't know why I did those two stupied
mistakes in my original posting. I was just translating the general
formula
	volume of a k-simplex in n-dimensions =
		sqrt(|det(W * W^T)|)/k!
where 
	W = [v1-v0,v2-v0,..,vk-v0]
into 3D without thinking and doublechecking.

Thanks you both for corrections,
	Pearu