[quote name='joohooo' timestamp='1354205457' post='5005341']
Yes So it doesn't prove my formula with vertices ??
The aim of this formula is to not use distance but just vertices to gain time !
Why not?
For tetrahedron: A*d/3 == Det(v1-v0,v2-v0,v3-v0)/6, where 'A' is the area of some triangle and 'd' is the distance from the opposing vertex to the plane of the triangle. In the Det formula v1,v2,v3 define the same triangle, while v0 is the opposing vertex.
[/quote]
One more time thanks !
But ... I have one more question?? (yes again)
I agree with you for the Det but in the proof we have already use the origin for x0 ! Or in my formula the origin will be your V0 in the det formula as the opposing vertex for each triangle in the mesh. It's not a wrong thing to use the origin for the X0 in F and for the opposing vertex. In my mind , it's look like a ruse... no ?