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Member Since 28 Nov 2012
Offline Last Active Dec 04 2012 10:03 AM

Topics I've Started

Compute volume from mesh Mathematical demonstration

29 November 2012 - 02:14 AM


I start a new topic from an older because I have a tiebreaker !
the older topic : http://www.gamedev.n...ume-for-a-mesh/

My question is: How can we prove the formula V= sum(each tetrahedron volume with the origin)
[source lang="cpp"]float volume = 0;int* index = I;for (i = 0; i < T; i++){ Vector3 v0 = V[*index++]; Vector3 v1 = V[*index++]; Vector3 v2 = V[*index++]; volume += Dot(v0,Cross(v1,v2));}volume /= 6;[/source]

I know I must use 3D integrals and Fourier moments but I don't know how I can do that !
Please someone give me some clues about a possible math proof ?

Thanks by advance

PS: I already try to find this formula with the gauss theorem as said in the older topic but I never find the result but an approximate result! I obtain the formuma here but with some addition in more...