hi xavier,

sum the determinants of the (coords of the vertices of the) triangles.
if the surface is closed and oriented, the sum is the volume
(or the negative of it) multiplied by 6 (= 3! in 3D).

marco

From: Xavier Pennec <Xavier.Pennec@inria.fr>
To: therion@speleo.sk
Sent: Wednesday, February 27, 2013 1:02 PM
Subject: Re: [Therion] the volume of a cave

Dear Marco,

Could you expand on how you computed the volume from the dxf file?
I would be very interested to perform that for (no so small) mines!

Thanks

Xavier


Le 27/02/2013 11:37, Marco Corvi a écrit :
hi,

it just happened that i was asked to estimate the volume of a "cave"
(actually a small mine).

therion dxf export is a triangulated surface of the cave wall.
if the surface were oriented
it would be extremely easy to compute the volume.
(the surface of a real cave is always orientable: no klein cave).

all recent versions of therion produce nice-looking dxf.
i tried 5.3.5 and the volume seemed reasonable.
then i tried 5.3.11 and i got an unreasonable value (there is also
a commented option for new 3d, and the result was even more unreasonable).

so i checked the dxf files.
it seems that none of them is oriented.
is it possible to make therion produce an oriented surface?
thanks.

marco



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