Re: Water surface in hexahedron

macio wrote:
The irregular hexahedron is a kind of tank. It can be oriented at
different angles so water surface gets different areas (fitting to the
shape of the tank). So I have the vector normal to the surface I also
know the vertices of the tank. It is convex hexahedron for simplicity.
The shape of the water volume can be quite complicated - not only
tetrahedron. I can imagine polyhedra shape of the volume occupied by
water.
I think also that the volume of the water is one of the key data needed
to get the area of the surface of the water.


I don't think Babua is claiming that the volume you need is a
tetrahedron, but that it can be partitioned into tetrahedrons. It's the
3D analog of finding the area of an irregular convex polygon by
partitioning it into triangles and summing their areas.

Incidentally, I often find it easier to think about problems like this
after some transformations. In particular, I would rotate this one so
that the water surface is parallel to the x,y plane, with the normal
parallel to the z axis. Then forget about the normal, and think in terms
of horizontal slices.

Patricia
.

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