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## Main Question or Discussion Point

Hello,

I'm trying to calculate the volume of a hexahedron. I know how to do this for any arbitrary hexahedron as long as the 4 points of each face are coplanar (by using shape functions to calculate the Jacobian in a parametric space or using 5 tetrahedrons). However, the catch is that two of the faces are not coplanar. Two of the faces opposite of each other are not coplanar while the 4 surrounding sides are. If it is MUCH easier to do this computation with only one side non-coplanar, then I'd still be interested in that as well.

I know the location of all 8 vertices, but I can't figure out how to get the area of the non-coplanar hexahedron.

The non-coplanar surfaces would be doubly ruled surfaces as the one shown below:

http://upload.wikimedia.org/wikipedia/commons/0/01/Hyperbolic-paraboloid.svg" [Broken]

Thanks,

Scott

I'm trying to calculate the volume of a hexahedron. I know how to do this for any arbitrary hexahedron as long as the 4 points of each face are coplanar (by using shape functions to calculate the Jacobian in a parametric space or using 5 tetrahedrons). However, the catch is that two of the faces are not coplanar. Two of the faces opposite of each other are not coplanar while the 4 surrounding sides are. If it is MUCH easier to do this computation with only one side non-coplanar, then I'd still be interested in that as well.

I know the location of all 8 vertices, but I can't figure out how to get the area of the non-coplanar hexahedron.

The non-coplanar surfaces would be doubly ruled surfaces as the one shown below:

http://upload.wikimedia.org/wikipedia/commons/0/01/Hyperbolic-paraboloid.svg" [Broken]

Thanks,

Scott

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