From Ohm

# Marching Tetrahedra

Observation:

Within in the domain of a tetrahedron the interpolated scalar value is linear function due to the barycentric interpolation. Therefore the gradient resp. normal vector is a constant vector.

Conclusion:

The iso surface within the tetrahedron must be a planar surface patch, which is defined by the intersections of the iso surface with the edges of the tetrahedron.