trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. it approximates the value of a function at an intermediate point formula_1 within the local axial rectangular prism linearly, using function data on the lattice points. for an arbitrary, unstructured mesh (as used in finite element analysis), other methods of interpolation must be used; if all the mesh elements are tetrahedra (3d simplices), then barycentric coordinates provide a straightforward procedure.