trilinear interpolation is the extension of linear interpolation, which operates in spaces with dimension formula_2, and bilinear interpolation, which operates with dimension formula_3, to dimension formula_4. these interpolation schemes all use polynomials of order 1, giving an accuracy of order 2, and it requires formula_5 adjacent pre-defined values surrounding the interpolation point. there are several ways to arrive at trilinear interpolation, which is equivalent to 3-dimensional tensor b-spline interpolation of order 1, and the trilinear interpolation operator is also a tensor product of 3 linear interpolation operators.