Editing Trilinear interpolation (section)

== Related methods ==

Trilinear interpolation is the extension of [[linear interpolation]], which operates in spaces with [[dimension]] <math>D = 1</math>, and [[bilinear interpolation]], which operates with dimension <math>D = 2</math>, to dimension <math>D = 3</math>. These interpolation schemes all use polynomials of order 1, giving an accuracy of order 2, and it requires <math>2^D = 8</math> 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.

For an arbitrary, [[unstructured grid|unstructured mesh]] (as used in [[finite element]] analysis), other methods of interpolation must be used; if all the mesh elements are [[tetrahedron|tetrahedra]] (3D [[simplex|simplices]]), then [[barycentric_coordinates_(mathematics)#Barycentric_coordinates_on_tetrahedra|barycentric coordinates]] provide a straightforward procedure.