Trilinear interpolation is a method of
multivariate interpolation
In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable; when the variates are spatial coordinates, it is also known as spatial interpolation.
The function to be interpolated is known at given po ...
on a
3-dimensional regular grid. It approximates the value of a function at an intermediate point
within the local axial rectangular
prism linearly, using function data on the lattice points. For an arbitrary,
unstructured mesh (as used in
finite element
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical models, mathematical modeling. Typical problem areas of interest include the traditional fields of struct ...
analysis), other methods of interpolation must be used; if all the mesh elements are
tetrahedra
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...
(3D
simplices), then
barycentric coordinates provide a straightforward procedure.
Trilinear interpolation is frequently used in
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...
,
data analysis
Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, en ...
, and