Interpolating Gridded Data - MATLAB & Simulink - MathWorks France (2024)

Grid Creation Functions

The meshgrid and ndgrid functions create grids of various dimensionality. meshgrid can create 2-D or 3-D grids, while ndgrid can create grids with any number of dimensions. These functions return grids using different output formats. You can convert between these grid formats using the pagetranspose (as of R2020b) or permute functions to swap the first two dimensions of the grid.

Interpolation Functions

The interp family of functions includes interp1, interp2, interp3, and interpn. Each function is designed to interpolate data with a specific number of dimensions. interp2 and interp3 use grids in meshgrid format, while interpn uses grids in ndgrid format.

Interpolation Objects

griddedInterpolant objects support interpolation in any number of dimensions for data in ndgrid format. These objects also support multivalued interpolation (as of R2021a), where each grid point can have multiple values associated with it.

There are memory and performance benefits to using griddedInterpolant objects over the interp functions. griddedInterpolant offers substantial performance improvements for repeated queries of the interpolant object, whereas the interp functions perform a new calculation each time they are called. Also, griddedInterpolant stores the sample points in a memory-efficient format (as a compact grid) and is multithreaded to take advantage of multicore computer processors.

Full Grid

A full grid is one in which all points are explicitly defined. The outputs of ndgrid and meshgrid define a full grid. You can create full grids that are uniform, in which points in each dimension have equal spacing, or nonuniform, in which the spacing varies in one or more of the dimensions. Uniform grids can have different spacing in each dimension, as long as the spacing is constant within each dimension.

An example of a uniform full grid is:

[X,Y] = meshgrid([1 2 3],[3 6 9 12])

X = 1 2 3 1 2 3 1 2 3 1 2 3Y = 3 3 3 6 6 6 9 9 9 12 12 12

Compact Grid

Explicitly defining every point in a grid can consume a lot of memory when you are dealing with large grids. The compact grid representation is a way to dispense with the memory overhead of a full grid. The compact grid representation stores only grid vectors (one for each dimension) instead of the full grid. Together, the grid vectors implicitly define the grid. In fact, the inputs for meshgrid and ndgrid are grid vectors, and these functions replicate the grid vectors to form the full grid. The compact grid representation enables you to bypass grid creation and supply the grid vectors directly to the interpolation function.

For example, consider two vectors, x1 = 1:3 and x2 = 1:5. You can think of these vectors as a set of coordinates in the x1 direction and a set of coordinates in the x2 direction, like so:

Each arrow points to a location. You can use these two vectors to define a set of grid points, where one set of coordinates is given by x1 and the other set of coordinates is given by x2. When the grid vectors are replicated, they form two coordinate arrays that make up the full grid:

Your input grid vectors might be monotonic or nonmonotonic. Monotonic vectors contain values that either increase in that dimension or decrease in that dimension. Conversely, nonmonotonic vectors contain values that fluctuate. If the input grid vector is nonmonotonic, such as [2 4 6 3 1], then [X1,X2] = ndgrid([2 4 6 3 1]) outputs a nonmonotonic grid. Your grid vectors should be monotonic if you intend to pass the grid to other MATLAB functions. The sort function is useful to ensure monotonicity.

Default Grid

In some applications, only the values at the grid points are important and not the distances between grid points. For example, most MRI scans gather data that is uniformly spaced in all directions. In cases like this, you can allow the interpolation function to automatically generate a default grid representation to use with the data. To do this, leave out the grid inputs to the interpolation function. When you leave out the grid inputs, the function automatically considers the data to be on a unit-spaced grid. The function creates this unit-spaced grid while it executes, saving you the trouble of creating a grid yourself.