Grid Creation Functions

Themeshgridandndgridfunctions create grids of various dimensionality.meshgridcan create 2-D or 3-D grids, whilendgridcan create grids with any number of dimensions. These functions return grids using different output formats. You can convert between these grid formats using thepagetranspose(as of R2020b) orpermutefunctions to swap the first two dimensions of the grid.

Interpolation Functions

Theinterpfamily of functions includesinterp1,interp2,interp3, andinterpn. Each function is designed to interpolate data with a specific number of dimensions.interp2andinterp3use grids inmeshgridformat, whileinterpnuses grids inndgridformat.

Interpolation Objects

griddedInterpolantobjects support interpolation in any number of dimensions for data inndgridformat. 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 usinggriddedInterpolantobjects over theinterpfunctions.griddedInterpolantoffers substantial performance improvements for repeated queries of the interpolant object, whereas theinterpfunctions perform a new calculation each time they are called. Also,griddedInterpolantstores the sample points in a memory-efficient format (as acompact grid) and is multithreaded to take advantage of multicore computer processors.

Full Grid

Afull gridis one in which all points are explicitly defined. The outputs ofndgridandmeshgriddefine a full grid. You can create full grids that areuniform, in which points in each dimension have equal spacing, ornonuniform, 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 3 Y = 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. Thecompact gridrepresentation is a way to dispense with the memory overhead of a full grid. The compact grid representation stores onlygrid vectors(one for each dimension) instead of the full grid. Together, the grid vectors implicitly define the grid. In fact, the inputs formeshgridandndgridare 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 = 1:3andx2 = 1:5. You can think of these vectors as a set of coordinates in thex1direction and a set of coordinates in thex2direction, like so:

每一个箭头指向的位置。您可以使用这些two vectors to define a set of grid points, where one set of coordinates is given byx1and the other set of coordinates is given byx2. When the grid vectors are replicated, they form two coordinate arrays that make up the full grid:

Your input grid vectors might bemonotonicornonmonotonic. 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. Thesortfunction 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 adefault gridrepresentation 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.