Note In a future release, interp3 will not accept mixed combinations of row and column vectors for the sample and query grids. In addition, the following syntaxes will be removed or changed in a future release:

interp3(...,'cubic')
interp3(...,*METHOD)

For more information, and recommendations for updating your code, see Interpolation and Computational Geometry Functionality Being Removed or Changed.

Syntax

VI = interp3(X,Y,Z,V,XI,YI,ZI) VI = interp3(V,XI,YI,ZI) VI = interp3(V,ntimes) VI = interp3(...,method) VI = interp3(...,method,extrapval)

Description

VI = interp3(X,Y,Z,V,XI,YI,ZI) interpolates to find VI, the values of the underlying three-dimensional function V at the points in arrays XI, YI and ZI. XI,YI, ZI must be arrays of the same size, or vectors. Vector arguments that are not the same size, and have mixed orientations (i.e. with both row and column vectors) are passed through meshgrid to create the Y1, Y2, Y3 arrays. Arrays X, Y, and Z specify the points at which the data V is given. Out of range values are returned as NaN.

VI = interp3(V,XI,YI,ZI) assumes X=1:N, Y=1:M, Z=1:P where [M,N,P]=size(V).

VI = interp3(V,ntimes) expands V by interleaving interpolates between every element, working recursively for ntimes iterations. The command interp3(V) is the same as interp3(V,1).

VI = interp3(...,method) specifies alternative methods:

'`nearest`'	Nearest neighbor interpolation
'`linear`'	Linear interpolation (default)
'`spline`'	Cubic spline interpolation
'`cubic`'	Cubic interpolation, as long as data is uniformly-spaced. `interp3` switches to `'spline'` and issues a warning if the data is not equally spaced.

VI = interp3(...,method,extrapval) specifies a method and a value for VI outside of the domain created by X, Y and Z. Thus, VI equals extrapval for any value of XI, YI or ZI that is not spanned by X, Y, and Z, respectively. You must specify a method to use extrapval. The default method is 'linear'.

Discussion

All the interpolation methods require that X,Y and Z be monotonic and have the same format ("plaid") as if they were created using meshgrid. X, Y, and Z can be non-uniformly spaced. For faster interpolation when X, Y, and Z are equally spaced and monotonic, use the methods '*linear', '*cubic', or '*nearest'.

Examples

To generate a coarse approximation of flow and interpolate over a finer mesh:

[x,y,z,v] = flow(10); 
[xi,yi,zi] = meshgrid(.1:.25:10, -3:.25:3, -3:.25:3);
vi = interp3(x,y,z,v,xi,yi,zi); % vi is 25-by-40-by-25
slice(xi,yi,zi,vi,[6 9.5],2,[-2 .2]), shading flat

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interp3 - 3-D data interpolation (table lookup)