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interp3 - 3-D data interpolation (table lookup)

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. Otherwise, this method is the same as 'spline'.

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

See Also

interp1, interp1q, interp2, interpn, meshgrid

interp2

interpft

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