Interpolate differently along different directions

I have a field (V) which is defined on a meshgrid X,Y,Z,V and a set of point on which I want the interpolated field, but I want it to be interpolated along x whith the nearest method (because of some conservation properties of the fields) and along z and y with the linear method is it possible? Can you provide a simple example. Thank you in advance

[Star Strider]

See if the interpn function will work to solve your problem. You apparently have a 4-D gridded matrix, and interpn may be appropriate for what I believe you want to do. See the documentation for examples.

[Andrea Somma]

The grid is 3d V is the value of the field on each point, interpn does not permit to split the interpolation method along coordinates as far as I know

Answer 1

[Aneela]

Hi Andrea,

“interpn” allows for interpolating within an N-dimensional space but assumes the same type of interpolation across all dimensions.

It does not support using different interpolation methods for different dimensions in a single call.

However, it is possible to interpolate along x with “nearest” method and along y and z with “linear” method manually.

Here’s a workaround:

[X, Y, Z] = meshgrid(1:10, 1:10, 1:10); % Original grid coordinates

V = sin(X) + cos(Y) + sin(Z);

% Define target points 

Xq = [3.5, 4.5, 5.5];

Yq = [2.5, 7.5, 4.5]; 

Zq = [1.5, 8.5, 5.5]; 

% Nearest interpolation along X

% For nearest neighbor along X, we find the closest X grid point for each query point

[~, idx] = min(abs(X(1,:,1) - Xq'), [], 2); % Find indices of nearest X grid points

Vq = zeros(size(Xq));

for i = 1:length(Xq)
    
    % Extract a 2D slice at the nearest X.
    
    V_slice = squeeze(V(:, idx(i), :));
    
    [Y_grid, Z_grid] = meshgrid(1:10, 1:10); 
    
    % Linear interpolation on the slice along Y and Z
    
    Vq(i) = interp2(Y_grid, Z_grid, V_slice, Yq(i), Zq(i), 'linear');
    
end

% Display the interpolated values

disp('Interpolated values at query points:');

Interpolated values at query points:

disp(Vq);

    0.7284   -0.4619   -1.1949