在Matlab中通过插值3D矩阵的层获取插值后的2D矩阵

Great question! Your manual linear interpolation approach is totally correct for this simple case, but MATLAB has built-in functions that can make this task cleaner, more efficient, and easier to scale if you ever need to interpolate multiple points or use different interpolation methods later.

Method 1: Using interp1 (Simplest for 3D layer interpolation) #

interp1 is designed for 1D interpolation, but you can specify the dimension to interpolate along (in this case, the 3rd dimension of your matrix). This is perfect for your use case since you're only interpolating between two layers along the z-axis.

Here's how to implement it:

A = zeros(3,3,3)*3; 
A(:,:,1) = [1 2 3; 3 2 1; 3 4 7]; 
A(:,:,2) = [4 5 6; 6 5 4; 2 5 8]; 
A(:,:,3) = [7 8 9; 9 8 7; 3 6 9];

l = 1;          % Starting layer (1 <= l <= size(A,3)-1)
x = 0.75;       % Interpolation position (0 = layer l, 1 = layer l+1)

% Define the node positions (layer indices)
nodes = [l, l+1];
% Calculate the exact query position along the 3rd dimension
query_pos = l + x;

% Perform linear interpolation along the 3rd dimension
interp_result = interp1(nodes, A, query_pos, 'linear', 'extrap', 'dim', 3);

Running this will give you exactly the 2D matrix you expected:

3.25  4.25  5.25
5.25  4.25  3.25
2.25  4.75  7.75

The 'dim', 3 argument tells interp1 to interpolate along the third dimension, and since linear interpolation is the default, you could even omit the 'linear' parameter if you want.

Method 2: Using interpn (More flexible for multi-dimensional interpolation) #

If you ever need to interpolate across multiple dimensions (not just layers), interpn is the way to go. It handles n-dimensional interpolation seamlessly, and works great here too:

% Create grid coordinates for your 3D matrix
[X,Y,Z] = meshgrid(1:size(A,2), 1:size(A,1), 1:size(A,3));

% Define the query position: keep X/Y the same as original, set Z to l + x
query_Z = l + x;
[Xq,Yq,Zq] = meshgrid(1:size(A,2), 1:size(A,1), query_Z);

% Perform multi-dimensional linear interpolation
interpn_result = interpn(X,Y,Z,A,Xq,Yq,Zq,'linear');
% Remove the singleton 3rd dimension to get a 2D matrix
interpn_result = squeeze(interpn_result);

This will produce the same result as the interp1 method, but it's more flexible if you ever need to interpolate at arbitrary (x,y,z) points instead of just fixed layers.

Why these methods are better than manual interpolation #

• Scalability: If you need to interpolate at multiple positions (e.g., 25%, 50%, 75% between layers), you can just pass a vector of query positions instead of repeating the manual calculation.
• Optimization: MATLAB's built-in interpolation functions are optimized for speed, especially with large matrices—they'll outperform manual element-wise operations in most cases.
• Flexibility: You can easily switch to other interpolation methods (like cubic or spline) by changing the method parameter (e.g., 'cubic' instead of 'linear').

内容的提问来源于stack exchange，提问作者Federico Gentile