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Matlab interpolating or oversampling algorithm for transformed 3D image, preferably sinc interpolation

I have one 3D data set and one 2D data set, which is a slice of the first volume. They are on different scales, resolutions and in a different coordinate system, but as I know the affine transformation to world coordinates. Then I think I know how to apply them, but how can I return an image from these transformed coordinates again using sinc interpolation? I would like to know how to do it / how it works. The first comments below already pointed me to existing functions inside matlab that perform linear interpolation, but I would also like to know how to do it myself, so I can use sinc interpolation (and others).

I can get around the coordinates and get the values ​​for those that will be the nearest neighbor interpolation. I would like to lose as little information as possible, regardless of the computation time, I think I should use interpolation then. When I have the transformed coordinates, how do I make (e.g. sinc) an interpolation algorithm?

eg:

    %%get data
A = rand(200,250,250); % I want to get the slice from this that corresponds to B
B = rand(1200,1200); % I want to get the data from A that corresponds to the same pixels

    %%get coordinates for A
siza = size(A); clear xx;clear yy;clear zz;
[xx,yy,zz] = meshgrid(1:siza(1), 1:siza(2), 1:siza(3));
coora = [xx(:)';yy(:)';zz(:)'; ones(size(zz(:)))'];
    %%get coordinates for B
sizb = size(B); clear xx;clear yy;clear zz;
[xx,yy] = meshgrid(1:sizb(1),1:sizb(2)); zz = zeros(size(xx));
coorb = [xx(:)';yy(:)';zz(:)'; ones(size(zz(:)))'];

    %%define affine transformation matrices
T3d = [-0.02  0.02  1    -88 ;
       -0.98  0    -0.02  130;
        0     0.98 -0.02 -110;
        0     0     0     1  ];
T2d = [-0.2   0     0     126;
        0     0.2  -0.2  -131;
        0     0     2     43 ;
        0     0     0     1  ];

    %%transform A coordinates to world coordinates and world coordinates to B coordinates
cooraInBref = T3d*inv(T2d)*coora;
aslice = zeros(size(B));

    %% then nearest neighbor would go something like this (dont exactly know how to do this either):
cooraInBround = round(cooraInBref);
for idx = 1:length(coorb);
    if cooraInBround(3,idx) == 0
        aslice(cooraInBround(1,idx),cooraInBround(2,idx)) = ...;% dont know how to do this
    end
end
    %% how would I implement sinc interpolation instead of rounding the transformed coordinates

Related questions that do not help me further:

Matlab 3D data interpolation

Nearest Neighbor Interpolation Algorithm in MATLAB

Nearest Neighbor Interpolation in MATLAB

How to apply affine transformation (4x4 matrix) to ndgrid / meshgrid results?

Interpolate 2D Matrix Data

scattered data interpolation

Python / PIL affinity transformation

How to rotate a 3D matrix 90 degrees counterclockwise?

Resize a 3D image (and resample)

image conversion

Matlab, chappjc anonsubmitter85 cape code:

http://mathworks.com/help/matlab/math/interpolating-scattered-data.html

http://mathworks.com/help/matlab/ref/griddata.html?refresh=true

SE,

Interpolant, , , NaN, .

+2
1

: 2d , 3- , interp3 . . , , , . , sinc.

%% transformation from one image to the other
Affine = inv(T2d)*T3d

%% get coordinates for B
sizb = size(B); clear xx;clear yy;clear zz;
[xx,yy] = meshgrid(1:sizb(1),1:sizb(2)); 
zz = ones(size(xx));
coorb = [xx(:)';yy(:)';zz(:)'; ones(size(zz(:)))'];

%% transformed coordinates
coorb_t = Affine*coorb;
idxX = reshape(coorb_t(:,1), sizb(1), sizb(2), 1);
idxY = reshape(coorb_t(:,2), sizb(1), sizb(2), 1);
idxZ = reshape(coorb_t(:,3), sizb(1), sizb(2), 1);

%% interpolate
Asliced = interp3(A, idxX, idxY, idxZ, 'cubic');

, Z.

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