Interpolation using scattered query points

2019 8 9
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更新时间：2019 8 9
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Hi
It is straight forward to use interpn or griddedInterpolant to perform n-dim interpolation. However, in these functions, the query points must be on a full grid. Is it possible to perform interpolation on a scattered set of query points?
As an example, for 2D interpolation, I don't want to perform interpolation on a full xy grid. I just want to perform interpolation on a set of points {(x1,y1), (x2,y2), (x3,y3), ...}. I know it can be done using a loop, but I was looking for a faster and more efficient vectorized solution.
The question at the link below is similar to my question, but the answer didn't give a vectorized solution.
https://www.mathworks.com/matlabcentral/answers/336027-interpolation-in-an-image-at-specific-query-points
Thanks

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the cyclist
the cyclist 2019-8-9

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I believe the solution you point to can be trivially vectorized:
load clown ;
imagesc(X);
colormap gray ;
[nx,ny] = size(X) ;
r = 1:ny ;
c = 1:nx ;
[R,C] = meshgrid(r,c) ;
%%do interpolation
Ri = [5 6]; Ci = [5 7]; % <------- I VECTORIZED THE CODE RIGHT HERE.
Xi1 = interp2(R,C,X,Ri,Ci) ;
% or can be used without mesh grid like below
Xi2 = interp2(r,c,X,Ri,Ci) ;

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Hesham
Hesham 2019-8-9
编辑：Hesham 2019-8-9
Thanks for your answer. But the code you provided will actually interpolate on the full grid, i.e., it will yield the result for 4 query points (5,5) (5,7) (6,5) (6,7).
What I actually need is similar to MATLAB's element wise operations. I just need the first element in Ri with first element in Ci, the 2nd with the 2nd, and so on, i.e., (5,5) and (6,7) only.
For two data points the question seems trivial, but I actually need to perform interpolation on a set of thousand specific query points that are not on a grid. Again, a loop will do the job, but I was looking for a faster solution.
Hesham
Hesham 2019-8-9
Here is a sample of a code that does NOT do what I need. I just need (1,3) and (2,4).
[x,y] = ndgrid(0:1:10);
z = x.^2 + y.^2;
F = griddedInterpolant(x,y,z);
xq = [1 2];
yq = [3 4];
vq = F({xq,yq'})
vq =
10 17
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the cyclist
the cyclist 2019-8-9
编辑：the cyclist 2019-8-9
Hm. For me, the output of the code I posted yields two points.
Xi1 = [61 55];
I wonder if it is a version issue? I am using R2019a.
Hesham
Hesham 2019-8-9
It turned out that the answer is quite simple! The code below works as I need.
@the cyclist: Many thanks for pointing out the solution is trivial!
[x,y] = ndgrid(0:1:10);
z = x.^2 + y.^2;
F = griddedInterpolant(x,y,z);
vq = F([1 3; 2 4])

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