griddata vs griddedinterpolant vs scatteredInterpolant for given data

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I wish to perform 2D interpolation of a data. The data is such that
X Y V
1 1 7
2 3 9
3 5 8
4 6 4
implying that V(1,1)= 7, V(2,3) =9, V(3,5)= 8 and V(4,6) = 4. I wish to find the values of V(1,3), V(1,5), V(1,6), V(2,1), V(2,5) and so on (basically all V(i,j), i not equal to j).
Since interp2 requires meshgrid format, from my reading of documentation, i guess that interp2 might not be a suitable function to use. Is it correct?
What is difference between griddata, griddedinterpolant and scatteredInterpolant to use for interpolation of this data? Can i use all of them for interpolation of such data givn above, how do I determine which is the most suitable to use for the above data
At the link 2D interpolation of data - MATLAB Answers - MATLAB Central (mathworks.com), scatteredInterpolant is suggested for interpolation. What if i use griddata or griddedinterpolant. Can i use it, what will be the difference?

Accepted Answer

Walter Roberson
Walter Roberson on 2 Nov 2022
griddedInterpolant -- if you do not pass in vector x and vector v (1D case) -- if you have 2 or more dimensions -- then the input coordinates must be in full gridded form, not individual samples.
griddata -- always x, y, v (scattered 2d input coordinates plus corresponding outputs). 'nearest', 'linear', 'natural', 'cubic', or 'v4' available
scatteredInterpolant -- can be scattered x, y, v, or can be scattered x, y, z, v . 'nearest', 'linear', or 'natural' available.
griddata() internally calls scatteredInterpolant for 'nearest', 'linear', and 'natural' options -- which is not a documented point and so is hypothetically subject to change.
  6 Comments
Bruno Luong
Bruno Luong on 2 Nov 2022
@Walter Roberson "griddata is always griddata(x, y, v, xq, yq, then options, and never supports griddata(x, y, z, v, xq, yq, zq"
Hmm... But The doc mentions
"Syntax

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More Answers (2)

Bruno Luong
Bruno Luong on 2 Nov 2022
Edited: Bruno Luong on 2 Nov 2022
gridded data interpolant (A set of points that are axis-aligned and ordered, generated by meshgrid/ndgrid on monotonic grid vectors ) are just like what required by interp2, so it's out since your data doesn't meet that requirement.
They are just different implementation, some of them perform interpolation in 2 steps for better workflow if needed.
  1 Comment
Bruno Luong
Bruno Luong on 2 Nov 2022
Edited: Bruno Luong on 2 Nov 2022
Recommendation for scattered data:
Use scatteredInterpolant is you need to interpolation of query points at various places for the same sample points
Use griddata if you use 'v4' method, which I find quite remarkable in some circumstance, and I regret it is not implemented in scatteredInterpolant. The 'v4' is initially developped for stalite data acquired on narow tracks on earth surface.

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Bjorn Gustavsson
Bjorn Gustavsson on 2 Nov 2022
griddedinterpolant expects points on a regular grid pretty much like interp2 - so that function seems unsuitable for your case. As to the difference between griddata and scatteredInterpolant the main difference as I understand it is that the latter gives you a function that you can effectively call multiple times and re-use the triangulation that both methods use to interpolate, while repeated calls to griddata on the same data-set will redo that triangulation again and again. In addition to the common interpolation methods griddata also gives you the option to use the legacy 'v4' interpolation-method (which if my memmory serves me OK was some kriging base/like method).
One point of concern for you is that the X-Y points are close to co-linear and their triangulation doesn't span much - therefore triangulation-based interpolation will be restricted to a very narrow triangular region - outside of that extrapolation will be used. And we all know the perils of extrapolation.
HTH

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