Unstructured grid to structured grid

Dear all, what would be the best way, in your opinion, to get a structured grid out of an unstructured grid?

What I have is something like this:

x  y   f

1  12  7
3  10  4
1  11  2
2.4  15  0

So basically x and y are totally random and in no specific order. What I need is to resample the values of f on a structured grid with a constant step.

I had a quick look at interp2 and it looks like it will only work if my vectors are strictly monotonic which is not the case as I have plenty of repeated values for x and y.

Thanks a lot

Answer 1

[David Young]

scatteredInterpolant may do what you need. Like this:

x = [1 3 1 2.4].';
y = [12 10 11 15].';
f = [7 4 2 0].';
si = scatteredInterpolant(x, y, f);   % using default linear interpolation

xint = (0.5:0.5:3.5).';      % regular grid
yint = (9.5:0.5:15.5).';
fint = si({xint yint})

[Lorenzo]

Great, thanks!

[haibo xu]

Hi. It is worth noting that scatteredInterpolant only works on the case that x-y-z has unique values. Otherwise it will merge same numbers into one which could be out of your expectation.

[Emanuel]

How does this work if you have a lookup table with x and y values only. So, transfer non-momotonic x values into a fixed (strictly momotonic) x step size with the corresponding (interpolated) y values ?

Answer 2

[Lorenzo]

Things are getting even more difficult… I actually don't have a grid but a set of cylindrical coordinates in a plane, namely a set of values for a radius and a set of values for an angle…

Is there any way in matlab to perform the interpolation in cylindrical coordinates? The issue with treating them as cartesian is that I end up with errors at the boundaries, in my case I lose the continuity information of my surface at theta=0° or theta=360°

Any idea?

Thanks again!

[David Young]

I'd have to think that through - but scatteredInterpolant doesn't depend on having a grid at any stage - you can use the returned function, called si in my answer, to sample at any required points. To avoid the discontinuity in theta I would expect that converting everything to Cartesian coordinates might be the right thing to do.