Create scatteredInterpolant for data with double value points

I have tabulated data, containing fluid properties, that I want to use for interpolation. The grid itself is not regular on some points, so I want to use scatteredInterpolant for interpolation.

Unfortunately, on some grid points I have two values that are then automatically removed or collapsed by scatteredInterpolant. However I want to preserve those as the vertical rise is necessary to maintain. I investigated groupsummary if this could help but I am not sure how to use it properly.

For me it would be acceptable if I could slightly distance the grid points and use an interpolated value for both grid points, one on the low side, the other on the high side and to have a steep rise instead of a vertical rise but I have no clue how to do it.

The thing is the points where this vertical rise exist are pretty scattered and I have several tables with this so manually it might by a bit hard to do.

Has anybody a good idea how to deal with this?

Example (simplified) of my data:

x     y     values   state
1     2     10       liquid
2     2     11       liquid
3     2     10.5     liquid
3     2     200      gaseous
4     2     202      gaseous
5     2     203      gaseous
1     3     9        liquid
2     3     9.9      liquid
3.1   3     10.8     liquid
3.1   3     195      gaseous
4     3     199      gaseous
5     3     201.5    gaseous
1     4     8.9      liquid
2     4     9.5      liquid
3.3   4     10.2     liquid
3.3   4     185      gaseous
4     4     191      gaseous
5     4     199      gaseous

I have this data in a struct variable, put x, y, and v in an array and tried to interpolate like this:

F = scatteredInterpolant(x,y,v);

For me it would be acceptable to modify the doubling where x collapses as follows explained for point x1 = 3.1 and y1 = 2:

I create a point x1.1 at let's say 3.0999, y1.1 = y1 = 2 and interpolate v1.1 by using as values (2,2) and (3.1,2).

This new point would replace the point (3.1,2,liquid).

Any other approach or solution would be fine, too!

Solution

Since your x and y are sorted in a sensible way, you should just be able to increment x at all points where the previous x value was the same, and the previous y value was the same.

In a loop this would be something like

ofst = 0.0001; % amount to increase duplicate axis values by
for ii = 2:numel(x)
    if (x(ii)<=x(ii-1)) && (y(ii)==y(ii-1))
        x(ii) = x(ii) + ofst;
    end
end

Without a loop it could be something like this, but be wary this wouldn't handle the edge-case where adding the offset could make one x value larger than the next one. The loop did handle this edge case by using <= and checking sequentially.

ofst = 0.0001;
bofst = [false; (diff(x)==0) & (diff(y)==0)];
x = x + bofst*ofst;