Interpolation outside the domain - meshgrid and griddata

Hello Matlab community,

I need your knowledge on a problem.

I have three vectors, two of them being (x,y) pairs, and the third being T=f(x,y).

I used meshgrid in the following way:

x_grid = linspace(min(x),max(x),1000);

y_grid = linspace(min(y),max(y),1000);

[xq,yq]=meshgrid(x_grid , y_grid );

Now I can plot my data in the following way:

T_interp = griddata(X,Y,T,xq,yq);

figure

contour(xq,yq,T_interp )

I attach an image with the cotour plot, and the domain I need superimposed (grey circles).

As seen in the image, I get an interpolation outside the boundaries of the domain I need.

Is there a way to avoid that?

Many thanks and best regards.

[Maria Angela Agizza]

Hello, I found some feasible options but it's not yet exactly what I need, and help from people that know better than me is needed.

I used the command "inpolygon" in the following way:

for r=1:size(T_interp ,1);

      for c=1:size(T_interp ,2);

          if inpolygon(xq(r,c),yq(r,c),x_poli,y_poli)==0;

              data_grid_3(r,c) = NaN;
          else

          end

      end

end

With x_poly and y_poly being the vertices of my domain.

The question now is, is there a way to extract the boundaries of the domain automatically? I could do it by hand as I did for this trial code, but my domain 

* is 3D (I posted a 2D picture for simplicity) and doing it by hand leads to errors
* is noe exactly sharp, and I need to capture the curvatures as well.

I tried with "boundary" in the following way:

k = boundary(x,y);

figure

plot(x(k),y(k))

hold on

plot(x,y,'o','color',[0.5 0.5 0.5])

As you see in the image attached the boundary does not exactly catch my domain.

Does someone have a suggestion?

I really appreciate any help.

Best regards.

[KSSV]

Yes it is very much possible to extract the boundary of the given domain. And using inpolygon is apt. Note that, you have used a loop for that, which in unnecessary and time consuming. Attach your data, so that we can help you further. Mean while, you can have a look on boundary to extract the boundaries of the grid.