Interpolation outside boundaries.

Hi guys,

I'm training myself in data interpolation for a project. With an example set of datas (6 points) I'm able to interpolate data using griddata as you can see in the code below. The question is : is possible to interpolate the surface also in [x,y] that are over x_max and y_max of my points?

As you can see, overall x_max and y_max in my data set is 20, but I created a grid that arrives till 30. Nevertheless the interpolation gives only values under x=20 and y=20.

Thank you.

P = [0 0 0;
     20 0 5;
     0 20 5 ; 
     5 5 2;
     10 10 10 ;
     20 20 10] ;
x = P(:,1) ; y = P(:,2) ; z = P(:,3) ;

ti = 0:1:30;

[XI,YI] = meshgrid(ti,ti);

ZI = (griddata(x,y,z,XI,YI,'cubic')); 

surf(XI,YI,ZI), hold
plot3(x,y,z,'ro'), hold off
colorbar

Answer 1

[Ameer Hamza]

griddata() does not have the option for extrapolation beyond the data-points. You can use scatteredInterpolant for this; however, it does not have a cubic interpolation option, and the extrapolation is also linear.

P = [0 0 0;
     20 0 5;
     0 20 5 ; 
     5 5 2;
     10 10 10 ;
     20 20 10] ;
x = P(:,1) ; y = P(:,2) ; z = P(:,3) ;

ti = 0:1:30;
[XI, YI] = meshgrid(ti,ti);
model = scatteredInterpolant(x, y, z, 'linear', 'linear');
ZI = model(XI, YI);

surf(XI,YI,ZI), hold
plot3(x,y,z,'ro'), hold off
colorbar

The best way to handle such cases is to have an equation of form z = f(x, y) and then use curve-fitting to estimate the unknown parameter in f(.). Then you can use f(.) to extrapolate the values.

[WILLIAM ZANIN]

All clear thank you very much!

[Ameer Hamza]

I am glad to be of help!