How do I fit a surface to this data properly?

Hi,

I have a set of datapoints (x,y,z) to which I want to fit a surface. I dont have a mathematical expression for the surface, so I tried to use the linear interpolation as in:

load ('data.mat')
PTSGRID = 256;
xs = min(x):(max(x)-min(x))/(PTSGRID-1):max(x);         
ys = min(y):(max(y)-min(y))/(PTSGRID-1):max(y); 
[xq, yq] = meshgrid(xs,ys); 
zq = griddata(x,y,z,xq,yq,'linear'); 
plot3(x,y,z,'mo')
hold on
mesh(xq,yq,zq);

However the fitted surface takes very strange values where there is no data defined, very different from what I would visually expect. Take a look for example at this figure, and the zone I circled:

How can I fit in a better way to avoid this behavior?

Thanks!

[darova]

Attach the data

[Pablo Fernandez]

Attached to the original post!

Answer 1

[KSSV]

Read this: https://in.mathworks.com/help/curvefit/fit.html

[Pablo Fernandez]

Thanks for the answer.

I already know how to fit a curve with Matlab. Is there a specific answer to my question in the link you posted?

[KSSV]

The same link has an example showing how to fit for a surface.

[Pablo Fernandez]

Yes, I understand.

The specific point in my questions is how to get rid of the artifacts that appear when I try to interpolate the points in my dataset.

Answer 2

[darova]

I don't have this problem

s = load('data.mat');
x = s.x;
y = s.y;
z = s.z;
xx = linspace(min(x),max(x),20);
yy = linspace(min(y),max(y),20);
[x1,y1] = meshgrid(xx,yy);
z1 = griddata(x,y,z,x1,y1);

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

mesh(x1,y1,z1)

[Pablo Fernandez]

Hi, thanks for the answer.

You are not seing the effect in that plot because you are evaluating the interpolation in few points. The reason for the interpolation is to evaluate between the data lines. Try changing 20 for 256 in xx and yy definitions and you will notice the effect when plotting.

Regards