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How do I fit a surface to this data properly?

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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');
hold on
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?

Answers (2)

KSSV on 16 Sep 2021
KSSV on 16 Sep 2021
The same link has an example showing how to fit for a surface.
Pablo Fernandez
Pablo Fernandez on 16 Sep 2021
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.

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darova on 19 Sep 2021
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.
  1 Comment
Pablo Fernandez
Pablo Fernandez on 19 Sep 2021
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.

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