How to draw a 3D surface with all the given discrete points？

I am trying to draw data from several curves into a 3D surface. I have extracted the points in the curves as discrete data points and tried to draw a surface plot based on scatter data. The problem is that discrete points in each curve may have multiple Z-values at the same X-Y coordinate. Command 'griddata' and 'surf' have been used, but it gives warning of duplicate data points have been detected and averaged.

I have realized that the rule of 'griddata' is that only the unique Z-value can be used in the xy plane, otherwise the average will be used. The data is contained in the attachment, and the code and results are given below.

close all; clear all

load XYZ_data

scatter3(x,y,z)

% figure
[X,Y,Z]=griddata(x,y,z,linspace(min(x),max(x))',linspace(min(y),max(y)),'v4');
figure,surf(X,Y,Z);
figure,meshc(X,Y,Z)

How can I get a smooth surface with all the given data? Any comments will be much appreciated.

Answer 1

[Mathieu NOE]

hello

of course I tried the standard solutions (surfir, griddata etc...) but as your shape is very specific , therefore also a specific code for you

try this

load XYZ_data
samples = numel(x);

[xu,ia,ic] = unique(x);
unique_curves = numel(ia);

N = samples/unique_curves; % this is length of one curve

% main loop 
for k =1:N 
    ind = k:N:samples;
    xx = x(ind);
    yy = y(ind);
    zz = z(ind);
    
    % Interpolate the scattered data
    xd(k,:) = linspace(min(xx),max(xx),100);
    yd(k,:) = interp1(xx,yy,xd(k,:));
    zd(k,:) = interp1(xx,zz,xd(k,:));

end
    
figure
subplot(1,2,1)
scatter3(x,y,z,8,'.k')
title('data points')

subplot(1,2,2)
h = surf(xd,yd,zd);
set(h,'edgecolor','none')
title('surface plot')    

[Danny]

Thank you! That's exactly what I wanted. You have solved my problem.

Best regards,

Danny

[Mathieu NOE]

my pleasure !

Answer 2

[Chunru]

load(websave("XYZ_data.mat", "https://www.mathworks.com/matlabcentral/answers/uploaded_files/1559554/XYZ_data.mat"))
whos

  Name           Size            Bytes  Class     Attributes

  cmdout         1x33               66  char                
  x           2870x1             22960  double              
  y           2870x1             22960  double              
  z           2870x1             22960  double              

figure
T = delaunay(x, y);

Warning: Duplicate data points have been detected and removed.
Some point indices will not be referenced by the triangulation.

% Seems that there are duplicate point for x, y (in addition to z?)


trisurf(T, x, y, z, "EdgeColor","none", "FaceColor","interp");
xlabel("x"); ylabel("y")
view(80, 30)

[Danny]

Thanks Chunru.

Perhaps I should explain my question further. Actually, these discrete data come from 5 curves, and I want to draw a surface that contains these curves. In other words, I want to restore these data completely on a surface. Commands "trisurf" or "surf" do give the rough shape of the surface, but the key is how to preserve these duplicate values.