contour for scatter data

Hi every one,

I have 3 columns of data X, Y, and T. I used "svd" function for T and now I need to visulaize T considering X, and Y. How could I use "contour" or "contourf" for this data? the problem is, I cann't use "meshgrid" function because the grid that I used is not organised.

Thanks in advance,

[Totanly]

see this link, i think it will solve your problem

https://www.youtube.com/watch?v=66WOwdZ-Vpk

Answer 1

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/38858-contour-plot-for-scattered-data

[Pegah]

Thanks, if you look at the end of data, the conectivity matrix in this case has four columns which seem Matlab doesn't accept. Could you please take a look at my data and let me know your oppoinion?

[John D'Errico]

@Pegah - how did you build that connectivity matrix? Did you use perhaps a delaunay triangulation? The triangulation must be in terms of X and Y. In that case, it will only define TRIANGLES. I would postulate that you used a triangulation on (X,Y,T). That would produce tetrahedra, which is NOT what you wanted to do at all.

For example...

XY = rand(100,2);
Z = sin(sum(XY,2)); % A really simple function.
tri = delaunayn(XY);
size(tri)

ans = 1×2

185 3

THREE columns, which define triangles. We can plot it.

trimesh(tri,XY(:,1),XY(:,2),Z)

I could also use a tricontouring tool on this now. Note that there will often be artifacts near the edges when you use a delaunay triangulation. This is due to those long, thin triangles that always appear at the edges. An alpha shape would have been a better choice to build that triangulation, but you should take one step at a time.

[Walter Roberson]

You have one value per face. If you color the face by interpolating the temperatures of the vertices, then you get

filename = 'export.csv';
xyzt = readmatrix(filename, 'Range', "7:512");
faceinfo = readmatrix(filename, 'Range', "515:969");
p = patch('Faces', faceinfo + 1, 'Vertices', xyzt(:,1:3), 'FaceColor', 'interp', 'FaceVertexCData', xyzt(:,4));
view(3)

It is worth looking at the scatter plot:

x = xyzt(:,1); y = xyzt(:,2); z = xyzt(:,3); t = xyzt(:,4);
figure
scatter3(x, y, z, [], t);

Now we can head towards interpolation. But there are two holes, so we need to avoid interpolating there (or at least not plot there if we do interpolate.)

One way to avoid plotting where there are holes is to create an occupancy map

F = scatteredInterpolant(x, y, t);
[dimmin, dimmax] = bounds([x,y], 1);
N = 50;
xvec = linspace(dimmin(1), dimmax(1), N+1);
yvec = linspace(dimmin(2), dimmax(2), N+2);

xbin = discretize(x, xvec);
ybin = discretize(y, yvec);
occupied = accumarray([ybin, xbin], 1) ~= 0;

occupied is now true for locations where data was found inside the grid point, and false for locations where no data was found inside the grid point

[XG, YG] = meshgrid(xvec(1:end-1), yvec(1:end-1));
TG = F(XG, YG);
whos XG YG TG occupied

  Name           Size            Bytes  Class      Attributes

  TG            51x50            20400  double               
  XG            51x50            20400  double               
  YG            51x50            20400  double               
  occupied      51x50             2550  logical              

figure
TG(~occupied) = nan;

nan out the unoccupied interpolated locations, and show them as pcolor

pcolor(XG, YG, TG)

That is fairly sparse. This goes back to the fair distance between locations because there is only one temperature per element.

We can proceed from here to contour...

figure

figure
contourf(XG, YG, TG); colorbar
xlabel('x'); ylabel('y');

but with the data being so sparse, the contour does not look good.

You could reduce the resolution by a factor of 5 or so so that the samples were beside each other -- but the resulting map would only be about 10 x 10, which is not very useful.

Or you could change the way you calculate occupancy. If you put all the vertex lists together separated by nan and then probe each point in XG YG using inpolygon() then you could probably do something useful. At the moment I do not know if there are any better ways.

[Pegah]

@Walter Roberson You solved my problem. This is the best solution for this problem. Thank you.

I just have one problem. In the first graph how can I save the contour with different colors without having the grid? because in the final case, I have 700,000 elements for the domain. so without clearing the grid, the domain seems black.

[Voss]

@Pegah: Include 'EdgeColor','none' in the call to patch():

filename = 'export.csv';
xyzt = readmatrix(filename, 'Range', "7:512");
faceinfo = readmatrix(filename, 'Range', "515:969");
p = patch( ...
    'Faces', faceinfo + 1, ...
    'Vertices', xyzt(:,1:3), ...
    'FaceColor', 'interp', ...
    'FaceVertexCData', xyzt(:,4), ...
    'EdgeColor', 'none');
view(3)

[Pegah]

It works, Thank you so much.

Answer 2

[John D'Errico]

Let me give an example of how to use a tricontouring tool for scattered data.

x = rand(100,1);
y = rand(100,1);

zfun = @(x,y) sin(x + y).*cos(x-2*y) - x;
z = zfun(x,y);

% Note the use of an alpha shape to generate the triangulation.
% This is important, as otherwise, there will be significant edge
% artifacts.
S = alphaShape(x,y);

S.Alpha = .3;
plot(S)

That is merely the triangulation. Again, it is based purely on the variables x and y.

trisurf(S.alphaTriangulation,x,y,z)

tricontour(S.alphaTriangulation,x,y,z,10)
hold on
plot(x,y,'ro')
colorbar