# Plot u=f(x,y,z) with all discrete data

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Retam Paul on 13 Jan 2023
Answered: Star Strider on 13 Jan 2023
Hi all,
I have four columns of data namely cartesian coordinates (x,y,z) and a variable 'u'. All the four data are DISCRETE points. I want to create a 3D plot to visualise the contours of u using a colorbar. Can anyone help?
Thanks
Retam Paul

Star Strider on 13 Jan 2023
The (x,y,z) vector data must be converted into a 2D matrix by some sort of computational magic so the contour can be plotted.
One approach —
x = randi( 9,50,1);
y = randi(49,50,1);
z = randi(99,50,1);
u = @(x,y,z) exp(-(x-mean(x)).^2) + exp(-(y-mean(y)).^2) + exp(-(z-mean(z)).^2); % Create 'u(x,y,z)'
[X,Y,Z] = ndgrid(x, y, z); % Create Matrices From The Vectors
U = mean(u(X,Y,Z),3) % Eliminate One Dimension To Create 2D MAatrix
U = 50×50
2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0824 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0013 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143 2.7143
figure
contour(U)
colormap(turbo)
colorbar
Another approach would be to plot the contours of each ‘page’ of a 3D matrix in different figures.
How you accomplish this depends on what the vectors are and what you want to do with them.
.

### More Answers (1)

Davide Masiello on 13 Jan 2023
Edited: Davide Masiello on 13 Jan 2023
x = rand(1,100);
y = rand(1,100);
z = rand(1,100);
u = rand(1,100);
scatter3(x,y,z,20,u,'filled')
colorbar