# Plot a function of three variables on a surface plot

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Fawad Farooq Ashraf on 30 Mar 2023
Edited: Torsten on 2 Apr 2023
Hello. I have some experimental data of electric field E. The values were measured along three axes x, y and z such that: along x axis (x=0:5:50), values of Ex were measured (Assume Ex = rand(size(x)) for reference), then along y axis (y=0:5:70), values of Ey were measured (Assume Ey = rand(size(y)) here for reference), and along z axis (0:5:20), Ez was measured (Ez = rand(size(z)) assumed here). I want to plot this data in a 3D surface plot. How can I do this?
Torsten on 2 Apr 2023
Edited: Torsten on 2 Apr 2023
So given a point (x,y,z) in 3d space, what do you want to plot at this point ? sqrt(Ex^2+Ey^2+Ez^2) ?

Star Strider on 30 Mar 2023
If all the data are vectors (that would appear to be true since ‘x’ is a vector), it would be necessary to use either the griddata or scatteredInterpolant function to create a surface from them.
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Fawad Farooq Ashraf on 2 Apr 2023
how to do that? I don't understand these functions.
Star Strider on 2 Apr 2023
Here is an example using scatteredInterpolant and random vectors —
x = randn(1,20); % Create Data Vector
y = randn(1,20); % Create Data Vector
z = randn(1,20); % Create Data Vector
xv = linspace(min(x), max(x), numel(x)); % Interpolatioon Vector
yv = linspace(min(y), max(y), numel(y)); % Interpolation Vector
[X,Y] = ndgrid(xv,yv); % Interpolation Matrices
F = scatteredInterpolant(x(:),y(:),z(:)); % Create Interpolant Function
Z = F(X,Y); % Calculate 'Z' By Interpolation
figure
surfc(X, Y, Z) % Plot Result
grid on
xlabel('X')
ylabel('Y')
zlabel('Z')
colormap(turbo) % Introduced In R2020b
colorbar
The griddata function works similarly, however has different arguments and produces a lsightly different result.
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