Discretize the 3-D surface into individual points in MATLAB

Hey guys!

how to discretize the 3-D surface into individual points in MATLAB.

For example, if I have a surface in x,y,z. I want to generate each curve (y,z) for x=-1,-0.9,-0.8 etc. Can you guys please give me some guidances for it, I would very appreciate it!

Answer 1

[KSSV]

Read about slice. This is your function.

Answer 2

[Walter Roberson]

F = @(X, Y) sin(X).^2 - cos(3*Y).^2;   %equation of the surface

xvec = -1:0.1:1;
yvec = -3.2:.1:3.2;
[x, y] = meshgrid(xvec, yvec);
z = F(x, y);

surf(x, y, z); xlabel('x'); ylabel('y'); zlabel('z')

z is your discretized data.

[LM]

Hi Walter!

Many thanks for your answer!

I am wondering if I have non-uniform data set for x, y, z and I used Thin-plate spline interpolation fitting in MATLAB APPS. Shown in this figure. At this time, how would I find the individual points in this surface.

Many thanks,

Mao

[KSSV]

Read about scatteredInterpolant/ griddata.

[LM]

This generated code for the surface should be like:

[xData, yData, zData] = prepareSurfaceData( LAP, ST, PL );

% Set up fittype and options.
ft = 'thinplateinterp';

% Fit model to data.
[fitresult, gof] = fit( [xData, yData], zData, ft, 'Normalize', 'on' );

% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot( fitresult, [xData, yData], zData );
legend( h, 'untitled fit 1', 'PL vs. LAP, ST', 'Location', 'NorthEast', 'Interpreter', 'none' );
% Label axes
xlabel( 'LAP', 'Interpreter', 'none' );
ylabel( 'ST', 'Interpreter', 'none' );
zlabel( 'PL', 'Interpreter', 'none' );
grid on
view( 70.2, 57.5 );

[Walter Roberson]

Where fitresult is the first output of fit(), then fitresult will be an "object" that can be called as a function to do the calculation.

interpolated_z = fitresult([xData, yData]);

then interpolated_z would be the result of applying the fitted model at locations [xData, yData] .

If you wanted the results over the larger grid, then pass in a wider set of x and y points.

[LM]

Thanks, Walter for getting back to me. If using your provided function. Should I can get such discretized plot? I know the surface is different than the previous one but I think this plot and output data sets are what I want, eventually.

[Walter Roberson]

Nx = 100;
Ny = 22;
xvec = linspace(min(xdata), max(xdata), Nx);
yvec = linspace(min(ydata), max(ydata), Ny);
[XQ, YQ] = meshgrid(xvec, yvec);
ZQ = reshape( fitresult([XQ(:), YQ(:)]), size(XQ) );

scatter3(XQ, YQ, ZQ, 'bo');

[LM]

Great thanks, Walter! Will give a try! Again, thank you so much!

Mao