Interpolated 2D sections out of 3D plot

I have a number of data for 3 variables - data points in 3D - which can be plotted using plot3(). I want to make 2D sections from this plot, keeping one of the 3 variables, lets call it z, constant at different values (set up an array of constant z values and make 2D sections in x-y plane for each value). I want to use interpolation to get the most accurate 2D section. Any help on how I can do this?

[John Doe]

Do you have an example? And some data if possible please.

[Ane Følgesvold Reines]

I cannot post the real data but lets say we have a data array of 3 columns and 100 rows (100 data points). I plot in 3D using

plot3(data(:,1),data(:,2),data(:,3))

Then I wanna make, lets say, ten different 2D plots in x-y-plane for z=[81:1:90].

How do I proceed for the interpolation of the data points?

Answer 1

[darova]

Use griddata() (use griddata(x,y,z,xq,yq,'method','cubic') if interpolation is needed) to build a surface

Use contour() to create a crossection at specific height

[Ane Følgesvold Reines]

Thank you for the answer! And yes, I have tried both.

But for the interpolation, how am I suppose to have two arrays of query points (xq, yq)? I only know what z-level I want to interpolate at, i.e. I only have one array of query points (the const z values).

For contour(), I dont understand how I am suppose to give the correct input to this function with the data points that I have. Each column of the data matrix is one dimension and there are 3 columns (3 dimensions). Each row in the data matrix corresponds to one data point.

I suppose I need to use meshgrid() somehow, but I dont understand how...

[darova]

You have some data (x,y,z)

You'll need to know boundaries of your data (where x and y begins and ends)

Once you know boundaries you can build a mesh

xq = linspace( min(x), max(x), 20 );        % boundary of x
yq = linspace( min(y), max(y), 20 );        % boundary of y
[X,Y] = meshgrid(xq,yq);

Don't worry about areas for those you don't have data (griddata() will place there a NaN value)

Z = griddata(x,y,z,X,Y,'method','cubid');

Once you have X,Y,Z as 2D matrix you can build a surface

surf(X,Y,Z)

and contour also

height = [1 2 3];            % height you want crossection at
hold on
contour(X,Y,Z,height)
hold off

see also contourf(), contour3()

Do you want to extract those contour data?

[Ane Følgesvold Reines]

This helped me a lot, thank you!

Quick question, using contour(X,Y,Z) it chooses the levels to plot in the contour itself, but when I specify a height array of levels by typing contour(X,Y,Z,height), those are the levels plotted?

Yes it would be nice to extract them as well!

[darova]

those are the levels plotted?

The answer is YES!

To extract contours: LINK

See HELP how data is stored ic ContourMatrix

[darova]

Please accept the answer if it helped