Interpolated 2D sections out of 3D plot

2019 9 27
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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?

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John Doe
John Doe 2019-9-27
Do you have an example? And some data if possible please.
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?

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darova
darova 2019-9-27

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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

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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
darova 2019-9-27
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?
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
darova 2019-9-27
those are the levels plotted?
The answer is YES!
To extract contours: LINK
See HELP how data is stored ic ContourMatrix
contour_matrix_diagram.png
darova
darova 2019-9-27
Please accept the answer if it helped

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