If you scroll up to the top of the page you shared you'll see a section that describes properties associated with levels that may help to understand levels.
Think of contour plots as maps of topographic maps of mountains. The levels in topographic maps define the height, typically above/below sea level, as shown in the image below.
Contour plots are the same but the levels show the height, depth, temperature, density, or whatever you're measuring along the z-axis.
The contour matrix output lists the coordinates that define each contour line and the coordinates are organized by level as shown in the documentation. Many users have found that organization to be confusing. There are several functions on the file exchange the reorganize the matrix so it's much easier to work with and understand.
contour(Z,v) draws a contour plot of matrix Z with contour lines at the data values specified in the monotonically increasing vector v. The number of contour levels is equal to length(v). To draw a single contour of level i, use contour(Z,[i i]). Specifying the vector v sets the LevelListMode to manual to allow user control over contour levels.
I would use a separate call tocontour. You may have to experiment with the approach in Yair Altman’s Undocumented MATLAB articleCustomizing contour plots part 2 to put thecontour plot on the same plane as the contours drawn by themeshc function.
When you get your code working, consider generalising your code to a function and then contribute it to the File Exchange. It seems useful.
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