Why Contour matrix M ( [M,c] = contour(__) ) contains the data points exceeding xmax/ymax?

I have a contour plot (fig 1), plotted according to [M,h]=contourf(f,8). With this I slice contour #8. Thus, I expect to have in matrix M all (x,y) coordinates of the 8th contour. These coordinates have (logically) not to exceed the xmax/ymax (250/250). Instead, when I plot matrix M i have some values that larger then xmax/ymax (figure 2). According to the documentation (https://de.mathworks.com/help/matlab/ref/contour.html#mw_27139ced-212f-437f-abab-0ff7c175e33b),

the first pair of data is the Level and the number of Vertices. But plotting the contour(f,8) in Fig1 I should have only first pair of data in returned M which describe the leve 8 l!!!

Please explain their origin of larger data.

Figure 1

Figure 2 (Plotted M)

[Stephen23]

"Instead, when I plot matrix M i have some values that larger then xmax/ymax"

Those are the contour level values and the number of vertices values. Because you requested 8 contours you will get 8 blocks of data, where each block starts with a contour level value and the number of vertices value (which gives the size of the data block). This matches with what you show in figure 2.

The contour vertex matrix M is explained here:

https://www.mathworks.com/help/matlab/ref/contourf.html#mw_7aeb4812-ecbf-4b13-a340-b3ce03f08808

[Sergii Snegir]

Thank one more time for the explanation. I guess, initially I did not get fully the meaning of n=8.Am I correct, that 8 means 8 consequently selected heights, data from which form the contour??

[Stephen23]

After the required input arguments (Z, or X, Y, Z), a trailing scalar numeric n is interpreted as a request for n levels (the heights of those levels will be automatically determined):

https://www.mathworks.com/help/matlab/ref/contourf.html#mw_e930b555-4fc5-4db1-8907-5d10f7aac1c0

A trailing non-scalar vector is used if you want to specify the heights yourself. The documentation explains how to specify exactly one height: "To draw contour lines at a single height k, specify levels as a two-element row vector [k k]"

[Sergii Snegir]

Ok, than, how the automatically determined height correlats with the min, max values of input Z????

[Stephen23]

"how the automatically determined height correlats with the min, max values of input Z????"

I have no idea: the documentation only states "automatically", it does not give an algorithm. But if you are interested:

• search this forum for other discussions on this topic.
• use the internet archive to see if previous versions of the documentation included information on the algorithm.

[Sergii Snegir]

many thanks. The documentation about Matlab is very unclear sometimes, I need to say.

Have a nice evening.

Answer 1

[Bruno Luong]

[M,h]=contourf(f,8)

Return contours of 8 levels, not single level of value 8.

You might use this function to decode the output array https://www.mathworks.com/matlabcentral/fileexchange/28447-contourcs-to-obtain-contourc-output-as-a-struct-array

[Sergii Snegir]

Dear Bruno. Sorry for dump question, but can you please explain what does mean n= 8 levels if I see on the figure1 one contour? I read one more time documentation, and can not get. I thought that "levels", means height of f, and thus, I slice from the top n=1 to the lower levels n=8.

[Bruno Luong]

The doc

"Use this argument to control the number and location of the contour lines. When you do not specify the levels, the contour function chooses the levels automatically.

• To draw contour lines at n automatically chosen heights, specify levels as the scalar value n.
• To draw the contour lines at specific heights, specify levels as a vector of monotonically increasing values.
• To draw contour lines at a single height k, specify levels as a two-element row vector [k k]."

I don't know what *you* see on your image, if I do this

f=peaks;
[M,h]=contourf(f,8)

I get this contour plot like there are 8 "heights" to me (counted from bright yellow to dark blue):