Is there a way to plot a contour with a 3-Dimensional matrix?

Hi,

I've asked a lot of questions here recently but I am coming to the business end of my project and the stuff I am trying to do is complex.

I have a 3-D matrix that is 40x180x40, full of scalars. They are all a function of the variables that give it the second two dimensions (so, the 180x40) so it is these values I want on the X and Y axes, and then the colour be determined by the values inside the 3-D matrix. Is this possible?

[jonas]

Sorry I completely misread the size of the matrix. Will come up with a better answer in a sec :)

[Harvey Rael]

No hassle! :)

[jonas]

The contour and surf functions are used for 3d surface. I'm not entirely sure what it is that you have in your matrix. Have you tried scatter3?

[Harvey Rael]

well, they're just values. You could replicate my code easily enough by randomly populating a 40x18x40 matrix with any numbers.

Then the X - axis being dictated by a 1x40 double, and the y-axis by a 180x1 double (or the other way around if it is easier).

I don't know if a scatter plot will do because I would like there to be colour mapping decided by the values in the 3-d matrix

[Harvey Rael]

Also, ideally I would like to just dump the values into a 2-D contour plot, but I don't know if that is possible.

[jonas]

But it seems you have multiple values (40 to be exact) per x and y coordinate? Thats not something you represent by a single surface. Sorry if I am still misunderstanding.

Note that you can color map by scatter3 as well. It will not interpolate between coordinates though.

[Harvey Rael]

Yeah I do. X and Y are are dates and times of flight, and the 3-D matrix is fuel cost - I'm trying to plot an interplanetary trajectory. So for example, departing on 01/01/18 and flying for 200 days has a number of fuel costs depending on the variation of another variable. That 3rd variable is significant because it allows me to see all the possible fuel costs, but plotting it isn't as significant. I am trying to plot all the fuel costs for each date and time of flight combination. Does that make sense?

[jonas]

Makes sense! You cannot plot the entire data set on a surface. You can plot a slice of your 3d matrix as a surface, but not the entire data set. I would try scatter3 with color coding, it may end up looking OK.

Start by something like this:

[X Y]=meshgrid(1:40,1:180);
A=randn(40,180,40);
X=repmat(X,1,1,40);
Y=repmat(Y,1,1,40);
scatter3(X(:),Y(:),A(:),[],A(:),'.');
colorbar

As you can see, this blob has a thickness and cannot be represented as a surface.

Answer 1

[Steven Lord]

I'm not certain, but from your description I think you might want an isosurface.

Answer 2

[Harvey Rael]

All have been helpful - I was being stupid. I think I can loop through the third dimension of the matrix, and keep hold on and contour plot that way? My only question arising from that would be - given the filled nature of contourf, would that mean hold on causes each contour plot to sit "on top" of one another, rather than fill it like I want?

[jonas]

You cannot stack contourf plots, because they are all plotted in the same plane. If you want to make something meaningful of this stack, then you have to adjust the hidden property "ContourZLevel". You will get something like this:

40 stacked plots will make for a colorful but unreadable image :)

See my answer for a better method.

Answer 3

[jonas]

You would probably be interested in using a contourslice plot.