MATLAB: Need to make a 4D plot (3D + Colour/Color)

Question

I need to make a 3D surface where colour will represent the fourth variable. I know "surf" is SIMILAR to what I need, but that's not quite it. Basically, I have the following variables:

t = [1:m]

y = [1:n]

a = [1:o]

These should be the three Cartesian corodinate axes.

I also have a variable S that is of dimensions m x n x o, and is basically the amplitude, a function of the previous three variables (i.e. S = f(t,y,a)). I want this to be represented by colour.

So to summarize, I need a graph of the form (t,y,a,S), where the first three variables are vectors of unequal sizes and the final variable is a multidimensional array whose dimensions are determined by the first three.

Thanks in advance.

Answer 1

SCATTER3 requires x, y and z and other grouping arguments to be equally-sized Nx1 vectors for a single series or NxM matrices for M series.

You have full space 3D data. To make equally-sized coordinate vectors use MESHGRID (or NDGRID) function:

[X, Y, Z] = meshgrid(t, y, a);

Then you can use SCATTER3:

scatter3( X(:), Y(:), Z(:), [], S(:) )

The problem is since it's full space data scatter3 will not be helpful specially if you have a lot of points.

You can probably filter your S variable (something like idx = S > 0), then you can plot filtered data.

If you really need to visualize all the data, look at Volume visualization in MATLAB documentation. I can recommend SLICE function, for example.

EDIT

Here is an example of full 3D space scatter plot for small vectors (m, n, o equal to 5) with S = rand([m,n,o]); scatter3( X(:), Y(:), Z(:), [], S(:), 'filled' )

EDIT 2

From your comments to the other answer I found that you have 32x76050x4 matrix. You can actually plot 2D slice one at a time. you can do it in 2D with IMAGESC function, or in 3D with SLICE function.

Try:

imagesc(S(:,:,k))

where k is a number from 1 to 4 for the 3rd dimension.

Or try

slice(S, [], [], 1:size(S,3))
shading flat

Answer 2

I've always used scatter3 for coloring/sizing pixels in 3d space. I believe the signature is:

scatter3(x,y,z, size, color)

The size and color can be scalar or vector of length equal to the coordinates. I usually use either the color or the size to reflect the fourth attribute, depending on what I'm showing. I don't have Matlab on this machine, so forgive me if my memory isn't completely accurate on the usage. "help scatter3" should describe it much better.

Answer 3

Maybe this user-created plotting routine can help.

Screnshot from the linked page: