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I have a 4d or higher ellipsoid in matrix form (which form is important). I wish to plot 3d dimensional plots (The projection on 3d hyperplane). Of the 4/5/6 dimensions I am projecting from, I want to be able to choose any three of the axes.

Now there two ways I think it can happen:

  1. I describe the matrix in 4 or higher dimension as a collection of points and then I can project the points on a 3d hyperplane (the projecting is easy).

For example plotting in 3d in matplotlib is by using numpy.linspace to create a coordinates (arrays of points). One solution is Plotting Ellipsoid with Matplotlib. But the prob I am facing is how the cartesian coordinates corresponding to sperical angles are created and how to extend this to 4 or higher dimensions. This is a very important prob. Can someone explain what exactly happens in these lines? I could extend this to higher dimensions.

# Cartesian coordinates that correspond to the spherical angles:
# (this is the equation of an ellipsoid):
x = rx * np.outer(np.cos(u), np.sin(v)) 
y = ry * np.outer(np.sin(u), np.sin(v))
z = rz * np.outer(np.ones_like(u), np.cos(v))
  1. Or I "reduce" the matrix A, which stores information in 4 or higher dimension to 3d and then plot. I am searching for a way to reduce.

Thanks in advance.

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  • I may completely have misinterpreted the problem, but what I think of is: would it be possible to use different colors for the fourth dimension? The colors would then represent some kind of "density" in that dimension. – patrik Sep 03 '14 at 14:32
  • @Schorsch the tag has been edited. I had mentioned matlab because some matlab users might have a theoretical solution of the second part, in which I have to reduce (project) the information matrix onto a hyperplane of lesser dimension. – MonsieurBeilto Sep 03 '14 at 16:12
  • @patrik I don't need to use colours, I need to show a 4/5/6 dimension matrix from different views (needing one/two/three independent vectors respectively) projected in a 3d space. If someone could explain the new edit, I think I could manage – MonsieurBeilto Sep 03 '14 at 16:16

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