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I am trying to plot sets like $$\left\{x \in \mathbb R ^3 : x_1,x_2,x_3 \geq 0, x_i \leq x_j + x_k \mbox{for all combinations of }i,j,k \in \{1,2,3\} \right\}$$ with MATLAB to include the figures in a document I am writing and I could not find a nice way to do this. Does anyone know how to do it?

Thanks for any help.

jan1892
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  • You want to a 3-D scatter plot of this set? If so, use plot3. However, I think you'll first need to better define the set numerically. For instance, are there uncountably many elements? If so, how could you ever hope to plot it? Or is it a shape of some sort, so that you could plot it using patches? You can always define a 3-D meshgrid and just test every point. Of course, that's just a discrete approximation of a subset of this set since you'll have to set upper and lower limits and define only a finite set of points. Regardless, more specificity is needed. – AnonSubmitter85 Aug 06 '14 at 01:44
  • I did not see your answer. These are of course uncountably many points. They form a convex cone in $\mathbb R^3$ with vertex at 0. Is there maybe another program, which is good for drawing stuff like that. I basically just need a figure. – jan1892 Aug 18 '14 at 13:16
  • Have you tried looking at these links? – AnonSubmitter85 Aug 18 '14 at 21:36
  • I did. The problem is, that I do not know exactly how this cone looks like (and similar stuff I wanted to plot). I hoped I find a way to let MATLAB handle the thinking. – jan1892 Aug 19 '14 at 06:32
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    If they form a convex cone, can't you calculate a set of points yourself and use that to plot the cone? For instance, by inspection it's obvious that $(0,0,0)$ is a member of the set. Can you start from that and find enough other points in the set so that you can define patches or the subset's convex hull? From that, plotting the cone should be easy. – AnonSubmitter85 Aug 19 '14 at 19:42
  • I think that's the way it will work. I am not sure how easy it will be to find enough points whose convex hull (I tried that before posting, but I stopped in hope of an easier way). Thanks for your help :) – jan1892 Aug 20 '14 at 12:04
  • You could try posting another question about finding/calculating the set rather than how to plot it. Most of the people around here do not use matlab, so be sure to include tags relating to convex analysis, optimization/minimization, and the like. I'm sure somebody around here knows a good way to do it. Best of luck to you. – AnonSubmitter85 Aug 20 '14 at 21:50

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