0
$\begingroup$

Suppose I have three coordinate functions of a vector of parameters: x[q], y[q], z[q] where q is at least a three-dimensional vector in some domain $Q$. Is it possible to plot in 3D the space spanned by q? By that I mean all the triplets {x',y',z'} such that there is at least one q in $Q$ such that x[q]=x', y[q]=y', z[q]=z'? Of course I would be happy if this worked with intervals (say $Q$ is the unit cube). And of course I would be happy with the surface of the subset.

I need to quickly check that this is a convex subset of $\mathbb{R}^3$. So any other method is welcome.

$\endgroup$
2
$\begingroup$

Assuming your three scalar functions x, y, and z have been defined, you'd do something like this:

n = 3;
q = Array[q1, n]; 
RegionPlot3D[
 Length[FindInstance[(x @@ q == x1) && (y @@ q == y1) && (z @@ q == z1), q]] > 
  0, {x1, -1, 1}, {y1, -1, 1}, {z1, -1, 1}]

Here, n is the dimension of $Q$. This is all I can do without knowing how the unknowns in your question are actually defined.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.