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I am interested in plotting the 3D region which is the intersection of functions of the form :

  • f1( x, y, z, u) = 0
  • f2( x, y, z, u) = 0
  • f3( x, y, z, u) = 0
  • gmin <= g(u) <= gmax

Note that there is a free variable u apart from the 3 coordinate vars - x,y,z

assume that it is NOT possible to simplify/eliminate the above into 3equations in x,y,z.

Is there a way this region can be plotted in Mathematica using a combination of RegionPlot3D and Boole functions?

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Answering to this is impossible if you don't specify your functions. It is not really constructive. – Artes Jan 1 at 11:23
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Three equations in four variables will give you, generically, a one-dimensional solution space, which will project to a curve in 3D. This looks like it's going to be tricky; certainly RegionPlot3D doesn't do curves. – Rahul Narain Jan 1 at 11:53
Voting to close until you give a manageable example. Finding one is much less work than answering your question, so please be the first to work on the issue. Thanks. – belisarius Jan 1 at 17:45
I am trying to get this to work : mathematica.stackexchange.com/questions/13378/…. Takes some time but solves the problem ! (dunno y the link was removed) – my account_ram Jan 2 at 14:31
Yes, this generically is a portion of a discrete union of curves, and it "lives" in 4D, not 3D. However, I believe the method I posted at mathematica.stackexchange.com/a/16238 applies and will yield a parameterization in the form of four functions of a single variable--despite the claim/assumption that this is not possible. (The method is numeric, not symbolic, and it has some limitations--it must avoid singular points.) Projecting those into 3D (such as by ignoring any one of the four functions) would be one way to make the plot. But it's not clear this is what is wanted. – whuber Jan 2 at 21:16

closed as not a real question by belisarius, rcollyer, Jens, Yves Klett, rm -rf♦ Jan 3 at 14:18

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.