I have a problem plotting a multivariable interpolated function when projected into two-dimensions using Resolve
and RegionPlot
.
I found the interpolation for a 5-variable list of data, which I call F[x1, x2, x3, x4, x5]
(the interpolation works fine), where the xi
are my variables. I want to plot a region for F
satisfying certain condition, i.e., between two numbers and then project onto a two-variable plane, say {x1, x2}
. I can do this when I fix the value of the rest of the variables, but I want to project onto x1, x2
the valid region of F
for all of the values admitted by the rest of my parameters. My code looks something like this:
ImpReg =
ImplicitRegion[-1 < F[x1, x2, x3, x4, x5] < 1,
{{x1, 1, 200}, {x2, 500, 5000}, {x3, 1, 351}, {x4, 1000, 4000}, {x5, 1, 4}]
graph =
RegionPlot[
Resolve[Exists[{x3, x4, x5}, {x1, x2, x3, x4, x5} ∈ ImpReg], Reals],
{x1, 1, 200}, {x2, 500, 5000}]
By the way, I followed the example given in Mathematica documentation for "Formula Region Projections" the only difference being that they do not use an interpolated function, but I do not see why this should be the problem.