# Intersect plot and parametric region

I have a vector plot and a region plot on the same scale and I wish to join them like when using Show[ , ]. Now, the vector plot has part outside the region that I would like to delete. Any idea how to do it ? Thanks !

Here repectively the region and vector plots:

The superimposition

So I would like to remove the segments of the lines lying outside the shaded area.

• Does something like StreamPlot[{x^2,y},Element[{x,y},ImplicitRegion[2x^3+y^2<1,{x,y}]],StreamScale->None] work?
Feb 22 at 2:02
• @cvgmt I'm essentially using ListStreamPlot[list, StreamScale -> None, StreamColorFunction -> None] with some list (the result of a numerical integration of a PDE) and RegionPlot[W] for some parametric region W. Feb 22 at 2:05
• @Adam It works, but I was looking for some solution after obtaining both plots. Getting each one of them takes considerable machine time so I did not want to run it again. Feb 22 at 2:07

Using the RegionFunction you can restrict the ListStreamPlot to a parametric region. I will have to create some data first.

ℛ =
ParametricRegion[{{s, (1 + t) s^2 - t}, -1 <= s <= 1 &&
0 <= t <= 1}, {s, t}];


data = Table[{{x, y}, {y, x - y}}, {x, -1.5, 1.5, 0.2}, {y, -2, 2,
0.2}];
ListStreamPlot[data
, AspectRatio -> Automatic
]


You can use RegionFunction like this:

ListStreamPlot[data
, RegionFunction ->
Function[{x, y}, RegionMember[ℛ, {x, y}]]
, AspectRatio -> Automatic
]


• Excellent !!! Thank you so much. Feb 22 at 8:28
• You are most welcome. Thanks for the accept.
– Syed
Feb 22 at 8:29