Intersecting RegionPlots [closed]

Does the Mathematica graphics system have any concept of intersecting regionplots? I've found about intersecting graphics but not regionplots so far. For example, if I want to show the intersection of these 2 regionplots:

RegionPlot[x^2 + y^3 < 2, {x, -2, 2}, {y, -2, 2}]
RegionPlot[x < 0.5, {x, -2, 2}, {y, -2, 2}]

I know I can use Opacity and place both regionplots on top of each other using:

PLOT1 = RegionPlot[x^2 + y^3 < 2, {x, -2, 2}, {y, -2, 2},PlotStyle -> {Yellow, Opacity[0.2]}, BoundaryStyle -> Directive[Yellow, Thick]]
PLOT2 = RegionPlot[x < 0.5, {x, -2, 2}, {y, -2, 2},PlotStyle -> {Red, Opacity[0.05]}, BoundaryStyle -> Directive[Red]]
Show[PLOT1, PLOT2, LabelStyle -> Directive[FontSize -> 20]] Or more simply:

RegionPlot[{x^2 + y^3 < 2, x < 0.5}, {x, -2, 2}, {y, -2, 2},PlotLegends->{"PLOT1", "PLOT2"}] However the common regions become less visible the more regionplots I want to intersect. I would like to exclude everything that is not part of the intersection and obtain this: I know that I could write:

RegionPlot[x^2 + y^3 < 2 && x < 0.5, {x, -2, 2}, {y, -2, 2}]

OR

A = x^2 + y^3 < 2
B = x < 0.5;
RegionPlot[And[A, B], {x, -2, 2}, {y, -2, 2}]

But if A and B are heavier expressions, or that I want to find the intersection of more than 2 regionplots, the calculations can become too heavy.

Is there a way, in my example, to draw separately RegionPlot1 and RegionPlot2 (the way I started with Opacity) and then get a unique RegionPlot but showing only the region where the 2 regionplots intersect (I wish there was a function 'RegionPlotIntersection[PLOT1,PLOT2]')?

Thanks a lot in advance.

So thank you so much for your comments! These functions were not on Mathematica 9 so I got Mathematica 10. Indeed, I get the graphic of the intersection using ImplicitRegion, RegionIntersection and BoundaryDiscretizedRegion!

PLOT1 = ImplicitRegion[x^2 + y^3 < 2, {{x, -2, 2}, {y, -2, 2}}];
PLOT2 = ImplicitRegion[x < 0.5, {{x, -2, 2}, {y, -2, 2}}];
BoundaryDiscretizeRegion[RegionIntersection[PLOT1,PLOT2]]

OR, what can be better sharing the weight of calculations among the 3 steps:

PLOT1=BoundaryDiscretizeRegion[ImplicitRegion[x^2 + y^3 < 2, {{x, -2, 2}, {y, -2, 2}}]];
PLOT2=BoundaryDiscretizeRegion[ImplicitRegion[x < 0.5, {{x, -2, 2}, {y, -2, 2}}]];
RegionIntersection[PLOT1,PLOT2] And pretty neat, it works with more than 2 regionplots!

PLOT1 = ImplicitRegion[x^2 + y^3 < 2, {{x, -2, 2}, {y, -2, 2}}];
PLOT2 = ImplicitRegion[x < 0.5, {{x, -2, 2}, {y, -2, 2}}];
PLOT3 = ImplicitRegion[y > 0, {{x, -2, 2}, {y, -2, 2}}];
BoundaryDiscretizeRegion[RegionIntersection[PLOT1,PLOT2,PLOT3]] NEW ADDITIONAL QUESTION: I get a naked graphic and I can't find the equivalent of 'AxesLabel' for discretized graphic, is there a way to keep the axes and values?

Answer: I didn't find something working including DiscretizeRegion and FrameLabel, but I keep the frame if I use RegionPlot instead:

PLOT1 = ImplicitRegion[x^2 + y^3 < 2, {{x, -2, 2}, {y, -2, 2}}];
PLOT2 = ImplicitRegion[x < 0.5, {{x, -2, 2}, {y, -2, 2}}];
RegionPlot[RegionIntersection[PLOT1,PLOT2],PlotRange->{{-2,2},{-2,2}}]
PLOT3 = ImplicitRegion[y > 0, {{x, -2, 2}, {y, -2, 2}}];
RegionPlot[RegionIntersection[PLOT1,PLOT2,PLOT3],PlotRange->{{-2,2},{-2,2}}]

My only concern is that I'm not entirely sure that I'm splitting the calculations for Mathematica. In terms on weight of calculations, I'm wondering whether it's not the same as writing:

PLOT = ImplicitRegion[x^2 + y^3 < 2 && x < 0.5 && y > 0, {{x, -2, 2}, {y, -2, 2}}];

closed as off-topic by MarcoB, user9660, Yves Klett, m_goldberg, ÖskåMar 11 '16 at 18:32

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – MarcoB, Community, Yves Klett, m_goldberg, Öskå
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• Probably it could help to share the code that define your regions so we can experience the problem. Would Reduce[And[A, B]] help? Did you try DiscretizeRegion? – rhermans Aug 24 '15 at 17:59
• Could you use a combination of RegionIntersection and ImplicitRegions? – MarcoB Aug 24 '15 at 19:44
• Look up Frame and FrameLabel. – J. M. will be back soon Aug 25 '15 at 5:57
• RegionPlot can handle more than one region: RegionPlot[{x < 0.5, x^2 + y^3 < 2}, {x, -2, 2}, {y, -2, 2}, PlotLegends -> Automatic] – Bob Hanlon Aug 25 '15 at 12:27
• Thank you, it's actually a better way than with Opacity but my question here was to keep only the intersecting region(s). – Elsa Aug 25 '15 at 16:11