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First I have

ContourPlot3D[{ (1 - p1) (1 - p2)^3 == p1 p2^3, p1 p2^6 (c p1 + (1 - c) p2)^3 ((1 - c) p1 + c p2)^2 == (1 - p1) (1 -p2)^6 (1 - c p1 - (1 - c) p2)^3 (1 - (1 - c) p1 - c p2)^2 }, {p1, 0.2, 0}, {p2, 1, 0.5}, {c, 0, 1}, Lighting -> ({"Directional", White, #} & /@ Tuples[{-1, 1}, 3]), Mesh -> None, BoxRatios -> {2, 2, 1}, ContourStyle -> {Yellow, Directive[Red, Opacity[0.5]]}, BaseStyle -> {FontWeight -> "Bold", FontSize -> 20}]

which will show me (please don't mind the labels)

enter image description here

I want Mathematica to plot the region between the yellow plane and the transparent red plane, so I use RegionPlot3D with the same set of equations.

RegionPlot3D[(1 - p1) (1 - p2)^3 > p1 p2^3 && p1 p2^6 (c p1 + (1 - c) p2)^3 (c p2 + (1 - c) p1)^2 > (1 - p1) (1 - p2)^6 (1 - (c p1 + (1 - c) p2))^3 (1 - (c p2 + (1 - c) p1))^2, {p1, 0, 0.2}, {p2, 0.5, 1}, {c, 0, 1}, Mesh -> None, FaceGrids -> All, ViewPoint -> Front,PlotPoints->100]

which will give me the following:

enter image description here

One will expect RegionPlot3D will give a single connected bulk but instead there are several rod-like artifacts. How to get a nice region plot with that set of equations? (Increasing plotpoints to 200 might work, but it takes so long...)

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1 Answer 1

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Maybe you can just plot the boundary surface of the region piece by piece, and then combine them together to shape the region:

funcSet = { (1 - p1) (1 - p2)^3 - p1 p2^3, -(1 - p1) (1 - p2)^6 (1 - c p1 - (1 - c) p2)^3 (1 - (1 - c) p1 - c p2)^2 + p1 p2^6 (c p1 + (1 - c) p2)^3 ((1 - c) p1 + c p2)^2 }; Clear[regionBoundaryPlot] regionBoundaryPlot[f1_, f2_, opts___] := With[ {f2$temp = f2 /. {p1 -> p1$, p2 -> p2$, c -> c$}}, ContourPlot3D[f1 == 0, {p1, 0, 0.2}, {p2, 0.5, 1}, {c, 0, 1}, opts, RegionFunction -> Function[{p1, p2, c}, f2$temp > 0] ]] Show[{ regionBoundaryPlot[funcSet[[1]], funcSet[[2]], Mesh -> True, MeshStyle -> Blue, MeshFunctions -> Function[{p1, p2, c}, Evaluate[funcSet[[2]]]], PlotPoints -> 40], regionBoundaryPlot[funcSet[[2]], funcSet[[1]], Mesh -> True, MeshStyle -> Gray, MeshFunctions -> Function[{p1, p2, c}, Evaluate[funcSet[[1]]]], PlotPoints -> 40] }, PlotRange -> {{0, .05}, All, All}, BoxRatios -> {.5, 1, .5}]

region plot

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  • $\begingroup$ Nice idea! Is there anything special with the variables (in your regionBoundaryPlot function) whose names contain "$"? $\endgroup$ Commented May 10, 2013 at 3:55
  • $\begingroup$ @wdg Thanks for accepting. It's because With renamed the variables inside it. Check this: With[{y = x}, Function[x, y]]. Note it may not be the best way to inject code into Function, please do search relevant posts on this site. $\endgroup$ Commented May 10, 2013 at 9:40

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