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Why doesn't this RegionPlot3D not plot anything?

RegionPlot3D[ 0 < Subscript[y, 1] < 1 && Subscript[y, 2] == 0 && Subscript[y, 3] == 1 - Subscript[y, 1] && Subscript[x, 1] == 1 && Subscript[x, 2] == 0 && Subscript[x, 3] == 0, {Subscript[y, 1], 0, 1}, {Subscript[y, 2], 0, 1}, {Subscript[y, 3], 0, 1}]

The result I would expect would be this one:

RegionPlot3D[ 0 < Subscript[y, 1] < 1 && Subscript[y, 2] == 0 && Subscript[y, 3] == 1 - Subscript[y, 1], {Subscript[y, 1], 0, 1}, {Subscript[y, 2], 0, 1}, {Subscript[y, 3], 0, 1}]

I have much more complicated expressions than this, where the common theme is that there will be 3 free variables which I specify where to plot (here, $y_1, y_2, y_3$) and all other variables will be given, like above (e.g., $x_1, x_2, x_3$ here) and I want to plot the resulting region. Is there a correct way of doing this?

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    – bbgodfrey
    Nov 14, 2021 at 22:18

1 Answer 1

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contrains = 
  0 < y[1] < 1 && y[2] == 0 && y[3] == 1 - y[1] && x[1] == 1 && 
   x[2] == 0 && x[3] == 0;
reg = ParametricRegion[{{y[1], y[2], y[3]}, 
    contrains}, {{y[1], 0, 1}, {y[2], 0, 1}, {y[3], 0, 1}, x[1], x[2],
     x[3]}];
DiscretizeRegion[reg, Boxed -> True]
Region[Style[reg, Thick, Blue], Boxed -> True]

enter image description here

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  • $\begingroup$ Is there really no way to use RegionPlot3D? I wanted its features, like the labels and all, or other future necessary things. Region seems to be very general, though. $\endgroup$
    – Jay
    Nov 15, 2021 at 6:10
  • $\begingroup$ @Jay Up to the 12.3.1 version, RegionPlot3D still can't draw such equations. We can use label in Region or use Show to add another objects in such figure. $\endgroup$
    – cvgmt
    Nov 15, 2021 at 6:57

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