The volumes are defined by constraints but , as I compute the volumes (constraints) in a loop, I could just have a list of constraints (constraint1, constraint2, ...constraintn).
I tryed to apply "And" upon the list but it doesn't work. I tried then to make the RegionPlot3D of each constraints and then use the "Intersection" of them, but it doesn't work too.
I join the code
RegionOfConstraint[P_, u_, v_, col_, o_] := Module[{x, y, z, laff},
laff = {};
RegionPlot3D[
P[[3]] - P[[1]]*x - P[[2]]*y <= z &&
P[[3]] - P[[1]]*x - P[[2]]*y > z - 1,
{x, u[[1]], v[[1]]}, {y, u[[2]], v[[2]]}, {z, u[[3]], v[[3]]},
PlotPoints -> 50, PlotRange -> All, Mesh -> None,
PlotStyle -> Directive[col, Opacity[o]]]
];
IntersectionOfRegions[P_, u_, v_, a_, b_, c_, d_] :=
Module[{x, y, z, laff, i, j, ll, col, lU, lL},
laff = {}; lU = {}; lL = {};
For[i = 1, i <= Length[P], i++,
If[a*P[[i]][[1]] + b*P[[i]][[2]] + c*P[[i]][[3]] == d,
col = Red; AppendTo[lU, P[[i]]];
AppendTo[laff,
RegionOfConstraint[P[[i]], {-10, -10, -10}, {10, 10, 10},
col, .1]],
If[a*P[[i]][[1]] + b*P[[i]][[2]] + c*P[[i]][[3]] == d + c - 1,
col = Blue; AppendTo[lL, P[[i]]];
AppendTo[laff,
RegionOfConstraint[P[[i]], {-10, -10, -10}, {10, 10, 10},
col, .1]],
col = LightGray
]
];
];
Show[Intersection[laff]]
];
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