How can I compute the intersection of several Regionplot3D?

Questions
,
1

Hi

In a loop I compute several volumes and put them in a list.

I need to compute their intersection.

The "intersection" function seems not applicable on this kind of list.

Could anyone tell me how to perform intersection of volumes obtained by RegionPlot3D?

Best regards

2

If the volumes are defined by constraints, you could do RegionPlot[ constraint1 && constraint2 && …]

3

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]]
   ];
4

To convert {cons1, cons2, …} to cons1 && cons2 && … you want to do
And @@ {cons1, cons2, …}

5

Thanks

And @@ {constraint1, ...., constraintn} works!