I have a problem which I cannot solve efficiently. I have a list of half-planes, disks and exteriors of disks and know that the intersection defines a bounded object, which I want to draw. RegionPlot doesn’t work as it takes too long and is also very imprecise. You could say I would like to do the following; Given several graphics primitives (in my particular case these are all disks and squares in general position, i.e. special polygons) I want to draw that object one gets when combining these graphics primitives by some of the set operations union, intersection and complement. Is there any easy way to do that?
You could try using Reduce to calculate the intersection using constraint definitions of the half-planes, disks, etc. and then use RegionPlot on the result.
One wants to use Boole[] and bring the functions from this old post Re: Fläche sich überlagernder Objekte into 3D to new life.
An overkill
Graphics3D[
Table[If[Boole[ x/2 + (3 y)/5 + (5 z)/6 > 0 && -(x/2) + (3 y)/5 + (5 z)/6 < -(2/3) &&
x/2 - (3 y)/5 + (5 z)/6 < -(1/2) && x/2 + (3 y)/5 - (5 z)/6 > -(1/2)] == 1, Sphere[{x, y, z}]],
{x,0, 6, 0.2}, {y, -6, 6, 0.2}, {z, -6, 6, 0.2}]]
and obviously confused by the many (useless) inner points
ListSurfacePlot3D[
DeleteMissing[
Flatten[Table[
If[Boole[x/2 + (3 y)/5 + (5 z)/6 > 0 && -(x/2) + (3 y)/5 + (5 z)/6 < -(2/3) &&
x/2 - (3 y)/5 + (5 z)/6 < -(1/2) && x/2 + (3 y)/5 - (5 z)/6 > -(1/2)] == 1, {x, y, z},
Missing[]], {x, 0, 6, 0.1}, {y, -6, 6, 0.1}, {z, -6, 6, 0.1}],
2]], MaxPlotPoints -> 50]
