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# Combining Graphics Primitives by Union, Intersection and Complement

Posted 10 years ago
 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?
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Posted 10 years ago
 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] Posted 10 years ago
 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.