Three-Set Venn Diagram with Varying Radii not Drawing Full Circles

Question

Here is the code that I have:

a = Disk[{0, 1}, 0.7];
b = Disk[{-0.5, 0}, 1.3];
c = Disk[{0.5, 0}];

subsets = Subsets[{a, b, c}, {1, 3}];

subsetscolors = Map[
   Function[
    {c},
    Blend[
     Flatten[
      Map[
       Table[
         Map[
          Append[#, 1.5/Length[c]] &,
          c
          ], 2
         ] &,
       c
       ]
      ]
     ]
    ],
   Subsets[{RGBColor["#f839ff"], RGBColor["#fff839"], 
     RGBColor["#40ff39"]}, {1, 4}]
   ];

RegionPlot[
 Evaluate[
  DiscretizeRegion[RegionDifference[
      BooleanRegion[And, #],
      BooleanRegion[Or, 
       Complement[{a, b, c, EmptyRegion[2]}, #]]]] & /@ subsets
  ],
 PlotLabels -> Callout[
   (Apply[
     StringJoin, {{"a"}, {"b"}, {"c"}, {"d"}, {"e"}, {"f"}, {"g"}}, \
{1}]),
   Center
   ],
 Sequence[
  PlotStyle -> subsetscolors,
  BoundaryStyle -> Directive[Thickness[0.01], Black],
  Frame -> True,
  LabelStyle -> {20},
  PerformanceGoal -> "Quality",
  ImageSize -> 400
  ]
 ]

Producing this output:

Because I vary the radii, not all of the circles are being drawn in full.

Sometimes (but I have been unable to reproduce this for StackExchange) varying the radii for the three disks will change the areas where the disks are not fully rendered.

I am guessing my issue is with the maybe to do with PerformanceGoal ->, but as I have this set to "Quality" I do not know what the problem is.

Answer 1

I refer to this similar post to solve your problem(just use the plotrange as bounding box via the second argument of DiscretizeRegion).

a = Disk[{0, 1}, 0.7];
b = Disk[{-0.5, 0}, 1.3];
c = Disk[{0.5, 0}];

subsets = Subsets[{a, b, c}, {1, 3}];

subsetscolors = 
  Map[Function[{c}, 
    Blend[Flatten[
      Map[Table[Map[Append[#, 1.5/Length[c]] &, c], 2] &, c]]]], 
   Subsets[{RGBColor["#f839ff"], RGBColor["#fff839"], 
     RGBColor["#40ff39"]}, {1, 4}]];

RegionPlot[
 Evaluate[DiscretizeRegion[
     RegionDifference[BooleanRegion[And, #], 
      BooleanRegion[Or, 
       Complement[{a, b, c, EmptyRegion[2]}, #]]], {{-2, 2}, {-2, 
       2}}] & /@ subsets], 
 PlotLabels -> 
  Callout[(Apply[
     StringJoin, {{"a"}, {"b"}, {"c"}, {"d"}, {"e"}, {"f"}, {"g"}}, \
{1}]), Center], 
 Sequence[PlotStyle -> subsetscolors, 
  BoundaryStyle -> Directive[Thickness[0.01], Black], Frame -> True, 
  LabelStyle -> {20}, PerformanceGoal -> "Quality", ImageSize -> 400],
  PlotRange -> Full]

It should be noted that the editor does not allow us to manually adjust the display size of the image, which is too inconvenient.

Answer 2

It's just a simple test.

{p, q, r} = {x^2 + (y - 1)^2 - 0.7^2 > 0, (x + 0.5)^2 + y^2 - 1.3^2 > 
    0, (x - 0.5)^2 + y^2 - 1^2 > 0};
boolean = 
  Reverse[List @@ 
    Distribute[And[Or[p, ! p], Or[q, ! q], Or[r, ! r]], Or, And]];
RegionPlot[boolean, {x, -2, 2}, {y, -2, 2}, 
 PlotLabels -> Placed[{"a", "b", "c", "d", "e", "f", "g"}, Center], 
 PlotStyle -> {Red, Orange, Yellow, Green, Blue, Cyan, Purple, Brown},
  PlotPoints -> 30, Frame -> False] 

Answer 3

Are the radius values important? This works for me:

a = Disk[{0, 1}, 0.5];
b = Disk[{-0.5, 0}];
c = Disk[{0.5, 0}];

Moving the centers by 0.1 also works:

a = Disk[{0, 1}, 0.7];
b = Disk[{-0.4, 0}, 1.3];
c = Disk[{0.6, 0}];