Bugs with computational geometry: versions 12.2 vs 13.2

Question

Updated

System Info: HONOR laptop AMD Ryzen 5 4600H 3Hz 6 cores 16GB Memory,
Windows 10 Pro 64 bit with updates.

Mathematica Info: Versions 12.2 and 13.2, both on the same laptop.

Examples:

p1 = RandomPolygon[{"Simple", 50}, DataRange -> {{1, 2}, {1, 2}}];
p2 = RandomPolygon[{"Simple", 50}, DataRange -> {{1, 2}, {1, 2}}];  

Timing[RegionIntersection[p1, p2] === EmptyRegion[2]]  

WM 12.2: 0.1-0.3 s vs WM 13.2: 3.1-3.6 s

Timing[RegionDifference[p1, p2]] 

WM 12.2: 0.3-0.34 s vs WM 13.2: 3.4-3.5 s

Timing[RegionUnion[p1, p2]]

WM 12.2: 0.1-0.2 s vs WM 13.2: 0.7-0.9 s

Other operations (graphs, big numbers) do not show such differences, but I still checking.

More specific question

For one demo, I'd like to create shapes like this one:

Not too complex (without holes and self-intersections), so the output is just simple polygon with 30-50 vertices:

bf[p_, s_] := 
  BSplineFunction[p, SplineClosed -> True, SplineDegree -> s];
initialShape = 
  With[{pts = RandomReal[{0.2, 0.6}, {9, 2}]*CirclePoints[9]},
   Polygon[Table[ bf[pts, 4][t], {t, 0, 1, 0.02}]]
   ];
shape[center_, size_] := 
  TranslationTransform[center][
   ScalingTransform[{size, size}][initialShape]];

For further I need to analyze the intersections of these figures. The problem with RegionDisjoint has already been described here, and in version 13.2 it still remained:

RegionDisjoint[shape[{1., 1.}, 1.], shape[{5., 5.}, 2.]]

Output:

OK, we can use RegionIntersection:

isNonIntersect[shape1_, shape2_] :=
  RegionIntersection[shape1, shape2] === EmptyRegion[2];

It works, but I found big oddities with the timing of RegionIntersection:

Result:
True Version 12.2: 0.06-0.08s Version 13.2: 1.2-1.3s
False Version 12.2: 0.0s Version 13.2: 0.01-0.2s

Why does it take longer to get True, and why Mathematica 13.2 is so slow?!
(all it runs on the same laptop with Win 10)

Answer 1

If simple polygons are given by lists of their vertices, then the fastest and most reliable way to check their intersection is:

myRegion[pts_] := 
  With[{bnd = Append[Range@Length@pts, 1]}, 
   BoundaryMeshRegion[pts, Line@bnd]];

isIntersect[verts1_, verts2_] :=
  UnsameQ[RegionIntersection[myRegion/@{verts1, verts2}], 
   EmptyRegion[2]];

It's 10-15 times faster than UnsameQ[RegionIntersection[Polygon@verts1, Polygon@verts2], EmptyRegion[2]] both on 12.2 and 13.2.