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7

Discretizing polygons first then difference facilitates. Apologies if I have misunderstood issue. pol = Cases[region, Line[x__] :> Polygon[x], Infinity]; rm = RegionDifference @@ (DiscretizeRegion /@ pol); rmf = RegionMember[rm] mx = Max[pol[[1, All, #]]] & /@ {1, 2}; mn = Min[pol[[1, All, #]]] & /@ {1, 2}; Manipulate[ ...


2

It seems your Sector returns a region for which RegionMember can calculate its formula. RegionPlot is quite a bit faster on this fairly simple formula than on the region. Further, you don't run into the symbolic-numeric problem of reducing the RegionIntersection in whatever way Mathematica does under the hood. (I suspect it is using a algebraic/symbolic ...


3

Manipulate typically changes the default value of the $PerformanceGoal control to "Speed" instead of "Quality", in order to speed up evaluation of dynamic content (see the first "basic example" in its documentation page). Typically this doesn't matter much, but in some cases this can influence the outcome of some algorithms that are sensitive to the working ...


6

The OP's updated example The OP's example exhibits some numerical problems about which the fastidious ToElementMesh and even some System functions complain. Since the OP is dealing with the System` Region* functions to produce graphics, I'll assume the warnings can be ignored as long as the functions do not fail. There are two things that lead to problems ...


7

First, it would seem there is a fair amount to say. On the other hand, there is even more not to say, as this shows all the unimplemented properties (both regions give the same result): mr = DiscretizeRegion@Disk[]; (* mr = DiscretizeRegion@ImplicitRegion[1/4 <= x^2 + y^2 <= 1, {x, y}] *) Pick[mr["Properties"], Quiet@Check[mr[#], Missing[#]] ...



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