DiscretizeRegion failing on macOS with 14.3

Questions
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1

The first graphic is from a notebook many years old, and the second is from the latest version of Mathematica. What’s going on?

Is this a known regression in functionality?

9870Untitled.jpg
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9363Untitled2.png
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n = 7; m = 3; dt = 2 Pi/n; dtm = 2 Pi/m; r = 
 1./(1 - Sin[dt/2]/Cos[dtm/2]); R = 1. r Cos[(dt + dtm)/2]/Cos[dtm/2];
ToMatrix[z_, 
   r_] := (I/r) {{z, r^2 - z Conjugate[z]}, {1, -Conjugate[z]}};
alist = Table[
  ToMatrix[r Exp[I t], r - 1], {t, dt/2, 2 Pi, dt}]; Tlist = 
 Join[{IdentityMatrix[2]}, alist];
homography[{{a_, b_}, {c_, d_}}, z_] := (a z + b)/(c z + d);
FindT[T0_, Tlist_] := 
  MemberQ[Tlist, 
   T_ /; Abs[homography[T, 0] - homography[T0, 0]] < 1.0*^-3];
i2 = 1; Do[i1 = i2 + 1; i2 = Length[Tlist]; 
 Do[Scan[(T = Tlist[[i]] . #; 
     If[! FindT[T, Tlist], Tlist = Append[Tlist, T]]) &, alist], {i, 
   i1, i2}], {2}];
plot = Show[
  Graphics[
   Map[Line[
      Table[z = homography[#, R Exp[I t]]; {Re[z], Im[z]}, {t, 0, 
        2 Pi, dt}]] &, Tlist], AspectRatio -> Automatic], 
  Axes -> True]

data = (Table[
      z = homography[#1, R Exp[I t]]; {Re[z], Im[z], 0.}, {t, 0, 
       2 \[Pi], dt}] &) /@ Tlist;
L = MeshRegion[Join @@ Most /@ data, 
   Line[Join @@ (Partition[#1, 2, 1, 1] &) /@ 
      Partition[Range[7 Length[data]], 7]]];
f = RegionDistance[L];
\[Theta]1 = 0.08;
\[Theta]2 = 0.01;
z =.
R1 = ImplicitRegion[
   f[{x, y, z}] <= \[Theta]1, {{x, -4, 4}, {y, -4, 4}, {z, -2, 2}}];
S1 = DiscretizeRegion[R1, MaxCellMeasure -> 0.0001]
2

Hi Eric,
Could you please include your code by using code format button in post editor to appear formatted like this:

int = Integrate[1/(x^3 - 1), x];
Map[Framed, int, Infinity]

or add notebook or attach one

Editor_WC_3.png
Editor_WC_3.png958×303 31.8 KB

3

Code to reproduce is attached. The exact same code worked in a previous version of Mma, circa 2019.

4

Works for me on version 14.3. What is your current version?
Also could you please try to evaluate the notebook below and let us know the outputs?

Open in Wolfram Cloud ↗
5

I’m using 14.3 on an M3 Ultra Mac Studio with 96 MB. When I evaluate the notebook you attached, I get

DiscretizeRegion[
 ImplicitRegion[
  RegionDistanceFunction[MeshRegion[< 3 >, < 1 >], <>][{x, y, z}] <= 
    0.08 && -4 <= x <= 4 && -4 <= y <= 4 && -2 <= z <= 2, {x, y, z}], 
 MaxCellMeasure -> 0.0001]

and not the region you got or I got in a previous version of Mma.

6

Just to add to the data.

On Wolfram Cloud, I get Ahmed’s results. (14.3.0 for Linux x86 (64-bit) (July 8, 2025)).

On my Mac, I get Eric’s result ("14.3.0 for Mac OS X ARM (64-bit) (July 8, 2025)").

Further:

This works:

BoundaryDiscretizeRegion[R1, MaxCellMeasure -> 0.0001]

But calling DiscretizeRegion[] on the output fails.

It’s probably a bug and Eric should report it to WRI (imo).

7

Thank you for investigating this. I was planning to fire up a VM and test with other OSs. Now I don’t have to.

8

Thank you @Michael Rogers for confirmation. I reported it to relevant Wolfram’s teams.

9

This is known now to the developers. They suggested this workaround, could you please try it?

S1 = BoundaryDiscretizeRegion[R1, MaxCellMeasure -> 0.001]
10

Yes, that works as Michael noted.