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I just updated my Mathematica for Windows to 13.3 and when I tried to use the "Graphics MeshFindIntersections" command it doesn't seem to work. Have they replaced it with some other command or is it a bug in the new update?

Code used

T[rh_, Q_, P_] := 1/(4 \[Pi] rh) (1 + 8 \[Pi] P rh^2 - Q^2/rh^2)
M[rh_, Q_, P_] := rh/2 + (4 \[Pi] P rh^3)/3 + Q^2/(2 rh)
V[rh_] := 4/3 \[Pi] rh^3
S[rh_] := \[Pi] rh^2
G[rh_, Q_, P_] = Simplify[M[rh, Q, P] - (T[rh, Q, P] S[rh])];
{rc, Pc} = 
  SolveValues[{D[T[rh, Q, P], {rh, 2}] == 0, 
     D[T[rh, Q, P], rh] == 0}, {rh, P}][[2]];
Vc = V[rc]; Tc = T[rc, Q, Pc]; Gc = G[rc, Q, Pc];
T = t Tc; P = p Pc; rh = z rc; G = g Gc;
t[z_, p_] = 
  SolveValues[{T == 1/(4 \[Pi] rh) (1 + 8 \[Pi] P rh^2 - Q^2/rh^2)}, 
    t][[1]];
g[z_, p_] = 
  SolveValues[{G == (3 Q^2)/(4 rh) + rh/4 - 2/3 P \[Pi] rh^3}, g][[1]];
pplt = ParametricPlot[Evaluate@{t[z, 0.5], g[z, 0.5]}, {z, 0, 10}, 
  PlotRange -> {{0.6, 1.3}, {0.8, 1.3}}, AspectRatio -> 1]
ip = Graphics`Mesh`FindIntersections@pplt
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  • $\begingroup$ Can you please load the code that failed? $\endgroup$
    – Syed
    Commented Aug 23, 2023 at 13:21
  • $\begingroup$ Sure. One minute, let me edit it! $\endgroup$
    – codebpr
    Commented Aug 23, 2023 at 13:22
  • $\begingroup$ T is a function name and a parameter name! $\endgroup$
    – Ulrich Neumann
    Commented Aug 23, 2023 at 13:36
  • $\begingroup$ Ah my mistake! Even if I change the name, the problem still exists. $\endgroup$
    – codebpr
    Commented Aug 23, 2023 at 13:38
  • $\begingroup$ t and g diverge at zero. Therefore, you can not plot from zero. You may plot z e.g.:{z, 0.1, 10} $\endgroup$
    – Daniel Huber
    Commented Aug 23, 2023 at 13:40

2 Answers 2

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$Version

"13.3.1 for Microsoft Windows (64-bit) (July 24, 2023)"

pt = Graphics`Mesh`FindIntersections[pplt // DiscretizeGraphics, 
  Graphics`Mesh`AllPoints -> False]
Show[pplt, Graphics[{Red, AbsolutePointSize[10], Point@pt}]]

{{0.757021, 1.07072}}

enter image description here

  • It must be a bug. Here we test another example.
Clear["Global`*"];
pp = ParametricPlot[{Sin[10 t], Sin[9 t]}, {t, 0, 2 π}];
intersections1 = Graphics`Mesh`FindIntersections[pp];
intersections2 = 
  Graphics`Mesh`FindIntersections[pp // DiscretizeGraphics, 
   Graphics`Mesh`AllPoints -> False];
{Show[pp, Epilog -> {Red, PointSize[Large], Point@intersections1}], 
 Show[pp, Epilog -> {Red, PointSize[Large], Point@intersections2}]}

enter image description here

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  • $\begingroup$ Are the new constraints required for the new 13.3 version of Mathematica or are they just for this particular problem? $\endgroup$
    – codebpr
    Commented Aug 23, 2023 at 14:01
  • 1
    $\begingroup$ @codebpr Seems be a bug. Here just a working around. $\endgroup$
    – cvgmt
    Commented Aug 23, 2023 at 14:05
  • $\begingroup$ @cvgmt And the code really runs on v13.3 without recursion error due to naming errors (function T[...]and parameter T) and others?? I tried v12.2 and got several errors. $\endgroup$
    – Ulrich Neumann
    Commented Aug 23, 2023 at 14:39
  • $\begingroup$ @UlrichNeumann Without any errors message in 13.3.1 $\endgroup$
    – cvgmt
    Commented Aug 23, 2023 at 14:42
  • $\begingroup$ @cvgmt Astonishing, thanks. $\endgroup$
    – Ulrich Neumann
    Commented Aug 23, 2023 at 14:46
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Same problem with Annotation is in Finding intersection of two curves using mesh functions:

Block[{Annotation = # &}, ip = Graphics`Mesh`FindIntersections@pplt]

(* {{0.757021, 1.07072}} *)
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