# GraphicsMeshFindIntersections not working in Mathematica 13.3

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 = GraphicsMeshFindIntersections@pplt

– Syed
Aug 23 at 13:21
• Sure. One minute, let me edit it! Aug 23 at 13:22
• T is a function name and a parameter name! Aug 23 at 13:36
• Ah my mistake! Even if I change the name, the problem still exists. Aug 23 at 13:38
• t and g diverge at zero. Therefore, you can not plot from zero. You may plot z e.g.:{z, 0.1, 10} Aug 23 at 13:40

\$Version


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

pt = GraphicsMeshFindIntersections[pplt // DiscretizeGraphics,
GraphicsMeshAllPoints -> False]
Show[pplt, Graphics[{Red, AbsolutePointSize[10], Point@pt}]]


{{0.757021, 1.07072}}

• 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 = GraphicsMeshFindIntersections[pp];
intersections2 =
GraphicsMeshFindIntersections[pp // DiscretizeGraphics,
GraphicsMeshAllPoints -> False];
{Show[pp, Epilog -> {Red, PointSize[Large], Point@intersections1}],
Show[pp, Epilog -> {Red, PointSize[Large], Point@intersections2}]}


• Are the new constraints required for the new 13.3 version of Mathematica or are they just for this particular problem? Aug 23 at 14:01
• @codebpr Seems be a bug. Here just a working around. Aug 23 at 14:05
• @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. Aug 23 at 14:39
• @UlrichNeumann Without any errors message in 13.3.1 Aug 23 at 14:42
• @cvgmt Astonishing, thanks. Aug 23 at 14:46