7
It looks like you have introduced non-manifold geometry into your model. I explain non-manifold in more detail in my answer here. Even full-featured CAD packages will fail to create non-manifold geometry, as shown here:
We can try an approach using FEMAddOns as shown below. The FEM mesher will tend to create watertight and isotropic meshes.
(*Uncommented ...
3
This is an extended comment rather than an answer.
DiscretizeRegion understands how to mesh 2D objects embedded in 3D to some degree as can be shown by the following:
reg = MeshRegion[{{0, 1, 0}, {1, 0, 0}, {1, 1, 0}, {1, 0, 1}},
Polygon[{{1, 2, 3}, {2, 3, 4}}]];
HighlightMesh[DiscretizeRegion[reg, MaxCellMeasure -> {"Area" -> #}],
1] ...
3
Add the options MeshFunctions {# &, #2 &, #3 &} and Mesh -> 10 when you create surfacegraph:
surfacegraph = ParametricPlot3D[sur[r, phi] + gauss[r*Sin[phi], r*Cos[phi]],
{r, 0, 1}, {phi, 0, Pi},
MeshFunctions -> {# &, #2 &, #3 &}, Mesh -> 10];
Show[handle, surfacegraph, boundary,
PlotRange -> {{-0.5, 2}, {-0.6, ...
1
I just learnt from this post (Possible Bug in DiscretizeRegion with Option MaxCellMeasure) that this might be a bug in Mathematica.
Using one of the solutions recommended here, I applied DiscretizeRegion with the MaxCellMeasure option to the meshed object produced by DiscretizeGraphics:
mr = DiscretizeGraphics[g];
DiscretizeRegion[mr, MaxCellMeasure -> {&...
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