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As a simple example for applying stl-files I took "cow" out of MMA example data. I'm able to discretize the Graphic without problems

kuh = ExampleData[{"Geometry3D", "Cow"}]
mesh=DiscretizeGraphics[kuh,MeshCellStyle -> {{1, All} -> Red}] (* MeshRegion *)

enter image description here

to get an stl-like triangle surface, which seems to be ok 

ConstantRegionQ[mesh]
(*True*)

for further meshing, but my attempt to create a volumemesh fails

Needs["NDSolve`FEM`"]
ToElementMesh[RegionBoundary[mesh]]
(*$Failed*)

What's wrong with my attempt? Thanks!

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  • $\begingroup$ Just drop the RegionBoundary and it should work. $\endgroup$
    – Pinti
    Commented Mar 7, 2019 at 11:02
  • $\begingroup$ Unfortunately no: ToElementMesh[mesh] (*$Failed*) $\endgroup$
    – Ulrich Neumann
    Commented Mar 7, 2019 at 11:11
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    $\begingroup$ Did you know that you can just do ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]? $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Mar 7, 2019 at 11:21
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    $\begingroup$ @ Piniti Thanks, it seems to be a problem of MMA version 11.0.1 $\endgroup$
    – Ulrich Neumann
    Commented Mar 7, 2019 at 11:23
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    $\begingroup$ However, FindMeshDefects[ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]] shows that a conversion to a volume mesh might not be straightforward. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Mar 7, 2019 at 11:23

2 Answers 2

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The cow mesh is an example of a "broken" mesh. Try 

mesh =  RepairMesh[mesh]

before sending it to ToElementMesh.

Among other nice meshes, you can find a free and "clean" cow mesh also on Keenan Crane's homepage:

https://www.cs.cmu.edu/~kmcrane/Projects/ModelRepository/

This is the model (without texture):

enter image description here

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  • $\begingroup$ Thanks, but nothing changes: meshR = RepairMesh[mesh ]; ToElementMesh[meshR] (*$Failed*) $\endgroup$
    – Ulrich Neumann
    Commented Mar 7, 2019 at 11:34
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    $\begingroup$ @Ulrich, running FindMeshDefects[meshR] should show what may be causing the failure. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Mar 7, 2019 at 11:37
  • $\begingroup$ Apparently version 11.3 can cope both with the unrepaired and the repaired mesh. So I don't know what to do. The mesh has self-intersections so tet-meshing it is nontrivial. $\endgroup$
    – Henrik Schumacher
    Commented Mar 7, 2019 at 11:39
  • $\begingroup$ Obviously the example isn't as simple as I hoped for. Thank you Henrik and J.M. $\endgroup$
    – Ulrich Neumann
    Commented Mar 7, 2019 at 11:41
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    $\begingroup$ @Ulrich By the way, a good and clean mesh is the "Triceratops". $\endgroup$
    – Henrik Schumacher
    Commented Mar 7, 2019 at 11:44
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As other's have stated, the issue is self intersecting facets:

mr = RepairMesh[ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]];

FindMeshDefects[mr]

If we could determine if a point is 'inside' the cow, we could use a naive variant of the powercrust algorithm. Here 'inside' is not necessarily well defined.

Luckily we can use isInside defined specifically for this model here!

dm = DelaunayMesh[MeshCoordinates[mr]];

powercrust = BoundaryMesh @ MeshRegion[
  MeshCoordinates[dm], 
  Pick[MeshCells[dm, 3], isInside /@ PropertyValue[{dm, 3}, MeshCellCentroid]]
];

Needs["NDSolve`FEM`"]

ToElementMesh[powercrust]

ElementMesh[{{-0.410816, 0.410816}, {-0.133851, 0.133851}, {-0.251619, 0.251619}}, {TetrahedronElement["<" 25368 ">"]}]
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