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Meshing the cow

Determine whether points lie within a cowCreating a 2D meshing algorithm in MathematicaHow to control the order of meshing？Meshing the surface of a non-convex objectMeshing of a cubeWhat is the difference between getting a boundary mesh from ToBoundaryMesh vs doing it with ToElementMesh?Behaviour of meshing in BoundaryDiscretizeRegionHexagonal meshing in Plot3DMeshing a thin tubeMeshing a cylindrical geometry with a notchTrouble meshing a Corbino disc

6

$begingroup$

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 *)

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!

mesh

share|improve this question

edited 9 hours ago

Ulrich Neumann

asked 9 hours ago

Ulrich NeumannUlrich Neumann

9,488516

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Just drop the RegionBoundary and it should work.
  $endgroup$
  – Pinti
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Unfortunately no: ToElementMesh[mesh] (*$Failed*)
  $endgroup$
  – Ulrich Neumann
  9 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Did you know that you can just do ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]?
  $endgroup$
  – J. M. is computer-less♦
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @ Piniti Thanks, it seems to be a problem of MMA version 11.0.1
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  However, FindMeshDefects[ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]] shows that a conversion to a volume mesh might not be straightforward.
  $endgroup$
  – J. M. is computer-less♦
  8 hours ago
  

  
  
  
  

 | 
show 2 more comments

6

$begingroup$

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 *)

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!

mesh

share|improve this question

edited 9 hours ago

Ulrich Neumann

asked 9 hours ago

Ulrich NeumannUlrich Neumann

9,488516

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Just drop the RegionBoundary and it should work.
  $endgroup$
  – Pinti
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Unfortunately no: ToElementMesh[mesh] (*$Failed*)
  $endgroup$
  – Ulrich Neumann
  9 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Did you know that you can just do ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]?
  $endgroup$
  – J. M. is computer-less♦
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @ Piniti Thanks, it seems to be a problem of MMA version 11.0.1
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  However, FindMeshDefects[ExampleData[{"Geometry3D", "Cow"}, "MeshRegion"]] shows that a conversion to a volume mesh might not be straightforward.
  $endgroup$
  – J. M. is computer-less♦
  8 hours ago
  

  
  
  
  

 | 
show 2 more comments

$begingroup$

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 *)

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!

mesh

share|improve this question

edited 9 hours ago

Ulrich Neumann

asked 9 hours ago

Ulrich NeumannUlrich Neumann

9,488516

$endgroup$

kuh = ExampleData[{"Geometry3D", "Cow"}]

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

ConstantRegionQ[mesh]

(*True*)    

Needs["NDSolve`FEM`"]

ToElementMesh[RegionBoundary[mesh]]

(*$Failed*)

share|improve this question

edited 9 hours ago

Ulrich Neumann

asked 9 hours ago

Ulrich NeumannUlrich Neumann

9,488516

share|improve this question

edited 9 hours ago

Ulrich Neumann

asked 9 hours ago

Ulrich NeumannUlrich Neumann

9,488516

asked 9 hours ago

Ulrich NeumannUlrich Neumann

9,488516

asked 9 hours ago

Ulrich NeumannUlrich Neumann

9,488516

2 Answers
2

active

oldest

votes

5

$begingroup$

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

mesh =  RepairMesh[mesh]

before sending it to ToElementMesh.

share|improve this answer

answered 8 hours ago

Henrik SchumacherHenrik Schumacher

55.6k576154

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks, but nothing changes: meshR = RepairMesh[mesh ]; ToElementMesh[meshR] (*$Failed*)
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @Ulrich, running FindMeshDefects[meshR] should show what may be causing the failure.
  $endgroup$
  – J. M. is computer-less♦
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Obviously the example isn't as simple as I hoped for. Thank you Henrik and J.M.
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Ulrich By the way, a good and clean mesh is the "Triceratops".
  $endgroup$
  – Henrik Schumacher
  8 hours ago
  

  
  
  
  

 | 
show 1 more comment

1

$begingroup$

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 ">"]}]

share|improve this answer

answered 3 hours ago

Chip HurstChip Hurst

21.9k15790

$endgroup$

add a comment | 

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5

$begingroup$

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

mesh =  RepairMesh[mesh]

before sending it to ToElementMesh.

share|improve this answer

answered 8 hours ago

Henrik SchumacherHenrik Schumacher

55.6k576154

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks, but nothing changes: meshR = RepairMesh[mesh ]; ToElementMesh[meshR] (*$Failed*)
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @Ulrich, running FindMeshDefects[meshR] should show what may be causing the failure.
  $endgroup$
  – J. M. is computer-less♦
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Obviously the example isn't as simple as I hoped for. Thank you Henrik and J.M.
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Ulrich By the way, a good and clean mesh is the "Triceratops".
  $endgroup$
  – Henrik Schumacher
  8 hours ago
  

  
  
  
  

 | 
show 1 more comment

5

$begingroup$

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

mesh =  RepairMesh[mesh]

before sending it to ToElementMesh.

share|improve this answer

answered 8 hours ago

Henrik SchumacherHenrik Schumacher

55.6k576154

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks, but nothing changes: meshR = RepairMesh[mesh ]; ToElementMesh[meshR] (*$Failed*)
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  
  
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  $begingroup$
  @Ulrich, running FindMeshDefects[meshR] should show what may be causing the failure.
  $endgroup$
  – J. M. is computer-less♦
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  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
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Obviously the example isn't as simple as I hoped for. Thank you Henrik and J.M.
  $endgroup$
  – Ulrich Neumann
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Ulrich By the way, a good and clean mesh is the "Triceratops".
  $endgroup$
  – Henrik Schumacher
  8 hours ago
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

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

mesh =  RepairMesh[mesh]

before sending it to ToElementMesh.

share|improve this answer

answered 8 hours ago

Henrik SchumacherHenrik Schumacher

55.6k576154

$endgroup$

mesh =  RepairMesh[mesh]

share|improve this answer

answered 8 hours ago

Henrik SchumacherHenrik Schumacher

55.6k576154

answered 8 hours ago

Henrik SchumacherHenrik Schumacher

55.6k576154

answered 8 hours ago

Henrik SchumacherHenrik Schumacher

55.6k576154

1

$begingroup$

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 ">"]}]

share|improve this answer

answered 3 hours ago

Chip HurstChip Hurst

21.9k15790

$endgroup$

add a comment | 

1

$begingroup$

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 ">"]}]

share|improve this answer

answered 3 hours ago

Chip HurstChip Hurst

21.9k15790

$endgroup$

add a comment | 

$begingroup$

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 ">"]}]

share|improve this answer

answered 3 hours ago

Chip HurstChip Hurst

21.9k15790

$endgroup$

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



FindMeshDefects[mr]

dm = DelaunayMesh[MeshCoordinates[mr]];



powercrust = BoundaryMesh @ MeshRegion[

  MeshCoordinates[dm], 

  Pick[MeshCells[dm, 3], isInside /@ PropertyValue[{dm, 3}, MeshCellCentroid]]

];



Needs["NDSolve`FEM`"]



ToElementMesh[powercrust]

share|improve this answer

answered 3 hours ago

Chip HurstChip Hurst

21.9k15790

answered 3 hours ago

Chip HurstChip Hurst

21.9k15790

answered 3 hours ago

Chip HurstChip Hurst

21.9k15790