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5

$begingroup$

Here is the code I am working with. I create a list of random coordinates, then I create a triangular mesh with the code:

list = RandomInteger[1, 10, 10, 2]
mesh = DelaunayMesh[
 list,
 MeshCellLabel -> 0 -> "Index",
 PlotTheme -> "Lines",
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black,
 Frame -> True
 ]

How can I select a specific triangle? For example, how can I select the triangle with vertices 10,7,2.

computational-geometry

share|improve this question

edited 8 hours ago

C. E.

52.8k33 gold badges102102 silver badges210210 bronze badges

asked 8 hours ago

Las des NestorLas des Nestor

6955 bronze badges

$endgroup$

add a comment | 

5

$begingroup$

Here is the code I am working with. I create a list of random coordinates, then I create a triangular mesh with the code:

list = RandomInteger[1, 10, 10, 2]
mesh = DelaunayMesh[
 list,
 MeshCellLabel -> 0 -> "Index",
 PlotTheme -> "Lines",
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black,
 Frame -> True
 ]

How can I select a specific triangle? For example, how can I select the triangle with vertices 10,7,2.

computational-geometry

share|improve this question

edited 8 hours ago

C. E.

52.8k33 gold badges102102 silver badges210210 bronze badges

asked 8 hours ago

Las des NestorLas des Nestor

6955 bronze badges

$endgroup$

add a comment | 

$begingroup$

Here is the code I am working with. I create a list of random coordinates, then I create a triangular mesh with the code:

list = RandomInteger[1, 10, 10, 2]
mesh = DelaunayMesh[
 list,
 MeshCellLabel -> 0 -> "Index",
 PlotTheme -> "Lines",
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black,
 Frame -> True
 ]

How can I select a specific triangle? For example, how can I select the triangle with vertices 10,7,2.

computational-geometry

share|improve this question

edited 8 hours ago

C. E.

52.8k33 gold badges102102 silver badges210210 bronze badges

asked 8 hours ago

Las des NestorLas des Nestor

6955 bronze badges

$endgroup$

list = RandomInteger[1, 10, 10, 2]
mesh = DelaunayMesh[
 list,
 MeshCellLabel -> 0 -> "Index",
 PlotTheme -> "Lines",
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black,
 Frame -> True
 ]

share|improve this question

edited 8 hours ago

C. E.

52.8k33 gold badges102102 silver badges210210 bronze badges

asked 8 hours ago

Las des NestorLas des Nestor

6955 bronze badges

share|improve this question

edited 8 hours ago

C. E.

52.8k33 gold badges102102 silver badges210210 bronze badges

asked 8 hours ago

Las des NestorLas des Nestor

6955 bronze badges

edited 8 hours ago

C. E.

52.8k33 gold badges102102 silver badges210210 bronze badges

edited 8 hours ago

C. E.

52.8k33 gold badges102102 silver badges210210 bronze badges

asked 8 hours ago

Las des NestorLas des Nestor

6955 bronze badges

asked 8 hours ago

Las des NestorLas des Nestor

6955 bronze badges

1 Answer
1

active

oldest

votes

6

$begingroup$

SeedRandom[1]
list = RandomInteger[1, 10, 10, 2];
mesh = DelaunayMesh[list, MeshCellLabel -> 0 -> "Index", 
 PlotTheme -> "Lines", 
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black, 
 Frame -> True]

You can create an association mapping face vertices to face indices using the property "FaceVertexConnectivityRules":

vertexToFace = Association[Reverse /@ mesh["FaceVertexConnectivityRules"]]

<|3, 8, 5 -> 1, 8, 3, 7 -> 2, 2, 5, 10 -> 3, 1, 5, 8 ->
4, 10, 5, 1 -> 5, 8, 9, 1 -> 6, 9, 7, 4 -> 7, 7, 9, 8 ->
8, 10, 4, 6 -> 9, 4, 10, 9 -> 10, 10, 6, 2 ->
11, 9, 10, 1 -> 12|>

HighlightMesh[mesh, Style[2, vertexToFace[3, 8, 5], Red]]

share|improve this answer

answered 8 hours ago

kglrkglr

202k1010 gold badges231231 silver badges462462 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How did you know about the faces vertex coordinates rules? I couldn't find it in the documentation.
  $endgroup$
  – Las des Nestor
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor Yes, these things are mostly undocumented. This is why Mathematica.StackExchange is so valuable: People try a lot of spelunking and also a few of the developers are around here.
  $endgroup$
  – Henrik Schumacher
  8 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor, try mesh["Properties"] to see a long list of properties. Since they are not documented it is by trial and luck that you discover quiet a few useful properties.
  $endgroup$
  – kglr
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Is there a way to extract that particular triangle, so I can compare them with the other ones? Let say that I select a triangle and I want to check if the triangle is part of the original plot.
  $endgroup$
  – Las des Nestor
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor, the triangle (polygon) can be obtained using MeshPrimitives[mesh, 2,1] or using MeshPrimitives[mesh, 2,vertexToFace[3,8,5]].
  $endgroup$
  – kglr
  6 hours ago
  

  
  
  
  

add a comment | 

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6

$begingroup$

SeedRandom[1]
list = RandomInteger[1, 10, 10, 2];
mesh = DelaunayMesh[list, MeshCellLabel -> 0 -> "Index", 
 PlotTheme -> "Lines", 
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black, 
 Frame -> True]

You can create an association mapping face vertices to face indices using the property "FaceVertexConnectivityRules":

vertexToFace = Association[Reverse /@ mesh["FaceVertexConnectivityRules"]]

<|3, 8, 5 -> 1, 8, 3, 7 -> 2, 2, 5, 10 -> 3, 1, 5, 8 ->
4, 10, 5, 1 -> 5, 8, 9, 1 -> 6, 9, 7, 4 -> 7, 7, 9, 8 ->
8, 10, 4, 6 -> 9, 4, 10, 9 -> 10, 10, 6, 2 ->
11, 9, 10, 1 -> 12|>

HighlightMesh[mesh, Style[2, vertexToFace[3, 8, 5], Red]]

share|improve this answer

answered 8 hours ago

kglrkglr

202k1010 gold badges231231 silver badges462462 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How did you know about the faces vertex coordinates rules? I couldn't find it in the documentation.
  $endgroup$
  – Las des Nestor
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor Yes, these things are mostly undocumented. This is why Mathematica.StackExchange is so valuable: People try a lot of spelunking and also a few of the developers are around here.
  $endgroup$
  – Henrik Schumacher
  8 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor, try mesh["Properties"] to see a long list of properties. Since they are not documented it is by trial and luck that you discover quiet a few useful properties.
  $endgroup$
  – kglr
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Is there a way to extract that particular triangle, so I can compare them with the other ones? Let say that I select a triangle and I want to check if the triangle is part of the original plot.
  $endgroup$
  – Las des Nestor
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor, the triangle (polygon) can be obtained using MeshPrimitives[mesh, 2,1] or using MeshPrimitives[mesh, 2,vertexToFace[3,8,5]].
  $endgroup$
  – kglr
  6 hours ago
  

  
  
  
  

add a comment | 

6

$begingroup$

SeedRandom[1]
list = RandomInteger[1, 10, 10, 2];
mesh = DelaunayMesh[list, MeshCellLabel -> 0 -> "Index", 
 PlotTheme -> "Lines", 
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black, 
 Frame -> True]

You can create an association mapping face vertices to face indices using the property "FaceVertexConnectivityRules":

vertexToFace = Association[Reverse /@ mesh["FaceVertexConnectivityRules"]]

<|3, 8, 5 -> 1, 8, 3, 7 -> 2, 2, 5, 10 -> 3, 1, 5, 8 ->
4, 10, 5, 1 -> 5, 8, 9, 1 -> 6, 9, 7, 4 -> 7, 7, 9, 8 ->
8, 10, 4, 6 -> 9, 4, 10, 9 -> 10, 10, 6, 2 ->
11, 9, 10, 1 -> 12|>

HighlightMesh[mesh, Style[2, vertexToFace[3, 8, 5], Red]]

share|improve this answer

answered 8 hours ago

kglrkglr

202k1010 gold badges231231 silver badges462462 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How did you know about the faces vertex coordinates rules? I couldn't find it in the documentation.
  $endgroup$
  – Las des Nestor
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor Yes, these things are mostly undocumented. This is why Mathematica.StackExchange is so valuable: People try a lot of spelunking and also a few of the developers are around here.
  $endgroup$
  – Henrik Schumacher
  8 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor, try mesh["Properties"] to see a long list of properties. Since they are not documented it is by trial and luck that you discover quiet a few useful properties.
  $endgroup$
  – kglr
  8 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Is there a way to extract that particular triangle, so I can compare them with the other ones? Let say that I select a triangle and I want to check if the triangle is part of the original plot.
  $endgroup$
  – Las des Nestor
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @LasdesNestor, the triangle (polygon) can be obtained using MeshPrimitives[mesh, 2,1] or using MeshPrimitives[mesh, 2,vertexToFace[3,8,5]].
  $endgroup$
  – kglr
  6 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

SeedRandom[1]
list = RandomInteger[1, 10, 10, 2];
mesh = DelaunayMesh[list, MeshCellLabel -> 0 -> "Index", 
 PlotTheme -> "Lines", 
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black, 
 Frame -> True]

You can create an association mapping face vertices to face indices using the property "FaceVertexConnectivityRules":

vertexToFace = Association[Reverse /@ mesh["FaceVertexConnectivityRules"]]

<|3, 8, 5 -> 1, 8, 3, 7 -> 2, 2, 5, 10 -> 3, 1, 5, 8 ->
4, 10, 5, 1 -> 5, 8, 9, 1 -> 6, 9, 7, 4 -> 7, 7, 9, 8 ->
8, 10, 4, 6 -> 9, 4, 10, 9 -> 10, 10, 6, 2 ->
11, 9, 10, 1 -> 12|>

HighlightMesh[mesh, Style[2, vertexToFace[3, 8, 5], Red]]

share|improve this answer

answered 8 hours ago

kglrkglr

202k1010 gold badges231231 silver badges462462 bronze badges

$endgroup$

SeedRandom[1]
list = RandomInteger[1, 10, 10, 2];
mesh = DelaunayMesh[list, MeshCellLabel -> 0 -> "Index", 
 PlotTheme -> "Lines", 
 MeshCellHighlight -> 1, All -> Green, 0, All -> Black, 
 Frame -> True]

vertexToFace = Association[Reverse /@ mesh["FaceVertexConnectivityRules"]]

HighlightMesh[mesh, Style[2, vertexToFace[3, 8, 5], Red]]

share|improve this answer

answered 8 hours ago

kglrkglr

202k1010 gold badges231231 silver badges462462 bronze badges

answered 8 hours ago

kglrkglr

202k1010 gold badges231231 silver badges462462 bronze badges

answered 8 hours ago

kglrkglr

202k1010 gold badges231231 silver badges462462 bronze badges