Information concerning undocumented function “Region`Mesh`MeshNearestCellIndex[r ]”
I'm looking for further information of the undocumented function Region`Mesh`MeshNearestCellIndex[r] (Thanks to Henrik Schumacher!)
The function considers a meshregion r and detects the nearest cell to a given point. Trying to understand I look at a very simple triangle mesh in space:
pi={{0., 0., 0.303}, {1., -0.5, 0.09}, {0.7, 0.8, -0.233}, {0.,1., -0.584}, {-0.8, -0.7, -0.734}}
Δi = {{1, 2, 3}, {1, 3, 4}, {1, 4, 5}, {1, 5, 2}};
r = MeshRegion[pi , Triangle[Δi]];
HighlightMesh[r, {Labeled[0, "Index"], Labeled[2, "Index"]}]
Now I want to evaluate the nearest cells of point 1
Region`Mesh`MeshNearestCellIndex[r , pi[[1]] ]
(*{2, 1}*)
Expecting four possible cells as nearest neighbors MMA returns element #1.
My question:
How does MMA evaluate the priority of the possible cells? Thanks!
mesh meshfunction
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
add a comment |
I'm looking for further information of the undocumented function Region`Mesh`MeshNearestCellIndex[r] (Thanks to Henrik Schumacher!)
The function considers a meshregion r and detects the nearest cell to a given point. Trying to understand I look at a very simple triangle mesh in space:
pi={{0., 0., 0.303}, {1., -0.5, 0.09}, {0.7, 0.8, -0.233}, {0.,1., -0.584}, {-0.8, -0.7, -0.734}}
Δi = {{1, 2, 3}, {1, 3, 4}, {1, 4, 5}, {1, 5, 2}};
r = MeshRegion[pi , Triangle[Δi]];
HighlightMesh[r, {Labeled[0, "Index"], Labeled[2, "Index"]}]
Now I want to evaluate the nearest cells of point 1
Region`Mesh`MeshNearestCellIndex[r , pi[[1]] ]
(*{2, 1}*)
Expecting four possible cells as nearest neighbors MMA returns element #1.
My question:
How does MMA evaluate the priority of the possible cells? Thanks!
mesh meshfunction
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
Can you read theDownValues? That’s the place to start if they’re available. If not we’re at the mercy of WRI developers or wherever one can find the function used in the source code.
– b3m2a1
Jan 1 at 22:37
@b3m2a1 Nope,Needs["GeneralUtilities`"]; PrintDefinitions[Region`Mesh`MeshNearestCellIndex]returnsRegion`Mesh`MeshNearestCellIndex[___] := <<kernel function>>;...
– Henrik Schumacher
Jan 1 at 22:40
add a comment |
I'm looking for further information of the undocumented function Region`Mesh`MeshNearestCellIndex[r] (Thanks to Henrik Schumacher!)
The function considers a meshregion r and detects the nearest cell to a given point. Trying to understand I look at a very simple triangle mesh in space:
pi={{0., 0., 0.303}, {1., -0.5, 0.09}, {0.7, 0.8, -0.233}, {0.,1., -0.584}, {-0.8, -0.7, -0.734}}
Δi = {{1, 2, 3}, {1, 3, 4}, {1, 4, 5}, {1, 5, 2}};
r = MeshRegion[pi , Triangle[Δi]];
HighlightMesh[r, {Labeled[0, "Index"], Labeled[2, "Index"]}]
Now I want to evaluate the nearest cells of point 1
Region`Mesh`MeshNearestCellIndex[r , pi[[1]] ]
(*{2, 1}*)
Expecting four possible cells as nearest neighbors MMA returns element #1.
My question:
How does MMA evaluate the priority of the possible cells? Thanks!
mesh meshfunction
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
I'm looking for further information of the undocumented function Region`Mesh`MeshNearestCellIndex[r] (Thanks to Henrik Schumacher!)
The function considers a meshregion r and detects the nearest cell to a given point. Trying to understand I look at a very simple triangle mesh in space:
pi={{0., 0., 0.303}, {1., -0.5, 0.09}, {0.7, 0.8, -0.233}, {0.,1., -0.584}, {-0.8, -0.7, -0.734}}
Δi = {{1, 2, 3}, {1, 3, 4}, {1, 4, 5}, {1, 5, 2}};
r = MeshRegion[pi , Triangle[Δi]];
HighlightMesh[r, {Labeled[0, "Index"], Labeled[2, "Index"]}]
Now I want to evaluate the nearest cells of point 1
Region`Mesh`MeshNearestCellIndex[r , pi[[1]] ]
(*{2, 1}*)
Expecting four possible cells as nearest neighbors MMA returns element #1.
My question:
How does MMA evaluate the priority of the possible cells? Thanks!
mesh meshfunction
mesh meshfunction
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
edited Jan 1 at 22:39
Henrik Schumacher
49.8k469143
49.8k469143
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
asked Jan 1 at 22:24
Ulrich NeumannUlrich Neumann
7,725516
7,725516
Can you read theDownValues? That’s the place to start if they’re available. If not we’re at the mercy of WRI developers or wherever one can find the function used in the source code.
– b3m2a1
Jan 1 at 22:37
@b3m2a1 Nope,Needs["GeneralUtilities`"]; PrintDefinitions[Region`Mesh`MeshNearestCellIndex]returnsRegion`Mesh`MeshNearestCellIndex[___] := <<kernel function>>;...
– Henrik Schumacher
Jan 1 at 22:40
add a comment |
Can you read theDownValues? That’s the place to start if they’re available. If not we’re at the mercy of WRI developers or wherever one can find the function used in the source code.
– b3m2a1
Jan 1 at 22:37
@b3m2a1 Nope,Needs["GeneralUtilities`"]; PrintDefinitions[Region`Mesh`MeshNearestCellIndex]returnsRegion`Mesh`MeshNearestCellIndex[___] := <<kernel function>>;...
– Henrik Schumacher
Jan 1 at 22:40
Can you read the
DownValues? That’s the place to start if they’re available. If not we’re at the mercy of WRI developers or wherever one can find the function used in the source code.– b3m2a1
Jan 1 at 22:37
Can you read the
DownValues? That’s the place to start if they’re available. If not we’re at the mercy of WRI developers or wherever one can find the function used in the source code.– b3m2a1
Jan 1 at 22:37
@b3m2a1 Nope,
Needs["GeneralUtilities`"]; PrintDefinitions[Region`Mesh`MeshNearestCellIndex] returns Region`Mesh`MeshNearestCellIndex[___] := <<kernel function>>;...– Henrik Schumacher
Jan 1 at 22:40
@b3m2a1 Nope,
Needs["GeneralUtilities`"]; PrintDefinitions[Region`Mesh`MeshNearestCellIndex] returns Region`Mesh`MeshNearestCellIndex[___] := <<kernel function>>;...– Henrik Schumacher
Jan 1 at 22:40
add a comment |
1 Answer
1
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oldest
votes
If I had to make a guess, I'd say Mathematica breaks ties by choosing the cell with the smallest index:
Δi = {{1, 3, 4}, {1, 2, 3}, {1, 4, 5}, {1, 5, 2}};
Table[
r = MeshRegion[pi, Triangle[Δi[[perm]]]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]]],
{perm, PermutationList /@ Permutations[Range[4]]}
]
{{2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}}
By the way, I just found out that you can also obtain the $n$ nearest cells as follows:
r = MeshRegion[pi, Triangle[Δi]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]], 10]
{{2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}}
Apparently, superfluous cells obtain the index 0...
Oh, an apparently, there is also an operator version of the Region`Mesh`MeshNearestCellIndex, similarly as for Nearest:
cellfun = Region`Mesh`MeshNearestCellIndex[r];
cellfun[pi[[1]]]
{2, 2}
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
@ Henrik Thanks. Without the superfluous cells the ordering of the returned list seems to be arbitrary.
– Ulrich Neumann
Jan 1 at 22:54
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
If I had to make a guess, I'd say Mathematica breaks ties by choosing the cell with the smallest index:
Δi = {{1, 3, 4}, {1, 2, 3}, {1, 4, 5}, {1, 5, 2}};
Table[
r = MeshRegion[pi, Triangle[Δi[[perm]]]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]]],
{perm, PermutationList /@ Permutations[Range[4]]}
]
{{2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}}
By the way, I just found out that you can also obtain the $n$ nearest cells as follows:
r = MeshRegion[pi, Triangle[Δi]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]], 10]
{{2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}}
Apparently, superfluous cells obtain the index 0...
Oh, an apparently, there is also an operator version of the Region`Mesh`MeshNearestCellIndex, similarly as for Nearest:
cellfun = Region`Mesh`MeshNearestCellIndex[r];
cellfun[pi[[1]]]
{2, 2}
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
@ Henrik Thanks. Without the superfluous cells the ordering of the returned list seems to be arbitrary.
– Ulrich Neumann
Jan 1 at 22:54
add a comment |
If I had to make a guess, I'd say Mathematica breaks ties by choosing the cell with the smallest index:
Δi = {{1, 3, 4}, {1, 2, 3}, {1, 4, 5}, {1, 5, 2}};
Table[
r = MeshRegion[pi, Triangle[Δi[[perm]]]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]]],
{perm, PermutationList /@ Permutations[Range[4]]}
]
{{2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}}
By the way, I just found out that you can also obtain the $n$ nearest cells as follows:
r = MeshRegion[pi, Triangle[Δi]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]], 10]
{{2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}}
Apparently, superfluous cells obtain the index 0...
Oh, an apparently, there is also an operator version of the Region`Mesh`MeshNearestCellIndex, similarly as for Nearest:
cellfun = Region`Mesh`MeshNearestCellIndex[r];
cellfun[pi[[1]]]
{2, 2}
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
@ Henrik Thanks. Without the superfluous cells the ordering of the returned list seems to be arbitrary.
– Ulrich Neumann
Jan 1 at 22:54
add a comment |
If I had to make a guess, I'd say Mathematica breaks ties by choosing the cell with the smallest index:
Δi = {{1, 3, 4}, {1, 2, 3}, {1, 4, 5}, {1, 5, 2}};
Table[
r = MeshRegion[pi, Triangle[Δi[[perm]]]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]]],
{perm, PermutationList /@ Permutations[Range[4]]}
]
{{2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}}
By the way, I just found out that you can also obtain the $n$ nearest cells as follows:
r = MeshRegion[pi, Triangle[Δi]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]], 10]
{{2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}}
Apparently, superfluous cells obtain the index 0...
Oh, an apparently, there is also an operator version of the Region`Mesh`MeshNearestCellIndex, similarly as for Nearest:
cellfun = Region`Mesh`MeshNearestCellIndex[r];
cellfun[pi[[1]]]
{2, 2}
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
If I had to make a guess, I'd say Mathematica breaks ties by choosing the cell with the smallest index:
Δi = {{1, 3, 4}, {1, 2, 3}, {1, 4, 5}, {1, 5, 2}};
Table[
r = MeshRegion[pi, Triangle[Δi[[perm]]]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]]],
{perm, PermutationList /@ Permutations[Range[4]]}
]
{{2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}, {2, 1}}
By the way, I just found out that you can also obtain the $n$ nearest cells as follows:
r = MeshRegion[pi, Triangle[Δi]];
Region`Mesh`MeshNearestCellIndex[r, pi[[1]], 10]
{{2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}, {2, 0}}
Apparently, superfluous cells obtain the index 0...
Oh, an apparently, there is also an operator version of the Region`Mesh`MeshNearestCellIndex, similarly as for Nearest:
cellfun = Region`Mesh`MeshNearestCellIndex[r];
cellfun[pi[[1]]]
{2, 2}
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
edited Jan 1 at 22:47
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
answered Jan 1 at 22:38
Henrik SchumacherHenrik Schumacher
49.8k469143
49.8k469143
@ Henrik Thanks. Without the superfluous cells the ordering of the returned list seems to be arbitrary.
– Ulrich Neumann
Jan 1 at 22:54
add a comment |
@ Henrik Thanks. Without the superfluous cells the ordering of the returned list seems to be arbitrary.
– Ulrich Neumann
Jan 1 at 22:54
@ Henrik Thanks. Without the superfluous cells the ordering of the returned list seems to be arbitrary.
– Ulrich Neumann
Jan 1 at 22:54
@ Henrik Thanks. Without the superfluous cells the ordering of the returned list seems to be arbitrary.
– Ulrich Neumann
Jan 1 at 22:54
add a comment |
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Can you read the
DownValues? That’s the place to start if they’re available. If not we’re at the mercy of WRI developers or wherever one can find the function used in the source code.– b3m2a1
Jan 1 at 22:37
@b3m2a1 Nope,
Needs["GeneralUtilities`"]; PrintDefinitions[Region`Mesh`MeshNearestCellIndex]returnsRegion`Mesh`MeshNearestCellIndex[___] := <<kernel function>>;...– Henrik Schumacher
Jan 1 at 22:40