Calculate total length of edges in select Voronoi diagramCropping a Voronoi diagramImplementing an algorithm...
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Calculate total length of edges in select Voronoi diagram
Cropping a Voronoi diagramImplementing an algorithm for finding the largest circle that contains a single point in a set (and no other point)Bounded Voronoi DiagramVoronoi diagram for line segmentsVoronoiMesh without edgesHow to draw this 3D Voronoi Diagram?Color code Voronoi cell areas depending on number of verticesHyperbolic Voronoi diagram for the Poincaré model, using RegionPlotHow can I get the vertices of each polygon of a Voronoi diagram?Calculate of total length of edges in Voronoi diagram
$begingroup$
I want to calculate the total length of edges in a Voronoi diagram like this
I can calculate this with
lengths = RegionMeasure /@ MeshPrimitives[VoronoiMesh[pts], 1];
Total[lengths]
but, I want to eliminate from the calculation the diagrams touching the border of the image. I can select this diagrams like here
and I can keep with the orange diagrams
but I don't know how to calculate the total length of the edges of the last graphic. Any suggestions?
computational-geometry
asked 3 hours ago
Mati GerMati Ger
483
$endgroup$
add a comment |
$begingroup$
I want to calculate the total length of edges in a Voronoi diagram like this
I can calculate this with
lengths = RegionMeasure /@ MeshPrimitives[VoronoiMesh[pts], 1];
Total[lengths]
but, I want to eliminate from the calculation the diagrams touching the border of the image. I can select this diagrams like here
and I can keep with the orange diagrams
but I don't know how to calculate the total length of the edges of the last graphic. Any suggestions?
computational-geometry
asked 3 hours ago
Mati GerMati Ger
483
$endgroup$
1
$begingroup$
Can you add the code to select the inner cells and the definition ofpts?
$endgroup$
– MarcoB
3 hours ago
$begingroup$
The distribution of points pts comes from a picture but could be random numbers. For example: SeedRandom[332] pts = RandomReal[1, {100, 2}]; xy = VoronoiMesh[pts, {{0, 1}, {0, 1}}]; i2 = MeshCellIndex[xy, {2, "Interior"}] ; HighlightMesh[xy, Style[i2, LightOrange]]
$endgroup$
– Mati Ger
3 hours ago
add a comment |
$begingroup$
I want to calculate the total length of edges in a Voronoi diagram like this
I can calculate this with
lengths = RegionMeasure /@ MeshPrimitives[VoronoiMesh[pts], 1];
Total[lengths]
but, I want to eliminate from the calculation the diagrams touching the border of the image. I can select this diagrams like here
and I can keep with the orange diagrams
but I don't know how to calculate the total length of the edges of the last graphic. Any suggestions?
computational-geometry
asked 3 hours ago
Mati GerMati Ger
483
$endgroup$
I want to calculate the total length of edges in a Voronoi diagram like this
I can calculate this with
lengths = RegionMeasure /@ MeshPrimitives[VoronoiMesh[pts], 1];
Total[lengths]
but, I want to eliminate from the calculation the diagrams touching the border of the image. I can select this diagrams like here
and I can keep with the orange diagrams
but I don't know how to calculate the total length of the edges of the last graphic. Any suggestions?
computational-geometry
computational-geometry
asked 3 hours ago
Mati GerMati Ger
483
asked 3 hours ago
Mati GerMati Ger
483
asked 3 hours ago
Mati GerMati Ger
483
asked 3 hours ago
Mati GerMati Ger
483
asked 3 hours ago
Mati GerMati Ger
483
483
1
$begingroup$
Can you add the code to select the inner cells and the definition ofpts?
$endgroup$
– MarcoB
3 hours ago
$begingroup$
The distribution of points pts comes from a picture but could be random numbers. For example: SeedRandom[332] pts = RandomReal[1, {100, 2}]; xy = VoronoiMesh[pts, {{0, 1}, {0, 1}}]; i2 = MeshCellIndex[xy, {2, "Interior"}] ; HighlightMesh[xy, Style[i2, LightOrange]]
$endgroup$
– Mati Ger
3 hours ago
add a comment |
1
$begingroup$
Can you add the code to select the inner cells and the definition ofpts?
$endgroup$
– MarcoB
3 hours ago
$begingroup$
The distribution of points pts comes from a picture but could be random numbers. For example: SeedRandom[332] pts = RandomReal[1, {100, 2}]; xy = VoronoiMesh[pts, {{0, 1}, {0, 1}}]; i2 = MeshCellIndex[xy, {2, "Interior"}] ; HighlightMesh[xy, Style[i2, LightOrange]]
$endgroup$
– Mati Ger
3 hours ago
1
1
$begingroup$
Can you add the code to select the inner cells and the definition of
pts?$endgroup$
– MarcoB
3 hours ago
$begingroup$
Can you add the code to select the inner cells and the definition of
pts?$endgroup$
– MarcoB
3 hours ago
$begingroup$
The distribution of points pts comes from a picture but could be random numbers. For example: SeedRandom[332] pts = RandomReal[1, {100, 2}]; xy = VoronoiMesh[pts, {{0, 1}, {0, 1}}]; i2 = MeshCellIndex[xy, {2, "Interior"}] ; HighlightMesh[xy, Style[i2, LightOrange]]
$endgroup$
– Mati Ger
3 hours ago
$begingroup$
The distribution of points pts comes from a picture but could be random numbers. For example: SeedRandom[332] pts = RandomReal[1, {100, 2}]; xy = VoronoiMesh[pts, {{0, 1}, {0, 1}}]; i2 = MeshCellIndex[xy, {2, "Interior"}] ; HighlightMesh[xy, Style[i2, LightOrange]]
$endgroup$
– Mati Ger
3 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
SeedRandom[1]
pts = RandomReal[1, {100, 2}];
vm = VoronoiMesh[pts];
"Interior"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Interior"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm , {1, "Interior"}]]
19.4739
Alternatively,
Total[RegionMeasure /@ MeshPrimitives[vm, {1, "Interior"}]]
19.4739
RegionMeasure[MeshRegion[MeshCoordinates[vm], MeshCells[vm, {1, "Interior"}]]]
19.4739
"Boundary"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Boundary"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Boundary"}]]
5.92015
"Frontier"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Frontier"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Frontier"}]]
5.357575
All lines
Total[vm["EdgeLengths"]]
30.75167
Total[ArcLength /@ MeshPrimitives[vm , 1]]
30.751672460568727
answered 3 hours ago
kglrkglr
187k10203421
$endgroup$
$begingroup$
So long as none of the cells adjacent to the boundary aren't in fact the full Voronoi cell. This would only happen in contrived cases though.
$endgroup$
– Chip Hurst
3 hours ago
$begingroup$
@ChipHurst, good point.
$endgroup$
– kglr
3 hours ago
$begingroup$
I am impressed by the speed and clarity in your response, kglr. I am very grateful with you. Thank you.
$endgroup$
– Mati Ger
2 hours ago
$begingroup$
@MatiGer, my pleasure. Thank you for the kind words and accept.
$endgroup$
– kglr
2 hours ago
add a comment |
Your Answer
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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
$begingroup$
SeedRandom[1]
pts = RandomReal[1, {100, 2}];
vm = VoronoiMesh[pts];
"Interior"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Interior"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm , {1, "Interior"}]]
19.4739
Alternatively,
Total[RegionMeasure /@ MeshPrimitives[vm, {1, "Interior"}]]
19.4739
RegionMeasure[MeshRegion[MeshCoordinates[vm], MeshCells[vm, {1, "Interior"}]]]
19.4739
"Boundary"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Boundary"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Boundary"}]]
5.92015
"Frontier"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Frontier"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Frontier"}]]
5.357575
All lines
Total[vm["EdgeLengths"]]
30.75167
Total[ArcLength /@ MeshPrimitives[vm , 1]]
30.751672460568727
answered 3 hours ago
kglrkglr
187k10203421
$endgroup$
$begingroup$
So long as none of the cells adjacent to the boundary aren't in fact the full Voronoi cell. This would only happen in contrived cases though.
$endgroup$
– Chip Hurst
3 hours ago
$begingroup$
@ChipHurst, good point.
$endgroup$
– kglr
3 hours ago
$begingroup$
I am impressed by the speed and clarity in your response, kglr. I am very grateful with you. Thank you.
$endgroup$
– Mati Ger
2 hours ago
$begingroup$
@MatiGer, my pleasure. Thank you for the kind words and accept.
$endgroup$
– kglr
2 hours ago
add a comment |
$begingroup$
SeedRandom[1]
pts = RandomReal[1, {100, 2}];
vm = VoronoiMesh[pts];
"Interior"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Interior"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm , {1, "Interior"}]]
19.4739
Alternatively,
Total[RegionMeasure /@ MeshPrimitives[vm, {1, "Interior"}]]
19.4739
RegionMeasure[MeshRegion[MeshCoordinates[vm], MeshCells[vm, {1, "Interior"}]]]
19.4739
"Boundary"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Boundary"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Boundary"}]]
5.92015
"Frontier"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Frontier"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Frontier"}]]
5.357575
All lines
Total[vm["EdgeLengths"]]
30.75167
Total[ArcLength /@ MeshPrimitives[vm , 1]]
30.751672460568727
answered 3 hours ago
kglrkglr
187k10203421
$endgroup$
$begingroup$
So long as none of the cells adjacent to the boundary aren't in fact the full Voronoi cell. This would only happen in contrived cases though.
$endgroup$
– Chip Hurst
3 hours ago
$begingroup$
@ChipHurst, good point.
$endgroup$
– kglr
3 hours ago
$begingroup$
I am impressed by the speed and clarity in your response, kglr. I am very grateful with you. Thank you.
$endgroup$
– Mati Ger
2 hours ago
$begingroup$
@MatiGer, my pleasure. Thank you for the kind words and accept.
$endgroup$
– kglr
2 hours ago
add a comment |
$begingroup$
SeedRandom[1]
pts = RandomReal[1, {100, 2}];
vm = VoronoiMesh[pts];
"Interior"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Interior"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm , {1, "Interior"}]]
19.4739
Alternatively,
Total[RegionMeasure /@ MeshPrimitives[vm, {1, "Interior"}]]
19.4739
RegionMeasure[MeshRegion[MeshCoordinates[vm], MeshCells[vm, {1, "Interior"}]]]
19.4739
"Boundary"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Boundary"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Boundary"}]]
5.92015
"Frontier"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Frontier"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Frontier"}]]
5.357575
All lines
Total[vm["EdgeLengths"]]
30.75167
Total[ArcLength /@ MeshPrimitives[vm , 1]]
30.751672460568727
answered 3 hours ago
kglrkglr
187k10203421
$endgroup$
SeedRandom[1]
pts = RandomReal[1, {100, 2}];
vm = VoronoiMesh[pts];
"Interior"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Interior"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm , {1, "Interior"}]]
19.4739
Alternatively,
Total[RegionMeasure /@ MeshPrimitives[vm, {1, "Interior"}]]
19.4739
RegionMeasure[MeshRegion[MeshCoordinates[vm], MeshCells[vm, {1, "Interior"}]]]
19.4739
"Boundary"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Boundary"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Boundary"}]]
5.92015
"Frontier"
HighlightMesh[vm, Style[MeshCellIndex[vm, {1, "Frontier"}], Red]]
Total[ArcLength /@ MeshPrimitives[vm, {1, "Frontier"}]]
5.357575
All lines
Total[vm["EdgeLengths"]]
30.75167
Total[ArcLength /@ MeshPrimitives[vm , 1]]
30.751672460568727
answered 3 hours ago
kglrkglr
187k10203421
edited 2 hours ago
answered 3 hours ago
kglrkglr
187k10203421
answered 3 hours ago
kglrkglr
187k10203421
answered 3 hours ago
kglrkglr
187k10203421
187k10203421
$begingroup$
So long as none of the cells adjacent to the boundary aren't in fact the full Voronoi cell. This would only happen in contrived cases though.
$endgroup$
– Chip Hurst
3 hours ago
$begingroup$
@ChipHurst, good point.
$endgroup$
– kglr
3 hours ago
$begingroup$
I am impressed by the speed and clarity in your response, kglr. I am very grateful with you. Thank you.
$endgroup$
– Mati Ger
2 hours ago
$begingroup$
@MatiGer, my pleasure. Thank you for the kind words and accept.
$endgroup$
– kglr
2 hours ago
add a comment |
$begingroup$
So long as none of the cells adjacent to the boundary aren't in fact the full Voronoi cell. This would only happen in contrived cases though.
$endgroup$
– Chip Hurst
3 hours ago
$begingroup$
@ChipHurst, good point.
$endgroup$
– kglr
3 hours ago
$begingroup$
I am impressed by the speed and clarity in your response, kglr. I am very grateful with you. Thank you.
$endgroup$
– Mati Ger
2 hours ago
$begingroup$
@MatiGer, my pleasure. Thank you for the kind words and accept.
$endgroup$
– kglr
2 hours ago
$begingroup$
So long as none of the cells adjacent to the boundary aren't in fact the full Voronoi cell. This would only happen in contrived cases though.
$endgroup$
– Chip Hurst
3 hours ago
$begingroup$
So long as none of the cells adjacent to the boundary aren't in fact the full Voronoi cell. This would only happen in contrived cases though.
$endgroup$
– Chip Hurst
3 hours ago
$begingroup$
@ChipHurst, good point.
$endgroup$
– kglr
3 hours ago
$begingroup$
@ChipHurst, good point.
$endgroup$
– kglr
3 hours ago
$begingroup$
I am impressed by the speed and clarity in your response, kglr. I am very grateful with you. Thank you.
$endgroup$
– Mati Ger
2 hours ago
$begingroup$
I am impressed by the speed and clarity in your response, kglr. I am very grateful with you. Thank you.
$endgroup$
– Mati Ger
2 hours ago
$begingroup$
@MatiGer, my pleasure. Thank you for the kind words and accept.
$endgroup$
– kglr
2 hours ago
$begingroup$
@MatiGer, my pleasure. Thank you for the kind words and accept.
$endgroup$
– kglr
2 hours ago
add a comment |
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1
$begingroup$
Can you add the code to select the inner cells and the definition of
pts?$endgroup$
– MarcoB
3 hours ago
$begingroup$
The distribution of points pts comes from a picture but could be random numbers. For example: SeedRandom[332] pts = RandomReal[1, {100, 2}]; xy = VoronoiMesh[pts, {{0, 1}, {0, 1}}]; i2 = MeshCellIndex[xy, {2, "Interior"}] ; HighlightMesh[xy, Style[i2, LightOrange]]
$endgroup$
– Mati Ger
3 hours ago