Cell indices and cell coordinates from Voronoi diagram

Questions
1

Dear All,

Let’s say I have a Voronoi diagram of some points:

voronoidata=VoronoiMesh[0.5+{{9,86},{89,64},{28,49},{21,47},{31,70},{6,36},{3,24},{68,75},{25,55},{47,21}}]

this will get me the Voronoi mesh:

ScreenShot2016-01-27at13.35.11.png
ScreenShot2016-01-27at13.35.11.png714×548 9.02 KB

I know I can do MeshCoordinates[voronoidata] to get the coordinates of the mesh. How do I get the indices to make the polygons:

basically what I want are the indices:

ToExpression[StringReplace[ToString[voronoidata//FullForm],"MeshRegion"->"List"]][[2]]

{Polygon[{{11, 6, 10, 2}, {18, 4, 13, 22}}], 
 Polygon[{{16, 9, 17, 20, 21}, {1, 3, 7, 2, 10}, {5, 1, 10, 6,8}, {15, 11, 2, 7, 14}, {13, 4, 5, 8, 12}, {14, 7, 3, 9, 16}}], 
 Polygon[{{19, 12, 8, 6, 11, 15}}], 
 Polygon[{{17, 9, 3, 1, 5, 4, 18}}]}

I would consider this to be a ‘hack’ as voronoidata is an atom, however the data can still be seen by FullForm(?) This procedure is however a bit cumbersome as you understand…

2

MeshPrimitives looked like a good function, however this returns the ‘real’ coordinates, not the indices…

3

MeshCells[voronoidata, 2]
{Polygon[{11, 6, 10, 2}], Polygon[{18, 4, 13, 22}], Polygon[{16, 9,
17, 20, 21}], Polygon[{1, 3, 7, 2, 10}], Polygon[{5, 1, 10, 6, 8}],
Polygon[{15, 11, 2, 7, 14}], Polygon[{13, 4, 5, 8, 12}],
Polygon[{14, 7, 3, 9, 16}], Polygon[{19, 12, 8, 6, 11, 15}],
Polygon[{17, 9, 3, 1, 5, 4, 18}]}

4

Thank @Jaebum Jung! That was easy, feel kinda embarrassed! I somehow missed the MeshCells function…Thanks for the help!