Boundary cells of a mesh?

This is an offspring of answering another question.

Consider

data = {{4.4, 14}, {6.7, 15.25}, {6.9, 12.8}, {2.1, 11.1},
{9.5, 14.9}, {13.2, 11.9}, {10.3, 12.3}, {6.8, 9.5},
{3.3, 7.7}, {0.6, 5.1}, {5.3, 2.4}, {8.45, 4.7},
{11.5, 9.6}, {13.8, 7.3}, {12.9, 3.1}, {11, 1.1}};

vor = VoronoiMesh[data];


All indices of the interior faces can be obtained with

i2 = MeshCellIndex[vor, {2, "Interior"}] (* undocumented *)


thence

HighlightMesh[vor, Style[i2, Red]]


It works also for points (0) and lines (1):

i0 = MeshCellIndex[vor, {0, "Interior"}]
i1 = MeshCellIndex[vor, {1, "Interior"}]


I found (by trial-and-error) that there's also "Boundary":

b0 = MeshCellIndex[vor, {0, "Boundary"}]
b1 = MeshCellIndex[vor, {1, "Boundary"}]


giving

Unfortunately,

MeshCellIndex[vor, {2, "Boundary"}]


{}

doesn't work.

Questions:

1. Is there something similar to "Interior" for the bordering faces (i.e., the missing MeshCellIndex[vor, {2, "Boundary"}] output)? They can be obtained with Complement[MeshCellIndex[vor, 2], i2], but it looks too cumbersome compared to the "Interior" simplicity.
2. Regarding the lines (1), "Interior" and "Boundary" don't give all of them (i.e., the ones leading from the interior to the boundary); the remaining can be obtained with Complement[MeshCellIndex[vor, 1], b1, i1], but again it would be nice to have a one-word description.

Found by trial-and-error that MeshCellIndex[vor,{2,"Frontier"}] gives what you are looking for:

HighlightMesh[vor, Style[ MeshCellIndex[vor,{2,"Frontier"}], Red]]


or

MeshRegion[vor,  MeshCellStyle -> ({2,"Frontier"}->Red)]


To get the lines leading from the interior to the boundary you can simply replace 2 above with 1. For example,

MeshRegion[vor,  MeshCellStyle -> ({1,"Frontier"}->Red}]


• How to find those all undocument string?
– yode
Aug 29, 2017 at 1:25
• @yode, just tried some of the properties returned by vor["Properties"].
– kglr
Sep 7, 2017 at 14:25