As a simple example of what I want to do, let's say I have a Voronoi mesh in a $10\times10$ area with $10$ random "seed points":
SeedRandom[1];
randMesh=VoronoiMesh[RandomReal[{1, 10}, {10, 2}], {{1, 10}, {1, 10}}]
And I am interested in all integer points within this area. i.e. the $100$ points determined by
points = Flatten[Table[{x, y}, {x, 10}, {y, 10}], 1]
What is an efficient way to group the points by the mesh section they reside in?
One way I have thought of doing this is is just going point-by-point and checking each region, such as something like
{5, 5} \[Element] # & /@ MeshPrimitives[randMesh, 2]
{False, False, True, False, False, False, False, False, False, False}
but applied to each point, and then grouping the points based on which mesh primitive they belong in. But this is not very efficient, as in what I am actually doing I have a $512\times512$ area with about $1000$ seed points for the mesh. Is there a better way to approach this?