How might someone find the deformed coordinate via Python or otherwise when using a subdivision modifier with the 'show on cage' option?

For example, a subdivided cube with cage enabled and a vertex selected shows the location of the vertex at 1,1,1 but when manually placing the cursor near on the surface it is closer to .5,.5,.5

I know the vertex location needs to be at its non-deformed location for subdivision to even work but would like to get more accurate point locations at the surface without having to apply to mesh.

enter image description here


Vertex Parenting

Among other ways can be done with vertex parenting.

Test script, run with mesh in edit mode, adds a vertex parented empty for each selected vert and prints vertex's global location to the console.

import bpy
import bmesh

context = bpy.context
scene = context.scene
obj = context.edit_object
mesh = obj.data
bm = bmesh.from_edit_mesh(mesh)
empties = []
# selected verts
for v in [v for v in bm.verts if v.select]:
    empty = bpy.data.objects.new("Empty", None)
    empty.parent = obj
    empty.parent_type = 'VERTEX'
    empty.parent_vertices = [v.index] * 3
    empties.append((v.index, empty))

# update the scene
for index, empty in empties:    
    print("Vert %d location: " % index, empty.matrix_world.to_translation())

Test result on default cube with subsurf (cat-clark) 3 subdivisions.

Vert 0 location:  <Vector (0.5015, 0.5015, -0.5015)>
Vert 1 location:  <Vector (0.5015, -0.5015, -0.5015)>
Vert 2 location:  <Vector (-0.5015, -0.5015, -0.5015)>
Vert 3 location:  <Vector (-0.5015, 0.5015, -0.5015)>
Vert 4 location:  <Vector (0.5015, 0.5015, 0.5015)>
Vert 5 location:  <Vector (0.5015, -0.5015, 0.5015)>
Vert 6 location:  <Vector (-0.5015, -0.5015, 0.5015)>
Vert 7 location:  <Vector (-0.5015, 0.5015, 0.5015)>
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