UV cube projection preserving vertex coordinates

Question

When I apply "UV > Cube projection" it centers all the islands somewhere around (0.5,0.5) UV coordinates. I'd like, however, to preserve the the local vertex coordinates. For example if the vertex is located at (1,2,3), and is projected along the Z axis, then I want the UV coordinate of that vertex to become (1,2) rather than some arbitrarily translated value. Is it possible?

Rationale: I want the textures of different islands to be aligned with respect to each other.

EDIT: Example of cube projection (left) and desired result (right):

The center of the leftmost cube is located at (0,0,0) in this example.

Answer 1

Cube Projection.

In the python script templates there is a UV operator that sets the UV to the xy vertex coordinates.

Here is a minor edit to that

• Made a dictionary of the three axes eg axes["x"] = (1, 0, 0)
• For each face sort its keys by absolute value face normal dot axis.
• The most aligned is last
• Use first two coordinates to get coordinate
• Note may want to test and flip for faces pointing opposite.

Template script with edits.

import bpy
import bmesh
from mathutils import Matrix

def main(context):
    obj = context.active_object
    me = obj.data
    bm = bmesh.from_edit_mesh(me)

    uv_layer = bm.loops.layers.uv.verify()
    axes = {a : vec for a, vec in zip("xyz", Matrix.Identity(3))}
    
    # adjust uv coordinates
    for face in bm.faces:
        axis = sorted(
            "xyz", 
            key=lambda a : abs(face.normal.dot(axes[a]))
            ).pop()
                
        for loop in face.loops:
            loop_uv = loop[uv_layer]
            # use xy position of the vertex as a uv coordinate
            loop_uv.uv = getattr(loop.vert.co, "xyz".replace(axis, ""))

    bmesh.update_edit_mesh(me)


class UvOperator(bpy.types.Operator):
    """UV Operator description"""
    bl_idname = "uv.simple_operator"
    bl_label = "Simple UV Operator"

    @classmethod
    def poll(cls, context):
        obj = context.active_object
        return obj and obj.type == 'MESH' and obj.mode == 'EDIT'

    def execute(self, context):
        main(context)
        return {'FINISHED'}


def register():
    bpy.utils.register_class(UvOperator)


def unregister():
    bpy.utils.unregister_class(UvOperator)


if __name__ == "__main__":
    register()

    # test call (requires edit mode)
    bpy.ops.uv.simple_operator()

Answer 2

Instead of building a UV map, I can calculate the UV with an OSL node with the following script:

shader cubemap(vector Position = P, vector Normal = N, output vector UV = 0.0) {
    vector p = Position;
    vector n = abs(Normal);
    if(n.x > n.y && n.x > n.z)
        UV = vector(p.y,p.z,0);
    else if(n.y > n.x && n.y > n.z)
        UV = vector(p.z,p.x,0);
    else
        UV = vector(p.x,p.y,0);
}

Position and Normal can be connected to the corresponding inputs in the Texture Coordinate node to get local coordinates (or else it defaults to world coordinates).