Transform UV coordinates to world space

InverseUVMapping.py

bl_info = {
    "name": "InverseUVMapping",
    "description": "Inverse UV coordinate",
    "author": "TheBusyTypist",
    "category": "Object"
}

import bpy
import bmesh
import mathutils
from mathutils.geometry import barycentric_transform, intersect_point_tri_2d

class InverseUVMapping(bpy.types.Operator):
    """Inverse UV coordinate"""
    bl_idname = "object.inverse_uv"
    bl_label = "Inverse UV coordinate"
    bl_options = {"REGISTER"}

    def execute(self, context):
        for area in context.screen.areas:
            if area.type == "IMAGE_EDITOR":
                image_editor = area.spaces.active

        uv_cursor = image_editor.cursor_location.to_3d()
        uv_cursor.x /= image_editor.image.size[0]
        uv_cursor.y /= image_editor.image.size[1]

        bm = bmesh.new()
        bm.from_mesh(context.object.data)
        bmesh.ops.triangulate(bm, faces=bm.faces)

        uv_layer = bm.loops.layers.uv.active

        for face in bm.faces:
            u, v, w = [l[uv_layer].uv.to_3d() for l in face.loops]
            if intersect_point_tri_2d(uv_cursor, u, v, w):
                x, y, z = [v.co for v in face.verts]
                co = barycentric_transform(uv_cursor, u, v, w, x, y, z)
                world_matrix = context.object.matrix_world
                p = world_matrix * co
                print(p)
                context.scene.cursor_location = p
                break

        return {"FINISHED"}

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

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

if __name__ == "__main__":
    register()