Undo/Redo on Meshes - This code works, but how?

From reading many questions asking whether it is possible to perform an undo and redo on Unity meshes the typical answers are no, because they are not serializable, or you need to use the SerializedObject class, derive from the ScriptableObject or MonoBehaviour classes, and many other suggestions like custom mesh classes, etc.

I've been after a solution to this that is simple and reliable for a long time and have now come up with a working solution, but, I don't know how it works. The following code demonstrates a custom editor window that takes a game object and transforms the vertices of the mesh. After clicking apply you can then use ctrl-z and ctrl-y to undo and redo the operation.

The magic is in the Undo.undoRedoPerformed callback called MyUndoRedoCallback. It simply copies the vertices and assigns them straight back to the mesh. It only works when placed in this callback and nowhere else.

I'm going to go ahead and use this as it is and also wanted to share the solution with others, but maybe someone can explain how or why this works.

Thanks.

 using UnityEngine;
 using UnityEditor;
 
 public class MeshUndoRedo: EditorWindow
 {
     [MenuItem("Window/Undo Redo", false, 0)]
     static void ShowTheWindow()
     {
         MeshUndoRedo myWindow = (MeshUndoRedo)EditorWindow.GetWindow(typeof(MeshUndoRedo), false, "Undo Redo");
         myWindow.minSize = new Vector2(200.0f, 150.0f);
     }
 
     public GameObject theObject = null;
     public Vector3 factor = new Vector3(1f, 1f, 1f);
 
     void OnFocus()
     {        
         Undo.undoRedoPerformed -= this.MyUndoRedoCallback;
         Undo.undoRedoPerformed += this.MyUndoRedoCallback;
     }
     
     public void MyUndoRedoCallback()
     {
         if (theObject == null)
             return;
 
         MeshFilter meshFilter = theObject.GetComponent<MeshFilter>();
         UnityEngine.Mesh mesh = meshFilter ? meshFilter.sharedMesh : null;
         
         if (mesh)
         {            
             Vector3[] copyVertices = new Vector3[mesh.vertices.Length];
             copyVertices = mesh.vertices;                
             mesh.vertices = copyVertices;
         }
 
         SceneView.RepaintAll();
     }
 
     public void ApplyVertexFactors(Vector3 factor)
     {
         if (theObject == null)
             return;
         
         MeshFilter meshFilter = theObject.GetComponent<MeshFilter>();
         UnityEngine.Mesh mesh = meshFilter ? meshFilter.sharedMesh : null;
         
         Undo.RecordObject(mesh, "Modify Vertices");
         
         if (mesh)
         {            
             Vector3[] copyVertices = new Vector3[mesh.vertices.Length];
             copyVertices = mesh.vertices;
             
             for (int i = 0; i < copyVertices.Length; i++)
             {
                 copyVertices[i].x *= factor.x;
                 copyVertices[i].y *= factor.y;
                 copyVertices[i].z *= factor.z;
             }
             
             mesh.vertices = copyVertices;
         }
         SceneView.RepaintAll();            
     }
     
     public void OnGUI()
     {
         GUILayout.Space(5);
 
         theObject = (GameObject)EditorGUILayout.ObjectField(theObject, typeof(GameObject), true);
         
         GUILayout.Label("Current Factors");
 
         GUILayout.Label("X: " + factor.x.ToString() + " Y: " + factor.y.ToString() + " Z: " + factor.z.ToString());
         
         if (GUILayout.Button("Expand", GUILayout.Height(17)))
         {
             factor *= 2f;
         }
 
         if (GUILayout.Button("Shrink", GUILayout.Height(17)))
         {
             factor /= 2f;
         }
 
         if (GUILayout.Button("Apply", GUILayout.Height(20)))
         {
             ApplyVertexFactors(factor);
         }
     }
 }