LOD, for those who are unfamiliar with this term, means "Level of Details". To explain in simple words, it is the idea that the farther away the camera is, the more simplified the geometry will be. In our case the proposal is to have a LOD subdivision. Then we can conclude that the farther away the camera stays, the less subdivisions will be applied to the geometry. The advantage of using this technique is it makes the scene lighter to render, optimizing the number of used polygons.
It has too many applications, but generally I think the best application of this technique is for rough and detailed places, such as deserts with dunes or oceans - forms that can be composed using modifiers such as Displace. I developed this technique because I needed to make an ocean. I had a vast area of animated water that needed waves, but weak machines to withstand the processing of many polygons.
So, as I think others may have specific needs, you can find new applications for this technique, different from what I quoted above.
To explain the implementation and operation of this technique, we use a Plane with 10x10 segments as a basis (Fig.01).
The next step is to create a controller. He'll have two functions, the first indicates the area to be selected, and the second is the ability to make a link between the subdivision and the camera. This driver should be geometry; it can't be a helper because helpers are null objects. For our example we'll use a sphere, but you can use any other object (Fig.02).
Now comes the first secret part of the technique operation. Our subdivision will be selective and mobile, just in case the camera will be animated and we want a subdivision only where the camera is. So the subdivision shall follow the camera where it is. We will use the Vol. Select modifier to make the selection of the area, and this selection will be made with our controller reference.
Pay attention to the settings used in the modifier. In Stack Selection Levels we will use Vertex, Selection Method should be Add (later I'll explain why) and finally in Select By we will use the option Mesh Object. Now select our controller and then we can see the selected vertexes inside the volume controller. In the case of this sample image we have only one vertex (Fig.03).
The next step is to adjust the total area to be affected by the first level of subdivision. This must be done in the Soft Selection still in the Vol. Select modifier (Fig.04).
The values used to configure Falloff and Pinch may change according to the dimensions of the scene, the scale and their own need. After setting the Vol. Select we will apply the MeshSmooth modifier so it will act only in the region that is selected. It is important to warn that the TurboSmooth modifier doesn't work (Fig.05).
Another important detail is to uncheck "Apply To Whole Mesh" so that the subdivision is only applied to our selection.
Now we have the first level of subdivision ready, but we need more levels so that the effect works better, so we'll replicate what was already done. To be more practical we will only copy and paste both modifiers selected (Fig.06).