Each terrain patch can have its own morphing amount. This morphing amount is shared among all its vertices. At a given LOD, the morphing amount can range from 0.0 (finest) to 1.0 (coarsest). Four adjacent patches from the same LOD with a morphing amount of 1.0 (coarsest) can be seamlessly replaced by a single patch from the next coarser LOD with a morphing amount of 0.0 (finest), and vice versa.
This screenshot shows patches that are shaded according to the sum of its LOD and its morphing amount:
At first, it seemed easy to figure out the morphing amount for a patch. At any given LOD, just make the morph amount a linear blend between 0.0 and 1.0 based on its distance from the viewer. Unfortunately, as I looked closer, I noticed that this method has a serious flaw. Take a look at the patch outlined in red:
... morphs to ... 
In the left image, this patch is about to be split into four patches. In the right image, the split occurs, but each patch has a different morphing amount because their distances from the viewer are not the same. This will appear as a noticable "pop" to the viewer.
To fix this problem, I changed the formula for determining the morphing amount. Instead of a linear blend between 0.0 and 1.0, I changed it to a linear blend between 0.0 and 2.0 and clamped the resulting amount to 1.0. This way, when a patch is close enough to the viewer to be split into four smaller patches, these patches are guaranteed to have a morphing amount of 1.0:
... morphs to ... 
Now I wanted to see what the morphing looks like in 3D. I quickly hacked in some wireframe code that I stole from my original version of Land-o-Rama. I loaded a 3-arcsecond (90-meter) SRTM heightmap of the West Kootenay region of British Columbia (N49W118.hgt) and rendered it. Here's a screenshot of Elephant Mountain, just north of Nelson BC:
(This is a rendering of a 1024 x 1024 section of the original 1201 x 1201 height map. Land-o-Rama automatically applies artificial detail to the height map, resulting in a resolution of 32k x 32k. The patch size is 33 x 33.)
Moving around the heightmap, it appears that the vertex morphing is working correctly. You can see the vertices smoothly change when you get closer or farther away from a patch! However, there are big gaps between adjacent patches. This will be fixed soon.
