Procedural Generation

Recently I’ve gotten really into procedural generation and decided to move on to 3D. I managed to follow this tutorial: http://www.gameprogrammer.com/fractal.html#heightmaps and generate nice looking 3D terrain from a heightmap. My question is how to take that terrain and wrap it around a sphere? I want to start making procedural planets, then moons, then asteroids, etc. and once I can figure out how to generate planets I assume most astronomical objects will be pretty easy. Also, how do I implement LOD and quad trees to be able to render whole objects at a distance? I’m not very familiar with how procedural planets work as there aren’t many examples I can find so any help, articles, links, etc. will be very much appreciated.