Planetoids

This update is actually going to be referencing some older stuff I had been working on as I'm knee deep in finishing up a little iPhone app and don't really have anything interesting to show for it (it's a Blackjack game, woohoo...).

About 4 years ago I was playing quite a bit with procedural planet creation specifically using the techniques outlined in the book Texturing and Modeling: A Procedural Approach (a fantastic and highly recommended read for graphics programmers). What I was hoping to get from this was the ability to procedurally generate planets for the Star Trader universe, more as an offline tool to save time than as a real-time galaxy generator as some people have implemented. The results were very good and I ended up with a great tool to generate pretty decent looking planets completely on the fly for rapid iteration (utilizing perlin noise on the GPU in real-time). These could then be saved off to a cubemap and potentially converted to a spherical map (to be applied to the planetary spheres).

This tool has sadly been lost to the sands of time (I've adopted a much better project archiving system to avoid this) but my interest in creating procedurally generating planets hasn't vanished. Recently I revisted this from another viewpoint -- since the cube map can be used to represent a spherical environment, how could I take the planetary cube map I generated and turn that into an actual geometric representation instead of just using it as a texture. This isn't a very trivial thing to do considering terrains are normally fixed to a single ground plane.

My first attempt involved directly translating the faces of a cube map (painted with a hastily made noise based terrain and another with just the axis triad) to a cube, with each cube face as a seperate terrain. After this I applied a spherization formula that basically generates a unit (normalized) sphere, then, for each vertex, takes the sampled height value and outwardly projects it's position relative to that. Viola, a sphere made of six terrains (here's another option that also works but for some reason the results don't look as good to me: link). Here are some screenshots to demonstrate;

Getting the geometry in spherical form isn't the only thing that needs to be done. The normals must also be transformed from their original representation to the spherized version. This is the tricky part. After trying quite a number of techniques, Alex Peterson (thanks again Alex!!) pointed me to a great little article on building a rotation matrix from one vector to another. Since the original position and the new position are vectors, getting their rotation matrix and transforming the normal by that became a pretty trivial matter! You can find the article here. I'll post some screenshots of the final result next time.