Many people have started to contact me with much concern for my health and wellbeing since I have not written in my journal for some time now. I would like to thank these people for carring enough to check in on me and let everyone else know that I am very much alive and doing well. The short explanation for my long absence is that I have been very busy and have had my hands full with all of the contract work that I do. It is also hard for me to write at times because I have so much going on in my head that it is hard to find the words to explain it all without taking long hours or even days to bring someone up to speed on my thoughts. I believe that it is this, besides my business obligations, that prevents me most from writing and documenting things more. My way of thinking seems to be a neverending run-on thought that shows up when I do write. Now that I have personally identified some of my own shortcomings I will try to work on writing more and formatting it better. Besides the previously mentioned health inquires I have recieved many requests for more information on planet construction. Hopefully the two are not related.



For the astute among you that read my journal the above picture will give you a clue on what I will be talking about in this entry. The main focus will be on rendering geometry and becuase the scale of a planet sized terrain is so huge only a level of detail algorithm can be used. The big problem is that there are many wrong LOD systems for this job. Most systems stick with the old slice and stack spheres and just map a grid of height values on them using polar coordinates. These sort of solutions lead to problems because of overly dense triangulations, distortions, and singularities at the the poles. Other methods hide or get around most of these issues but are usualy difficult or inefficient with texturing. This leads me to the LOD model that I use, pictured above, and is a Gnomonic map projection on a expanded spherical cube. This expanded cubic grid is basically a quadtree on each face and should not really need much further explanation. This setup is well suited for cube mapping, has a more regular and greatly simplified structure, and is faster in generation and visualization. This LOD has a 1:1 mapping for almost all of the system but has a maximum distortion of about 1:1.73 near the face edges. Even with this slight distortion I believe the overall benefits of this system outweighs most of the problems inherent with other LOD approaches. A similar approach that would lessen this distortion, a conformal expanded spherical cube, does have a more quasi-uniform grid structure but does not scale as well this Gnomonic expansion does.

Earth as an example:


Click for larger image