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Could you point me at any references on equal-volume cubic tesselations? I've found Dr. Sahr's work on DGGS incredibly accessible given my rudimentary understan

Could you point me at any references on equal-volume cubic tesselations? I've found Dr. Sahr's work on DGGS incredibly accessible given my rudimentary understanding of the math disciplines involved. An unfortunate aspect of all this, is how few good implementations of these algorithms exist outside of big commercial GIS packages. I'm extremely grateful that a public university financed this particular research originally, or we might not have gotten a well funded open source library.

jandrewrogers 9y ago
So a few things: I have been writing a blog post that elaborates on the specification of what I believe is the state of the art DGGS for most applications. It is a specification of the best DGGS I know how to design. This is not proprietary IP, just esoteric knowledge. Will be pushed sometime over the next few If you look closely, I am one of the authors of the standards for such systems. :) There is a boundary where cartographic systems and technology cease to be useful. One of the big advantages of the 3D embedding DGGS is that the math is dead simple compared to the forced 2D versions. They are extremely powerful in terms of expressiveness, performance, and precision but also relatively transparent. The mere fact of attacking the 2D problem in 3-space reduces its complexity. People just aren’t used to it. The implicit dimensional reduction of 2-space has consequences. In a few years I think all geospatial data will be handled this way.
- espeed 9y ago
  Isn't the prevailing wisdom to skip 3-space and go directly to 4-space, which makes things even simpler and more powerful -- note 4D projective space (homogeneous coordinates, not quaternions and not counting a time dimension). Reasons for going to 4D are numerous and varied, such as symplectic geometry only works in even dimensions, image/video reconstruction, matrix multiplication, transformations, and other reasons related to computer vision, gauge theory, and topology.

jandrewrogers 9y ago

So a few things: I have been writing a blog post that elaborates on the specification of what I believe is the state of the art DGGS for most applications. It is a specification of the best DGGS I know how to design. This is not proprietary IP, just esoteric knowledge. Will be pushed sometime over the next few If you look closely, I am one of the authors of the standards for such systems. :) There is a boundary where cartographic systems and technology cease to be useful. One of the big advantages of the 3D embedding DGGS is that the math is dead simple compared to the forced 2D versions. They are extremely powerful in terms of expressiveness, performance, and precision but also relatively transparent. The mere fact of attacking the 2D problem in 3-space reduces its complexity. People just aren’t used to it. The implicit dimensional reduction of 2-space has consequences. In a few years I think all geospatial data will be handled this way.

espeed 9y ago
Isn't the prevailing wisdom to skip 3-space and go directly to 4-space, which makes things even simpler and more powerful -- note 4D projective space (homogeneous coordinates, not quaternions and not counting a time dimension). Reasons for going to 4D are numerous and varied, such as symplectic geometry only works in even dimensions, image/video reconstruction, matrix multiplication, transformations, and other reasons related to computer vision, gauge theory, and topology.