Geodetic data in PostGIS - Spherical indexing schemes

Here at Refractions we're starting to think about how we can provide better support in PostGIS for geodetic data. Geodetic data is data which is defined in a true spherical coordinate system (in particular, of course, the surface of the Earth).

Currently PostGIS provides some geodetic-aware functions (such as distance between two geodetic points). But it's current spatial data model is fundamentally planar, so there are definite limitations to modelling geodetic data (e.g. such as the notorious "line crossing the Date Line" problem). As PostGIS gets used for larger datasets and more ambitious projects, the utility of having a full-function geodetic data model is becoming increasingly obvious.

Handling geodetic data in a correct and efficient way presents quite a few challenges. A major one is: how can geodetic geometry be spatially indexed? Conventional spatial indexes (such as 2D R-trees) all rely on geometry being embedded in a planar space. They don't handle data which can "wrap around", as can occur in a spherical space.

There have been various clever proposals for spherical indexing strategies. Some prominent ones are listed below:

• Hierarchical Triangular Mesh - this is essentially a "quad-tree for the sphere". It has a lot of appeal for use with point data, since it provides a hierarchical key which can be indexed using a conventional B-tree index. (It was co-developed by the late, great Jim Gray in order to index astronomical data). The mathematics to determine the index key for a non-point object would seem to be somewhat complicated. It also seems like HTM would suffer from the usual disadvantage of quadtrees of not being very self-tuning. Another disadvantage from the PostGIS point of view is that this would likely be a brand new index type (i.e. lots of difficult code to write)

• Hipparchus Voronoi-based index. This index can be thought of as a fixed-grid index using a custom Voronoi cell coverage for the globe. IBM's DB/2 Geodetic extension uses this scheme. I must say that this concept, while ingenious, seems a bit baroque to me. This index has the usual disadvantage of fixed-grid indexes of not handling widely-varying data sizes well. And it also requires extremely complex cell coverage structures, which have to be selected specifically for the expected data composition. DB/2 supplies 13 different ones based on various data densities (G7 industrial output, anyone?). I'm not sure what you are supposed to do if your data has some other density distribution - it doesn't seem very feasible to make your own Voronoi grid. And what if you don't know your data distribution, or it changes over time?
  

• 3D Bounding Box - this is the approach used by the pgSphere project. It's pretty straightforward. The key concept is to embed the sphere in 3-space, so that it is possible to compute 3D bounding boxes for geometries on the embedded sphere. The bounding boxes can then be indexed using a 3D R-tree (exactly analogous to a 2D R-tree spatial index). The GIST index supplied with PostgreSQL can be customized to provide the required 3D R-tree. One possible issue is that apparently R-trees become "less effective" in higher-dimensional spaces. It remains to be seen whether this is truly a serious problem.
  

Out of these options, it seems like the 3D Bounding Box approach is the most straightforward scheme. There's some challenges in developing the mathematics required (at least, for a planar/linear guy like me), but I'm hopeful that we can deal with these issues and arrive at a efficient, maintainable solution.