Joe Berry tipped me off to an interesting development effort in solid 3D referencing that promises to revolutionize GIS modeling. The thoughts and efforts of a company called PYXIS are along the lines of Berry’s thoughts for Referencing the Future that he expressed in the April 2007 issue of GeoWorld.
The unique PYXIS Digital Earth Reference Model (DERM) partitions the Earth with a hexagonal grid instead of traditional rectangular coordinates. Rather than the latitude, longitude and elevation of a point, with the discrete model of the DERM, the location in space is assigned to a PYXIS cell.
Unlike square or rectangular tiles, the hexagonal tile can’t be divided into congruent smaller hexagons. The unique index instead is built on two different child relationships to the parent cell based on vertex
and centroid relationships. Each cell references three smaller cells underneath it, and those three more, etc. The result is a hierarchy of cells layered on top of each other. Instead of quad tree indexing, it becomes icosahedron indexing. The model and its complex algebraic relationships is beautifully explained in detail on the PYXIS wiki here.
What’s compelling to me is that the DERM has been designed to solve geographic data integration problems. PYXIS indicates that spatial data can be conflated and fully integrated on-the-fly by using the DERM, providing for a unique opportunity for sharing distributed spatial data.
The model has been supported by the conservation and biodiversity community through the Global Biodiversity Information Facility. It has also been utilized within the Conservation Commons. The primary funding for this effort came from the Government of Canada for tactical military intelligence.
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Here’s a bit more detail from Perry Peterson, president of PYXIS:
Unlike square or rectangular tiles, the hexagonal tile can’t be divided into congruent smaller hexagons. The unique index instead is built on two different child relationships to the parent cell based on vertex and centroid relationships. Each cell references one smaller cell directly underneath it (centroid cell), while any cell created at a centoid can also foster cells at its vertex (vertex children), etc. The result is a hierarchy of cells layered on top of each other at a very efficient base 3. Instead of quad tree indexing, it becomes ternary indexing that converges like conventional coordinates to real numbers – i.e. you can replace geographic coordinates with this digital version. These hexagonal tiles are referenced to an Icosahedron and projected to any shape of the Earth surface – completely data, datum, projection, scale, data type independence.
And the point is, in using this system with data in this form, we can determine how far something is from something else, or whether it is included in an arbitrary region by looking at the DERM indices, and not requiring the complex spatial arithmetic—thus– we can do spatial analysis with Databases at integer arithmetic and matching speed VS. Floating point calculation speed.
Thus things that took long times with objects made up of points in Lat/Lon space, now are very quick when they are analyzed using the indices ….
let alone the advantages in modelling when UNIFORM areas can be assigned values and then because of the DERM model can be related directly…watershed, catchments, trade-areas, routes, etc…