What are the recommended ways of simplifying geometries? Keeping in mind projections, and simplifying state geometries for example.
I've heard about converting to an 'equi-distant' projection that allows simplification without distortion, and then converting back to your chosen projection.
Answer
As glennon mentioned, the standard algorithm for doing this is Douglas-Peucker, which is the default algorithm used in software such as PostGIS (i.e. GEOS) via St_Simplify, ArcGIS via Generalize and GRASS via v.generalize. The Wikipedia article also links to a Python implementation.
GRASS supports a number of different algorithms, as explained in the help page for v.generalize.
On the projection issue, I think in this case its a red herring which can be ignored. The only issue which comes to mind is potentially densifying lines to prevent them from being oversimplified.
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