I'm trying to get my head around how ST_ShortestLine (and ST_Distance and ST_LineLocatePoint) work with different projections. The result for the shortest line differs depending on which projection I use (either 4326 or 900913).
This is the result visualised as 4326 (pink is ST_ShortestLine on geometry left at 4326, blue is ST_ShortestLine on geometry transformed to 900913)
And this is the same result visualised as 900913 (pink is ST_ShortestLine on geometry left at 4326, blue is ST_ShortestLine on geometry transformed to 900913)
As you can see, they are both the shortest line depending on the projection you visualise in. So which one is actually the correct 'shortest line' in reality? The actual thing I'm visualising here is the nearest point on a road to a bus stop – the small difference in output is actually a big deal for geographic accuracy.
If it helps, the final output for this data will be in the 900913 projection (D3.js). I'm happy to go with the transformed 900913 output, I just want to understand what's happening and which one is actually truly shortest.