Take a line, mesh, region, and reduce it into a similar-but-simpler line, mesh, region.
The use case that caused me to ask is that I am making a map of Ireland's trails, and the trail data I have is extremely overspecified (let's say 1 point per 5 metres or so). It doesn't make sense to have data this granular for a map at a scale of hundreds of kilometres. I would like to be able to simplify the lines so that they look more or less the same from a distance, but have significantly fewer points.
It's not the only use case I have, and of course I'm sure there are applications abound for FEM and so on.
CanonicalizeRegion is a related function that doesn't quite do what I'm looking for.
Taking the idea of truncating sparse representations, like in JPEG, could it be enough to sort the mesh points by "relevance", and depending on the detail required, take as many points as necessary, few if zooming out and coarse mesh is acceptable, keep reading if finner details are required...
BTW, I'm somehow surprised by the large number of "data points" generated in simple plots like Plot[x,{x,0,1}], not very efficient.
@CarlLange For the specific example of a trail, then it sounds like Douglas-Peucker might help. I have used that in the past to visualize GPS data that had way too many points similar to your example.
