While most maps show a 2D view from above, Linear maps show a single route, with features and navigation points along that route. They tend to be used for long distance footpaths, cycle-ways (e.g. converted railways) and of course, railways themselves.
In these situations, positions get measured not in lat/long, but in miles from the start. So with one of these maps, you can navigate using just a simple pedometer, and points of interest take the form "bike hire at mile 0. toilets at mile 4. layby cafe at mile 11"
List the segments in order, then calculate the distance between each one. Store the absolute distance (from the start) of each node, and use that to render.
The distance measuring formula needs to work for very small distances, so (sqrt(dLat^2 + (dLong * cos(lat))^2) * 6400km) is probably OK
It might be useful to divide the route into sections between "significant" changes of direction (see corner detection), and put a bearing on each section to show what direction it's going.
Do a search of geograph images along the route, and display them as photos on the side of the map.
Stubs and nearby facilities
Would be useful to display stubs of things that cross the path, e.g. when going across a road - need to do a bit of maths to display those properly.
Nodes should be easier, just calculate perpendicular distance from the route, then use that both for filtering out anything further than a certain distance, and for deciding where to display it. (e.g. car parks, shops, "amenities")
There's a standard algorithm for this, where you specify the maxiumum deviation, and it goes through a 2D line detecting corners - anyone know the algorithm's name?
It might be possible to do things like using HTML tables to generate the map - would be wikipedia-compatible, and means you can create articles about (e.g. some river) with HTML on each segment linking to cities, or displaying images.
- Long distance footpaths, e.g. pennine way, or pembrokeshire coast path
- River guides for kayakers (marking falls, towns, campsites, etc.)
- Railway maps, and tourist railways (where stations are regularly spaced, rather than by exact distance)
- Navigation system for use on motorways (you don't care where the road curves, just what's at each junction)