Distance measure: As the crow flies, as the road builds and as the wheel turns

[zgrssd]

Distance measures are important. But I do not think there is one solution that fits all circumstances.
10 hexes away over a dirt road and 10 hexes away with 8 being mountain just do not compared
10 Hexes can be easily walked - or put the mountain into insurmountable.

But I think we can resolve it down to 3 basic measures:

As the crow flies
Also know as the "Beeline" or Geodesic", this is how far one can go if terrain does not mater. It only applies to Airplanes, OHQ Range and Adminstrain for now.

As the road builds
A thing I thought up to match "as the crow flies".
This is a measure of how expensive it would be to build a road to some place. How many IP multipliers there are and how high they sum up.
5.2.2.5. gives us a formula for road costs that is based on a AP measure. So "how far would 100 AP of road cost get you"? (this equals 200 IP for dirt, 500 for sealed)
If there already is a road part of the way, it would expand that range.
As it is based on the underlying AP measure, the type of road would not mater so much.

As the wheel turns
This is something I just thought up to match "as the crow flies".
This is how far a wheeled vehicle could go from a specific starting point. Basically: how far could a wheeled vehicle go on 100 AP?
Mostly this distance would follow roads or easy terrain, while being blocked by mountain.


When the game spawns a quest where I have to hold a position, it should not just be within a certain distance of "how the crow flies". But also be within a certain distance of "as the road builds". And failing that, at least "as the wheel turns".
(I orgiinally put wheel before road, but I realized roads are slighl cheaper and thus should go farther).


One of the best parts is that those measures are comparatively static over a turn. So they can be calculated once and then stored.
Another good part is that you can check for all 3 distances in a single pathfinding pass:
If it is beyond the crow fly range, wheel and road will not catch up.
If it is beyond road range, chances are wheels are too expensive anyway.