I'm trying to solve the problem of interpolating a point at a given distance (in meters) between two other lat/long points. (e.g. P1 (50,10), P2(50.01, 9.990), I want to interploate P3 at a distance "X" on the shortest route between P1 and P2, assuming that X is always smaller than the distance between P1 and P2)
Whilst at first this seemed kind of easy I couldn't for the life of me find an easy to implementation for this (e.g. a few lines of code and a few external constants, as to be easy to debug and quick to run).
Currently I'm using the formula:
val x : Double = RadiusOfEarth*Math.toRadians(lon)*CentralLatCos val y : Double = RadiusOfEarth*Math.toRadians(lat)
to project to 2d cartesian, I interpolate the point in cartesian coordinates (since for that there are loads of formulas that I actually understand and can use). And then I go back to lon/lat using:
val lat : Double = Math.toDegrees(y/RadiusOfEarth) val lon : Double = Math.toDegrees( x/(RadiusOfEarth*CentralLatCos) )
However, this seems to be causing quite large errors so I'm quite sure the way I project my points is flawed.
Could you help me by suggesting either and easy algorithm to project back/forth from sphere to cartesian (that keep heading&distance) or a way to interpolate a point between two other lon/lat points at a given distance ?
Also, please do provide some source material that "proves" you solution so that I can better understand it, I asked this question somewhere else and some formulas with no context where thrown at me (which doesn't really help, I can find loads of those using the internet).
Do note, I'm trying to do this for small distance, the largest of which might be something around the lines of 2-3k meters (distance between the tow original points I know). So I really have no need for a formula that's accurate on a global scale, if it has a small error but its easy to implement I'm more than fine with it.
(Note: I'm working on a map between lat 45 - 55 and lon 7-13)