On my previous question, it was advised I convert lat/lon/altitude to spherical or Cartesian coordinates. I'm not working near the poles and it would be safe to assume a spherical earth. What would be the best way to go about this with the minimal amount of operations? Would it be best to use x/y/z or phi/theta/rho? I'm working on a small microcontroller, with no hardware FPU (software FPU only!) so every cycle counts.
Note that "Lat/Lon/Alt" is just another name for spherical coordinates, and phi/theta/rho are just another name for latitude, longitude, and altitude. :) (A minor difference: altitude is usually measured from the surface of the sphere; rho is measured from the center -- to convert, just add/subtract the radius of the sphere.)
To convert phi/theta/rho to cartesian x/y/z where (0,0,0) is the center of the earth and rho is the distance from the center:
# python x = math.cos(phi) * math.cos(theta) * rho y = math.cos(phi) * math.sin(theta) * rho z = math.sin(phi) * rho # z is 'up'
(Note there's some slightly arbitrary choices here in what each axis means... you might want 'y' to point at the north pole instead of 'z', for example.)
The inverse, and a lot more information, can be found at Wikipedia: http://en.wikipedia.org/wiki/Spherical_coordinate_system