proper/best type for storing latitude and longitude

Question

In a system level programming language like C, C++ or D, what is the best type/encoding for storing latitude and longitude?

The options I see are:

• IEEE

Answer 1

What encoding is "best" really depends on your goals/requirements.

If you are performing arithmetic, floating point latitude,longitude is often quite convenient. Other times cartesian coordinates (ie x,y,z) can be more convenient. For example, if you only cared about points on the surface of earth, you could use an n-vector.

As for longer term storage, IEEE floating point will waste bits for ranges you don't care about (for lat/lon) or for precision you may not care about in the case of cartesian coordinates (unless you want very good precision at the origin for whatever reason). You can of course map either type of coordinates to ints of your preferred size, such that the entire range of said ints covers the range you are interested in at the resolution you care about.

There are of course other things to think about than merely not wasting bits in the encoding. For example, (Geohashes)[https://en.wikipedia.org/wiki/Geohash] have the nice property that it is easy to find other geohashes in the same area. (Most will have the same prefix, and you can compute the prefix the others will have.) Unfortunately, they maintain the same precision in degrees longitude near the equator as near the poles. I'm currently using 64-bit geohashes for storage, which gives about 3 m resolution at the equator.

The Maidenhead Locator System has some similar characteristics, but seems more optimized for communicating locations between humans rather than storing on a computer. (Storing MLS strings would waste a lot of bits for some rather trivial error detection.)

The one system I found that does handle the poles differently is the Military Grid Reference System, although it too seems more human-communications oriented. (And it seems like a pain to convert from or to lat/lon.)

Depending on what you want exactly, you could use something similar to the Universal polar sereographic coordinate system near the poles along with something more computationally sane than UTM for the rest of the world, and use at most one bit to indicate which of the two systems you're using. I say at most one bit, because it's unlikely most of the points you care about would be near the poles. For example, you could use "half a bit" by saying 11 indicates use of the polar system, while 00, 01, and 10 indicate use of the other system, and are part of the representation.

Sorry this is a bit long, but I wanted to save what I had learned recently. Sadly I have not found any standard, sane, and efficient way to represent a point on earth with uniform precision.

Edit: I found another approach which looks a lot more like what you wanted, since it more directly takes advantage of the lower precision needed for longitude closer to the poles. It turns out there is a lot of research on storing normal vectors. Encoding Normal Vectors using Optimized Spherical Coordinates describes such a system for encoding normal vectors while maintaining a minimum level of accuracy, but it could just as well be used for geographical coordinates.