encoding - 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-754 FP as degrees or radians
• degrees or radians stored as a fixed point value in an 32 or 64 bit int
• mapping of an integer range to the degree range: -> deg = (360/2^32)*val
• degrees, minutes, seconds and fractional seconds stored as bit fields in an int
• a struct of some kind.

The easy solution (FP) has the major down side that it has highly non uniform resolution (somewhere in England it can measure in microns, over in Japan, it can't). Also this has all the issues of FP comparison and whatnot. The other options require extra effort in different parts of the data's life cycle. (generation, presentation, calculations etc.)

One interesting option is a floating precision type that where as the Latitude increase it gets more bits and the Longitude gets less (as they get closer together towards the poles).

Related questions that don't quite cover this:

• What is the ideal data type to use when storing latitude / longitudes in a MySQL
• Working with latitude/longitude values in Java

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BTW: 32 bits gives you an E/W resolution at the equator of about 0.3 in. This is close to the scale that high grade GPS setups can work at (IIRC they can get down to about 0.5 in in some modes).

OTOH if the 32 bits is uniformly distributed over the earth's surface, you can index squares of about 344m on a side, 5 Bytes give 21m, 6B->1.3m and 8B->5mm.

I don't have a specific use in mind right now but have worked with this kind of thing before and expect to again, at some point.

Answer 1

The easiest way is just to store it as a float/double in degrees. Positive for N and E, negative for S and W. Just remember that minutes and seconds are out of 60 (so 31 45'N is 31.75). Its easy to understand what the values are by looking at them and, where necessary, conversion to radians is trivial.

Calculations on latitudes and longitudes such as the Great Circle distance between two coordinates rely heavily on trigonometric functions, which typically use doubles. Any other format is going to rely on another implementation of sine, cosine, atan2 and square root, at a minimum. Arbitrary precision numbers (eg BigDecimal in Java) won't work for this. Something like the int where 2^32 is spread uniformly is going to have similar issues.

The point of uniformity has come up in several comments. On this I shall simply note that the Earth, with respect to longitude, isn't uniform. One arc-second longitude at the Arctic Circle is a shorter distance than at the Equator. Double precision floats give sub-millimetre precision anywhere on Earth. Is this not sufficient? If not, why not?

It'd also be worth noting what you want to do with that information as the types of calculations you require will have an impact on what storage format you use.