Conversion between semicircles and latitude units

Question

I've recently come across the semicircle unit that is used to describe a latitude and longitude using the maximum precision allowed by a 32-bit number. The conversion here is given as

• degrees = semicircles * ( 180 / 2^31 )
• semicircles = degrees * ( 2^31 / 180 )

However it doesn't explain if this should be used differently for latitude since the maximum allowed number of semicircles is 2^31, and if you substitute this into the equation you get the answer "180 degrees", but latitude only goes up to 90.

Would a different conversion between latitude be used instead? Such as:

• degrees = semicircles * ( 90 / 2^31 )
• semicircles = degrees * ( 2^31 / 90 )

If so then you wouldn't be using the 'semicircle' as a unit for latitude, more like a quarter circle in this case.

Has anybody else come across this issue?

Answer 1

The constant 180 would still be used for latitude because the relationship is 1 degree to a half circle. The Max and Min semicircles for latitude will be different (.5 to -.5) vs. Max and Min semicircles for longitude (1.0 to -1.0).

Answer 2

I have problems with @longrider saying that

the relationship is 1 degree to a half circle.

which does not make sense mathematically. And I do not think is accurate. (please elaborate if I am wrong)

This answer is copied-pasted from http://www.logicio.com/HTML/navstopset.htm in case the link breaks.

A semicircle is a unit of location-based measurement on an arc. An arc of 180 degrees is made up of many semicircle units; 2^31 semicircles to be exact. Semicircles that correspond to North latitudes and East longitudes are indicated with positive values; semicircles that correspond to South latitudes and West longitudes are indicated with negative values.

The following formulas show how to convert between degrees and semicircles:

degrees = semicircles * (180 / 2^31)

semicircles = degrees * (2^31 / 180)

This explain better the relationship between degrees and semicircles units. What I take that @longrider wanted to say is that the range of values of a latitude measured in semicircles (or half-circles) is -0.5 to 0.5, while the longitude ones are -1.0 to 1.0. So multiplying by 180 was ok in both cases.