Java: Trigonometry and double inaccuracy causing NaN


I have a distance formula using latitude and longitude:

distance = EARTH_MILES_RADIUS * Math.acos(Math.sin(lat1 / RADIAN_CONV) * Math.sin(lat2 / RADIAN_CONV) + Math.cos(lat1 / RADIAN_CONV) * Math.cos(lat2 / RADIAN_CONV) * Math.cos((lng2 - lng1) / RADIAN_CONV));

lat1,lng1,lat2,lng2 are double primitives. They come to me as double primitives and there is nothing I can do about it.

The problem is that when I have a pair of longitude or latitudes that are the same the formula sometimes returns NaN. I believe this is because I am taking the arc cosine of a number very slightly greater than 1, when in fact it should be exactly 1. I would probably have problems if the points were antipodal as well, where they might be slightly less than -1.

How can I best fix this problem?


If you are indeed calculating great circle distance as I think you are, you should use the Vincenty formula instead of what you have.

<a href="http://en.wikipedia.org/wiki/Great-circle_distance" rel="nofollow">http://en.wikipedia.org/wiki/Great-circle_distance</a>


Check for two very close (ideally equal) values in your code. For example:

boolean doubleApproxEqual(double a, double b) { double PRECISION = 0.000001; if (Math.abs(a-b) < PRECISION) //not sure what the name of the function is //cannot be bothered to check return true; return false; }

if you get a True, do cos(1.0) or whatever


Simply checking for equality was enough to fix my problem:

if (lat1 == lat2 && lng1 == lng2) ...


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