Java: Trigonometry and double inaccuracy causing NaN

问题

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?

回答1:

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

http://en.wikipedia.org/wiki/Great-circle_distance

回答2:

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

回答3:

Simply checking for equality was enough to fix my problem:

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

来源：https://stackoverflow.com/questions/5725101/java-trigonometry-and-double-inaccuracy-causing-nan