Accuracy of sin(), cos(), etc?

Metzen

Hi,

I'm using this code to figure out the bearing between 2 points:

function calcBearing($lat1, $lon1, $lat2, $lon2){
$lat1 = deg2rad($lat1);
$lat2 = deg2rad($lat2);
$dLon = deg2rad($lon2) - deg2rad($lon1);

$y = sin($dLon) * cos($lat2);
$x = cos($lat1) * sin($lat2) - sin($lat1) * cos($lat2) * cos($dLon);

return atan2($y, $x);

}

echo calcBearing(38.6733111, -77.0258, 38.695425, -76.8723667) . "<br>\n";

It returns:
1.38737965387

But the answer should be (or closer to):
1.3881099876

Not a huge difference at first glance, but when using 1.38737965387 to plot a new point between the 2 points passed in it's off by about 10 feet.

Where is the error coming from? Is there a better formula to use to avoid these errors.

Thanks,
Metzen

laserlight

Are you sure your own computation is correct? I translated your code to C++ and my program gives 1.38738 as the result.

NogDog

It could simply be a case of the "joys" of floating point math imprecision. :rolleyes:

You might want to look at the [man]GMP[/man] and/or BC Math functions for greater precision.

laserlight

It could simply be a case of the "joys" of floating point math imprecision.

Possibly, but it is off on the 3rd decimal place, which seems rather unlikely to me in this case.

NogDog

laserlight wrote:
Possibly, but it is off on the 3rd decimal place, which seems rather unlikely to me in this case.

Except that there are 8 potential points of error, which could, in the right circumstance, have a cascading effect on the imprecision: 2 uses of deg2rad(), 4 multiplications, and 2 subtractions. But I'm just speculating: I have neither the skill nor inclination to manually do the math. 🙂 Also, since the PHP math functions were almost certainly written in C, it's probably not surprising that you got essentially the same result.

Metzen

Thanks for the replies (especially taking the time to try it in a different language!).

Using this Javascript calculator (http://williams.best.vwh.net/gccalc.htm) I was able to determine that the error isn't in the math, but in the earth model.

The formula I posted assumes a perfect sphere, which the earth is not. Using the WGS84 earth model on the Javascript calculator gives the correct answer (correct in terms of mapping).

So I just need to port that to PHP or find an existing formula.

Thanks again.

laserlight

Out of curiosity, I did the calculations myself using a hand held calculator. My final result was 1.388415818, but that probably can be attributed to the number of decimal places used (I simply saved intermediate results into memory). I think that it is indeed floating point inaccuracy, as I noticed that some of the intermediate results were not significant even at the 3rd decimal place.

Also, since the PHP math functions were almost certainly written in C, it's probably not surprising that you got essentially the same result.

Different implementations though, so it is possible that PHP's math could be buggy for the given platform.

NogDog

In any case, my gut instinct would be to use something other than the basic, built-in PHP math functions/operators to calculate things like spacecraft orbits. 😉