This is my 2nd in a series of three articles that shows how to use trigonometry to gain useful information about the Google Earth user environment.

In this article I'm providing the code for a PHP function to calculate the coordinates of an unknown point from a known position, range and bearing. This can be used with the LookAt variables sent to the server by NetworkLink to calculate the coordinates of the viewer, especially when the viewpoint is tilted and skewed and the viewpoint is far away from the BBOX.

My 3rd article shows a single PHP function to calculate both the location and altitude of the unknown viewpoint from just the LookAt data, and is a combination of this function and my previously published altitude() function.
Code:

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/**
* Calculate the unknown coordinates at bearing and distance from known coordinates
* 
* Developed by TJ (http://tjworld.net/software/kml/) for Google Earth applications
*
* @param	float	long		Longitude of known point (decimal degreees)
* @param	float	lat		Latitude of known point (decimal degrees)
* @param	float	distance	Distance to unknown point (meters)
* @param	float	bearing		Bearing (angle in degrees) to unknown point.
*					Measured from North=0, -ve going to west (-90), +ve going to east (90)
* @returns	array			Associative array containing unknown 'longitude' and 'latitude'
*/
$EARTH_RADIUS_EQUATOR = 6378140.0;
$RADIAN = 180 / pi();

function calcLatLong($long, $lat, $distance, $bearing) {
 global $EARTH_RADIUS_EQUATOR, $RADIAN;
 $b = $bearing / $RADIAN;
 $long = $long / $RADIAN;
 $lat = $lat / $RADIAN;
 $f = 1/298.257;
 $e = 0.08181922;
	
 $R = $EARTH_RADIUS_EQUATOR * (1 - $e * $e) / pow( (1 - $e*$e * pow(sin($lat),2)), 1.5);	
 $psi = $distance/$R;
 $phi = pi()/2 - $lat;
 $arccos = cos($psi) * cos($phi) + sin($psi) * sin($phi) * cos($b);
 $latA = (pi()/2 - acos($arccos)) * $RADIAN;

 $arcsin = sin($b) * sin($psi) / sin($phi);
 $longA = ($long - asin($arcsin)) * $RADIAN;
 return array('longitude' => $longA, 'latitude' => $latA);
}

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on this line:

Code:

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$psi = $distance/$R;

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what is $R? can you explain your code a bit or point to the formula? I'm having trouble following it. Thanks.


-gnlnx