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POImplementing Vincenty's Formula in PHP
 

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  1. POImplementing Vincenty's Formula in PHP
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    <p>I've been attempting to implement <a href="http://en.wikipedia.org/wiki/Vincenty%27s_formulae" rel="nofollow">Vincenty's formulae</a> with the following:</p> <pre><code> /* Implemented using Vincenty's formulae from http://en.wikipedia.org/wiki/Vincenty%27s_formulae, * answers "Direct Problem". * $latlng is a ('lat'=&gt;x1, 'lng'=&gt;y1) array * $distance is in miles * $angle is in degrees */ function addDistance($latlng, $distance, $bearing) { //variables $bearing = deg2rad($bearing); $iterations = 20; //avoid too-early termination while avoiding the non-convergant case //knowns $f = EARTH_SPHEROID_FLATTENING; //1/298.257223563 $a = EARTH_RADIUS_EQUATOR_MILES; //3963.185 mi $phi1 = deg2rad($latlng['lat']); $l1 = deg2rad($latlng['lng']); $b = (1 - $f) * $a; //first block $tanU1 = (1-$f)*tan($phi1); $U1 = atan($tanU1); $sigma1 = atan($tanU1 / cos($bearing)); $sinalpha = cos($U1)*sin($bearing); $cos2alpha = (1 - $sinalpha) * (1 + $sinalpha); $usquared = $cos2alpha * (($a*$a - $b*$b) / 2); $A = 1 + ($usquared)/16384 * (4096+$usquared*(-768+$usquared*(320 - 175*$usquared))); $B = ($usquared / 1024)*(256*$usquared*(-128 + $usquared * (74 - 47*$usquared))); //the loop - determining our value $sigma = $distance / ($b * $A); for($i = 0; $i &lt; $iterations; ++$i) { $twosigmam = 2*$sigma1 + $sigma; $delta_sigma = $B * sin($sigma) * (cos($twosigmam)+(1/4)*$B*(cos(-1 + 2*cos(cos($twosigmam))) - (1/6)*$B*cos($twosigmam)*(-3+4*sin(sin($sigma)))*(-3+4*cos(cos($twosigmam))))); $sigma = $distance / ($b * $A) + $delta_sigma; } //second block $phi2 = atan((sin($U1)*cos($sigma)+cos($U1)*sin($sigma)*cos($bearing)) / ((1-$f) * sqrt(sin($sinalpha) + pow(sin($U1)*sin($sigma) - cos($U1)*cos($sigma)*cos($bearing), 2)))); $lambda = atan((sin($sigma) * sin($bearing)) / (cos($U1)*cos($sigma) - sin($U1)*sin($sigma)*cos($bearing))); $C = ($f / 16)* $cos2alpha * (4+$f*(4-3*$cos2alpha)); $L = $lambda - (1 - $C) * $f * $sinalpha * ($sigma + $C*sin($sigma)*(cos($twosigmam)+$C*cos($sigma)*(-1+2*cos(cos($twosigmam))))); $alpha2 = atan($sinalpha / (-sin($U1)*sin($sigma) + cos($U1)*cos($sigma)*cos($bearing))); //and return our results return array('lat' =&gt; rad2deg($phi2), 'lng' =&gt; rad2deg($lambda)); } var_dump(addDistance(array('lat' =&gt; 93.129, 'lng' =&gt; -43.221), 20, 135); </code></pre> <p>The issue is that the results are not reasonable - I'm getting variances of up to 20 latitude and longitude keeping the distance at 20. Is it not in units of elliptical distance on the sphere? Am I misunderstanding something, or is my implementation flawed? </p>
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    1. COI'm aware that http://www.movable-type.co.uk/scripts/latlong.html has a simpler implementation of distance+bearing, but I'm interested in the higher accuracy of Vincenty's formula.
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    2. COI usually do this in sql (after cutting results with a simple boundary box). I'll see if I still have the php function for you.
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    3. COMight want to ask on http://gis.stackexchange.com
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