Get in between lat long from two lat long and direction - php

Question

I am working on one application where I need in between lat long from two lat long.
So for that what I have is
1) Lat long of start point
2) Lat long of end point
3) Direction, like south(180 degree) or north(0 degree)
4) Distance between two points
Now what I will do is I will divide whole path in some number of chunks, like I will divide whole path by 10 KM.
So lets say total distance is 100KM then I will get 10 chunks.
if 200KM then there will be 20 chunks.
So now I want to find out those point's lat long from two lat long.
So all 20 points should be in one line and at equal distance.
How to achieve that ?

Answer 1

You can try taking the difference between the two Lat Lon points, dividing them by the number of chunks. This will give the "increment". This can then be added, or taken away depending on the direction, in a loop to create the points in between.
Consider the following I did as a test:
//Position 1
$lat1 = 53.2226754;
$lon1 = 0.124584;
//Position 2
$lat2 = 52.212445;
$lon2 = -0.12458;
//Differences in Lat / Lon
$latDif = round($lat1 - $lat2, 7);
$lonDif = round($lon1 - $lon2, 7);
//Calculate Step / Increment
//I used 10 as an example for the number of steps
$chunks = 10;
$latStep = round($latDif / $chunks, 7);
$lonStep = round($lonDif / $chunks, 7);
//New Lat Lon starts at start point
$newLat = $lat1;
$newLon = $lon1;
echo $lat1 . ", " . $lon1 . "<br>"; //Start Point
for($i = 1; $i < $chunks; $i++){
//Direction could be substituted here
if($lat1 < $lat2){
$newLat = $newLat + $latStep; //Going North
} else {
$newLat = $newLat - $latStep; //Going South
}
if($lon1 < $lon2){
$newLon = $newLon + $lonStep; //Going East
} else {
$newLon = $newLon - $lonStep; //Going West
}
echo $newLat . ", " . $newLon . "<br>"; //New Point
}
echo $lat2 . ", " . $lon2 . "<br>"; //End Point
This leads to the following Lat Lon output:
53.2226754, 0.124584;
53.1216524, 0.0996676;
53.0206294, 0.0747512;
52.9196064, 0.0498348;
52.8185834, 0.0249184;
52.7175604, 0.0000002;
52.6165374, -0.0249144;
52.5155144, -0.0498308;
52.4144914, -0.0747472;
52.3134684, -0.0996636;
52.212445, -0.12458;
I plotted these on an online geoplanner and got the following:
GPS Results Link

Answer 2

As per #Piskvor's comment, my previous method would not have worked over long distances due to the Mercator Projection of maps.
After some Internet digging, some head-scratching and serious mind boggling, I think I've created a PHP method for calculating the Great Circle path between two Lat Lon points.
For the following example, I'm using the start point as London Heathrow Airport and end point as JFK Intl Airport.
Firstly, we need to calculate the distance between Point A and Point B along the Great Circle that connects them, using the Haversine Formula:
//Must convert to Radians for use with Trig functions
$lat1 = deg2rad(51.4700223); $lon1 = deg2rad(-0.4542955); // LHR
$lat2 = deg2rad(40.6413111); $lon2 = deg2rad(-73.7781391); // JFK
$eRadius = 6367000; // Earth Radius in metres
//Difference between lat and lon
$difLat = $lat2 - $lat1;
$difLon = $lon2 - $lon1;
//Some mathematical magic
$a = sin($difLat / 2) * sin($difLat / 2) +
cos($lat1) * cos($lat2) *
sin($difLon / 2) * sin($difLon / 2);
$c = 2 * atan2(sqrt($a), sqrt(1-$a));
//Distance from pA to pB along the great circle in metres
$t_distance = $eRadius * $c;
Now we have the total distance we can plan the points of the path:
//Step distance in metres
$sDist = 800000; //800km
//Lat Lon Storage;
$lat = []; //Short hand for array(); PHP > 5.4
$lon = [];
//Number of steps - rounded down!
$steps = floor($t_distance / $sDist);
//Percentage of distance for 1 step
$_f = 100 / $steps;
//CALCULATE POINTS
for($i = 0; $i <= $steps; $i++){
$f = ($_f * $i) / 100; // value between 0-1 corresponding with percentage of step with the step number
$_d = $t_distance / $eRadius; //Angular Distance
$a = sin((1- $f) * $_d) / sin($_d);
$b = sin($f * $_d) / sin($_d);
$x = ($a * cos($lat1) * cos($lon1)) + ($b * cos($lat2) * cos($lon2));
$y = ($a * cos($lat1) * sin($lon1)) + ($b * cos($lat2) * sin($lon2));
$z = ($a * sin($lat1)) + ($b * sin($lat2));
//New Lat Lon point
$nLat = round(atan2($z, sqrt(pow($x, 2) + pow($y, 2))),7);
$nLon = round(atan2($y, $x),7);
//Push to Lat Lon arrays, converting Radians back to Degrees
array_push($lat, rad2deg($nLat));
array_push($lon, rad2deg($nLon));
}
Using a simple foreach loop the Lat Long points are something like:
51.470024866283, -0.45429823575923
53.302510052872, -13.752895032598
53.561704700234, -27.704938735627
52.21669773532, -41.302699715615
49.42997998883, -53.701145438835
45.476181591127, -64.517161945995
40.6413111, -73.7781391
Plotting these points on the online geoplanner will give you this result:
I should also like to point out that these two websites really helped me when creating this method:
http://www.movable-type.co.uk/scripts/latlong.html
http://williams.best.vwh.net/avform.htm