How to move a marker 100 meters with coordinates

Question

I have 2 coordinates. Coordinate 1 is a 'person'. Coordinate 2 is a destination.

How do I move coordinate 1 100 meters closer to coordinate 2?

This would be used in a cron job, so only php and mysql included.

For example:

Person is at: 51.26667, 3.45417

Destination is: 51.575001, 4.83889

How would i calculate the new coordinates for Person to be 100 meters closer?

Solution 1

Use Haversine to calculate the difference between the two points in metres; then adjust the value of the person coordinates proportionally.

$radius = 6378100; // radius of earth in meters
$latDist = $lat - $lat2;
$lngDist = $lng - $lng2;
$latDistRad = deg2rad($latDist);
$lngDistRad = deg2rad($lngDist);
$sinLatD = sin($latDistRad);
$sinLngD = sin($lngDistRad);
$cosLat1 = cos(deg2rad($lat));
$cosLat2 = cos(deg2rad($lat2));
$a = ($sinLatD/2)*($sinLatD/2) + $cosLat1*$cosLat2*($sinLngD/2)*($sinLngD/2);
if($a<0) $a = -1*$a;
$c = 2*atan2(sqrt($a), sqrt(1-$a));
$distance = $radius*$c;

Feeding your values of:

$lat = 51.26667;        //  Just South of Aardenburg in Belgium
$lng = 3.45417;
$lat2 = 51.575001;      //  To the East of Breda in Holland
$lng2 = 4.83889;

gives a result of 102059.82251083 metres, 102.06 kilometers

The ratio to adjust by is 100 / 102059.82251083 = 0.0009798174985988102859004569070625

$newLat = $lat + (($lat2 - $lat) * $ratio);
$newLng = $lng + (($lng2 - $lng) * $ratio);

Gives a new latitude of 51.266972108109 and longitude of 3.4555267728867

Solution 2

If you understand JavaScript, you may want to check out the moveTowards() method in the following Stack Overflow post:

• How to add markers on Google Maps polylines based on distance along the line?

This method returns the destination point when given a start point, an end point, and the distance to travel along that line. You can use point 1 as the starting point, point 2 as the end point, and a distance of 100 meters. It's written in JavaScript, but I'm sure it can be easily ported to PHP or MySQL.

You may also want to check out this other Stack Overflow post which implements a part of the above JavaScript implementation, as a user defined function for SQL Server 2008, called func_MoveTowardsPoint:

• Moving a Point along a Path in SQL Server 2008

The above uses SQL Server 2008's in-built geography data type. However you can easily use two decimal data types for latitude and longitude in place of the single geography data type.

Both the SQL Server and the JavaScript examples were based on implementations from Chris Veness's article Calculate distance, bearing and more between Latitude/Longitude points.

Solution 3

Find the angle theta between the x-axis and the vector from person to destination.

theta = Atan2(dest.y-person.y, dest.x-person.x).

Now use theta and the amount you want to advance the point to calculate the new point.

newPoint.x = advanceDistance * cos(theta) + person.x

newPoint.y = advanceDistance * sin(theta) + person.y