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I have a line (Ax,Ay - Bx,By) over a mercator projection (google maps) and a random point (Cx,Cy) nearest to that line, i would to know the closest point (transparent blue on the image) over that line to point (blue in the image)

EDIT: to clarify that this is in a Mercator projection (spherical projection) enter image description here

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this post has very useful solution that may interest you – vinayan Dec 28 '12 at 14:38
That light blue doesn't look like the closest, the closest should create a 90 degrees angle when connected to the dark blue, is that what you mean ? – Glenn Plas Dec 28 '12 at 15:29
I made the pic by hand so yeah, it's posible – Colas Dec 28 '12 at 16:03
@vinayan The post you reference solves a different problem of finding the nearest point to a line, whereas what is needed here appears to want the nearest point to a line segment. – whuber Dec 28 '12 at 16:10
The segment should be around 20-100 meters long , the point from centimeters to 30 meters as much from the segment – Colas Dec 28 '12 at 16:56

check out this link , it made me use the following function to calculate distances to line segments.


function point_to_line_segment_distance($startX,$startY, $endX,$endY, $pointX,$pointY) {

   // list($distanceSegment, $x, $y) = point_to_line_segment_distance($startX,$startY, $endX,$endY, $pointX,$pointY);

    // Adapted from Philip Nicoletti's function, found here:

    $r_numerator = ($pointX - $startX) * ($endX - $startX) + ($pointY - $startY) * ($endY - $startY);
    $r_denominator = ($endX - $startX) * ($endX - $startX) + ($endY - $startY) * ($endY - $startY);
    $r = $r_numerator / $r_denominator;

    $px = $startX + $r * ($endX - $startX);
    $py = $startY + $r * ($endY - $startY);

    $s = (($startY-$pointY) * ($endX - $startX) - ($startX - $pointX) * ($endY - $startY) ) / $r_denominator;

    $distanceLine = abs($s) * sqrt($r_denominator);

    $closest_point_on_segment_X = $px;
    $closest_point_on_segment_Y = $py;

    if ( ($r >= 0) && ($r <= 1) ) {
       $distanceSegment = $distanceLine;
    else {
       $dist1 = ($pointX - $startX) * ($pointX - $startX) + ($pointY - $startY) * ($pointY - $startY);
       $dist2 = ($pointX - $endX) * ($pointX - $endX) + ($pointY - $endY) * ($pointY - $endY);
       if ($dist1 < $dist2) {
          $closest_point_on_segment_X = $startX;
          $closest_point_on_segment_Y = $startY;
          $distanceSegment = sqrt($dist1);
       else {
          $closest_point_on_segment_X = $endX;
          $closest_point_on_segment_Y = $endY;
          $distanceSegment = sqrt($dist2);

    return array($distanceSegment, $closest_point_on_segment_X, $closest_point_on_segment_Y);

You can then use projection functions to calculate distances, I'm using the above formula to calculate the time at that point given a average speed and it works really well.

If you want a good PHP library to calculate distances between coordinates in PHP, check out GeoCalc class

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Hey Glenn Plas, your class seem to have a little offset to the left or right,i made a screenshot on Google earth you will see that offset, the pic:link, the code i used point_to_line_segment_distance(41.421649, 2.600410, 41.413851, 2.594356, 41.415710, 2.600638)) – Colas Dec 28 '12 at 16:44
It's not my class, just found it after searching a lot ;-) But I use 8 digits precision in my problems, you seem to use 6. That could be the reason, I never noticed any offset here. Thanks for pointing it out, I will doublecheck this soon as I need to know. – Glenn Plas Dec 28 '12 at 16:55
Maybe you are rihgt, i can't obtain more decilmas on gEarth, btw in my last pic the segment was 1000 meters long, the offset was ~110meters – Colas Dec 28 '12 at 17:06
That's about the scale I use it on, no more than that. I use it to see at what time a bus (public transport) passes a stop the closest. I am going to doublecheck it though and put it in a map to 'see' if it projects well on a sphere. – Glenn Plas Dec 28 '12 at 17:18
Oh... I thought that function was made for spherical projections, so now i understand the offset – Colas Dec 28 '12 at 17:26

you can use computeDistanceBetween() function from google map api.

distance = google.maps.geometry.spherical.computeDistanceBetween(firstCoord, secondCoord);

The distance between two points is the length of the shortest path between them. This shortest path is called a geodesic. On a sphere all geodesics are segments of a great circle. To compute this distance, call computeDistanceBetween(), passing it two LatLng objects.

You may instead use computeLength() to calculate the length of a given path if you have several locations

i hope it helps you...

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first I need to know the point (light blue) to compute the distance between – Colas Dec 28 '12 at 16:12
My solution below does that, the point on the segment is unknown. I actually have a rather similar problem/solution as mentioned. You can safely use these on small scale's. – Glenn Plas Dec 28 '12 at 16:23

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