Distance between long/lat point and line segment

PHP
1

Hi folks,

I need to calculate if a long/lat point is within a given distance of a coastline (an array of long/lat line segments).

Does anyone happen to know how to do this in PHP?

2 
sqrt(($lat1-$lat2)*($lat1-$lat2)+($long1-$long2)*($long1-$long2));

essentially the distance formula,
but you’re going to have to convert the longitude and latitude into base 10 before you put it through there and then convert it back after you have the result.

3

Just thought I post what I finally came up with…

Feel free to critique it or make it better…

<?php
// distance between two points in kilometres
// 3958      - Earth's radius (miles)
// 3.1415926 - PI
// 57.29578  - Number of degrees/radian (for conversion)
// 1.609344  - meters = 0.001 mile
function get_geo_distance_point_to_point($lat1, $lon1, $lat2, $lon2)
{
	return 	(3958 * 3.1415926 * sqrt(($lat2 - $lat1) * ($lat2 - $lat1) 
			+ cos($lat2 / 57.29578) * cos($lat1 / 57.29578) * ($lon2 - $lon1) * ($lon2 - $lon1)) / 180) * 1.609344;
}

// get height from triangle where A or B are not obtuse
function get_height_from_base_triangle($ab, $ac, $bc)
{
	// find $s (semiperimeter) for Heron's formula
	$s = ($ab + $ac + $bc) / 2;
	
	// Heron's formula - area of a triangle
	$area = sqrt($s * ($s - $ab) * ($s - $ac) * ($s - $bc));
	
	// find the height of a triangle - ie - distance from point to line segment
	$height = $area / (.5 * $ab);
	
	return $area;
}

// returns angles of a triangle from the sides
function get_angles_from_sides($ab, $bc, $ac)
{
	$a = $bc;
	$b = $ac;
	$c = $ab;
	
	$angle['a'] = rad2deg(acos((pow($b,2) + pow($c,2) - pow($a,2)) / (2 * $b * $c)));
	$angle['b'] = rad2deg(acos((pow($c,2) + pow($a,2) - pow($b,2)) / (2 * $c * $a)));
	$angle['c'] = rad2deg(acos((pow($a,2) + pow($b,2) - pow($c,2)) / (2 * $a * $b)));
	
	return $angle;			
}

// $a, $b, $c lat lon array of line segments ($a and $b) and the off point ($c)
function get_geo_distance_point_to_segment($a, $b, $c)
{
	$ab = get_geo_distance_point_to_point($a['lat'], $a['lon'], $b['lat'], $b['lon']); // base or line segment
	$ac = get_geo_distance_point_to_point($a['lat'], $a['lon'], $c['lat'], $c['lon']);
	$bc = get_geo_distance_point_to_point($b['lat'], $b['lon'], $c['lat'], $c['lon']);
	
	$angle = get_angles_from_sides($ab, $bc, $ac);
	
	if($ab + $ac == $bc) // then points are collinear - point is on the line segment
	{
		return 0;
	}
	elseif($angle['a'] <= 90 && $angle['b'] <= 90) // A or B are not obtuse - return height as distance
	{
		return get_height_from_base_triangle($ab, $ac, $bc);
	}
	else // A or B are obtuse - return smallest side as distance
	{
		return ($ac > $bc) ? $bc : $ac;
	}

}
/*
	// line segment
	$a['lat'] = 37.083667;
	$a['lon'] = -1.84948;
	$b['lat'] = 37.069149;
	$b['lon'] = -1.849823;
	
	// point
	$c['lat'] = 37.14;
	$c['lon'] = -1.85;

	echo get_geo_distance_point_to_segment($a, $b, $c);
*/
?>