## How do you determine if a point lies within a polygon using PHP?

Determining Whether a Point Lies Within a Polygon

In the realm of spatial analysis, one often encounters the problem of determining if a given point lies within the boundaries of a polygon. This can be particularly challenging when dealing with complex geometric shapes defined by multiple vertices. MySQL's Geometry Datatype includes a polygon type to represent such shapes.

Consider the scenario where we have an array of latitudes and longitudes representing the vertices of a polygon, as shown below:

[{"x":37.628134,  "y":-77.458334},
{"x":37.629867,   "y":-77.449021},
{"x":37.62324,    "y":-77.445416},
{"x":37.622424,   "y":-77.457819}]

Additionally, we have a point with its own latitude and longitude coordinates:

$location = new vertex($_GET["longitude"], $_GET["latitude"]);

The task is to determine whether this point falls within the specified polygon. To accomplish this in PHP, we can employ the following function:

<?php
$vertices_x = array(37.628134, 37.629867, 37.62324, 37.622424);    // x-coordinates of the vertices of the polygon
$vertices_y = array(-77.458334,-77.449021,-77.445416,-77.457819); // y-coordinates of the vertices of the polygon
$points_polygon = count($vertices_x) - 1;  // number vertices - zero-based array
$longitude_x = $_GET["longitude"];  // x-coordinate of the point to test
$latitude_y = $_GET["latitude"];    // y-coordinate of the point to test

if (is_in_polygon($points_polygon, $vertices_x, $vertices_y, $longitude_x, $latitude_y)){
  echo "Is in polygon!";
}
else echo "Is not in polygon";

function is_in_polygon($points_polygon, $vertices_x, $vertices_y, $longitude_x, $latitude_y)
{
  $i = $j = $c = 0;
  for ($i = 0, $j = $points_polygon ; $i < $points_polygon; $j = $i++) {
    if ( (($vertices_y[$i]  >  $latitude_y != ($vertices_y[$j] > $latitude_y)) &amp;&amp;
     ($longitude_x < ($vertices_x[$j] - $vertices_x[$i]) * ($latitude_y - $vertices_y[$i]) / ($vertices_y[$j] - $vertices_y[$i]) + $vertices_x[$i]) ) )
       $c = !$c;
  }
  return $c;
}
?>

This function iterates over the vertices of the polygon and utilizes geometric calculations to determine if the point lies within its boundaries. Based on the result, it returns a flag indicating whether the point is inside or outside the polygon.

For more comprehensive functionality, consider using the polygon.php class. By creating an instance of this class with your polygon's vertices and calling the isInside() method with your point as input, you can leverage an alternative approach to solving this problem.

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