The point-in-polygon algorithm allows you to check if a point is inside a polygon or outside of it.

point-in-polygon.php

<?php
/*
Description: The point-in-polygon algorithm allows you to check if a point is
inside a polygon or outside of it.
Author: Michaël Niessen (2009)
Website: http://AssemblySys.com
 
If you find this script useful, you can show your
appreciation by getting Michaël a cup of coffee ;)
PayPal: [email protected]
 
As long as this notice (including author name and details) is included and
UNALTERED, this code is licensed under the GNU General Public License version 3:
http://www.gnu.org/licenses/gpl.html
*/
 
class pointLocation {
    var $pointOnVertex = true; // Check if the point sits exactly on one of the vertices?
 
    function pointLocation() {
    }
 
    function pointInPolygon($point, $polygon, $pointOnVertex = true) {
        $this->pointOnVertex = $pointOnVertex;
 
        // Transform string coordinates into arrays with x and y values
        $point = $this->pointStringToCoordinates($point);
        $vertices = array(); 
        foreach ($polygon as $vertex) {
            $vertices[] = $this->pointStringToCoordinates($vertex); 
        }
 
        // Check if the point sits exactly on a vertex
        if ($this->pointOnVertex == true and $this->pointOnVertex($point, $vertices) == true) {
            return "vertex";
        }
 
        // Check if the point is inside the polygon or on the boundary
        $intersections = 0; 
        $vertices_count = count($vertices);
 
        for ($i=1; $i < $vertices_count; $i++) {
            $vertex1 = $vertices[$i-1]; 
            $vertex2 = $vertices[$i];
            if ($vertex1['y'] == $vertex2['y'] and $vertex1['y'] == $point['y'] and $point['x'] > min($vertex1['x'], $vertex2['x']) and $point['x'] < max($vertex1['x'], $vertex2['x'])) { // Check if point is on an horizontal polygon boundary
                return "boundary";
            }
            if ($point['y'] > min($vertex1['y'], $vertex2['y']) and $point['y'] <= max($vertex1['y'], $vertex2['y']) and $point['x'] <= max($vertex1['x'], $vertex2['x']) and $vertex1['y'] != $vertex2['y']) { 
                $xinters = ($point['y'] - $vertex1['y']) * ($vertex2['x'] - $vertex1['x']) / ($vertex2['y'] - $vertex1['y']) + $vertex1['x']; 
                if ($xinters == $point['x']) { // Check if point is on the polygon boundary (other than horizontal)
                    return "boundary";
                }
                if ($vertex1['x'] == $vertex2['x'] || $point['x'] <= $xinters) {
                    $intersections++; 
                }
            } 
        } 
        // If the number of edges we passed through is odd, then it's in the polygon. 
        if ($intersections % 2 != 0) {
            return "inside";
        } else {
            return "outside";
        }
    }
 
    function pointOnVertex($point, $vertices) {
        foreach($vertices as $vertex) {
            if ($point == $vertex) {
                return true;
            }
        }
 
    }
 
    function pointStringToCoordinates($pointString) {
        $coordinates = explode(" ", $pointString);
        return array("x" => $coordinates[0], "y" => $coordinates[1]);
    }
 
}

// Tests


$pointLocation = new pointLocation();
$points = array("50 70","70 40","-20 30","100 10","-10 -10","40 -20","110 -20");
$polygon = array("-50 30","50 70","100 50","80 10","110 -10","110 -30","-20 -50","-30 -40","10 -10","-10 10","-30 -20","-50 30");
// The last point's coordinates must be the same as the first one's, to "close the loop"
foreach($points as $key => $point) {
    echo "point " . ($key+1) . " ($point): " . $pointLocation->pointInPolygon($point, $polygon) . "<br>";
}

// Results 
/*
This will output:

point 1 (50 70): vertex
point 2 (70 40): inside
point 3 (-20 30): inside
point 4 (100 10): outside
point 5 (-10 -10): outside
point 6 (40 -20): inside
point 7 (110 -20): boundary

*/