The point-in-polygon algorithm allows you to programmatically check if a particular point is inside a polygon or outside of it. A common way to tackle the problem is to count how many times a line drawn from the point (in any direction) intersects with the polygon boundary. If the line and the polygon intersect an even number of times (or not at all), then the point is outside. If they intersect an odd number of times, the point is inside. It is true even for complex forms that have a lot of coordinates and thus create a very precise boundary.

Let’s see a sample image before we get to the code.

Here, the lines drawn from point 1 intersect twice or not at all, because it is outside.

Point 2 is inside and thus the lines drawn from it intersect once or three times.

Even in special cases, such as point 3, we see that this method works: the line intersects twice and the point is therefore outside.

I use this approach in the PHP code below, which returns one of these 4 possible values:

*inside*if the point is inside the polygon.*outside*if, you guessed it, the point is outside of the polygon.*vertex*if the point sits exactly on a vertex AND*$pointOnVertex = true*(line 2)*boundary*if the point sits on the boundary. If*$pointOnVertex = false*, then*boundary*is also returned if the point is on a vertex.

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<?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: michael.niessen@assemblysys.com 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]); } } ?> |

## Using the point-in-polygon PHP code

Set the point(s) value(s) and an array containing your polygon vertices (in the form “Xcoordinate Ycoordinate”), then call the *pointInPolygon* function. **The first and last polygon coordinates must be identical**, to “close the loop”.

As you can see in the following example, it is easy to check multiple points at once. The code also works with negative coordinates, for the polygon as well as for the points to check.

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<?php $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>"; } ?> |

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

bvbnice!

MrDogVery nice and saved me a lot of work. But one query – you say the last point in the polygon must be the same as the first one to close the loop which I understand – but the first one is (-50,30) and the last one is (-50,-30) which are not the same – which implies to me that the last value is not really needed?

MichaelPost authorThanks for pointing that out!

It was a mistake (now corrected) in the sample. The last coordinate does have to be the same as the first one.

Regards

RhijulIs there a way to optimise the code to run the algorithm for searching multiple points. Basically if we can get the status of all the points whether they are inside or outside. I know we can run the same algorithm over all the points, but then the we will be repeating a lot of our intersection calculations and the algorithm would not be that efficient.

SVery nice. Thanks for this example.

DiegoThank you so much, the algorithm works like a charm with latitudes/longitudes… I will definitively buy you coffee

MichaelPost authorHi Diego,

Thank you very much for the coffee!

Nilesh NayakHi,

I have a set of points as detailed below.

$pointlocation = new pointLocation();

$pts[] = “51.22881787980134 -1.157684326171875″;

$pts[] = “51.138432319543924 -1.043701171875″;

$pts[] = “51.11990293528057 -0.998382568359375 “;

$pts[] = “51.12248887705868 -0.9455108642578125″;

$pts[] = “51.19483648846099 -0.778656005859375″;

$pts[] = “51.222367645529715 -0.701751708984375″;

$pts[] = “51.269648373496736 -0.696258544921875″;

$pts[] = “51.30443311306082 -0.71685791015625″;

$pts[] = “51.336617716006664 -0.770416259765625″;

$pts[] = “51.350771787631196 -0.9468841552734375″;

$centerpoint = “51.263217 -0.9525255999999445″;

echo $pointlocation->pointInPolygon($centerpoint, $pts);

This seems to show that the point is outside when in effect, it is inside.

If I am not wrong, the following statement causes the issue.

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']) {

I am not sure what this statement is trying to do.

Can you please shed light on this as we are using this in one of our projects.

MichaelPost authorHi Nilesh,

Don’t forget that, as mentionned in the article, the first and last point of the polygon array must be identical, to close it

So, just add

$pts[] = “51.22881787980134 -1.157684326171875″;as the last point and the script will returninside, as it should.Kind regards,

Michaël

Nilesh NayakHi Michael,

Thank you for very much for replying. Hadn’t noticed this. Will do the correction.

Regards

Nilesh

Parthhey this how i am using this but it always show outside as result

$pointLocation = new pointLocation();

$points=array(“22.560019387 72.907277656″);

$polygon = array(“72.9443135978394 22.5665187803137″,”72.9671445609741 22.5735726534814″,

“72.9671445609741 22.5735726534814″,”72.9735818626099 22.5691343034821″,”72.9702344657593 22.5570470009717″,

“72.9702344657593 22.5570470009717″,”72.9810920478516 22.5427786579349″,”72.9810920478516 22.5427786579349″,

“72.9810920478516 22.5427786579349″,”72.9496780158692 22.5259718289148″,”72.9496780158692 22.5259718289148″,

“72.9156890632324 22.5396077146951″,”72.9156890632324 22.5396077146951″,”72.9194656135254 22.5623576184676″,

“72.9440990211182 22.5663998917189″,”72.9443135978394 22.5665187803137″);

foreach($points as $key => $point) {

echo “point ” . ($key+1) . ” ($point): ” . $pointLocation->pointInPolygon($point, $polygon) . “”;

}

please help

parth

MichaelPost authorHi Parth,

It seems you switched the

xandyvalues of the point, but even if it were x=72.907277656 and y=22.560019387, it would clearly be outside, as none of the polygon coordinates hasxless than 7.91Regards,

Michaël

JonasHey,

great work!

I have a question, is there a way to make a “hole” in the middle of a polygon (like in the sample picture; point 3).

Kind Regards from Germany

Jonas

MichaelPost authorThanks Jonas,

It is indeed currently not supported, but I’ll try to add it in a future version of the script. Anyway, the basic idea is to check the number of intersections with both boundaries (the external polygon and the “hole”) and add them up. If the total is an odd number (or 0), then the point is either outside or in the hole. I hope that helps.

Michaël

akismet-80400ff01fa0a76a61544fe392b1cb6bIs there a way of inverting the search so that instead of searching for multiple points in a single polygon it searches for a single point in multiple polygons?

MichaelPost authorHi,

You just have to run the script in a loop, so it checks whether the point is inside/outside each of the polygons.

Regards,

Michaël

ideasbinariasangelhi, i need help please.

i have an array with coordinates:

$polygons :

[0] => 18.41059802826527 -88.03557809904612

[1] => 18.41580996014612 -88.24981149747505

[2] => 18.4716617793069 -88.249813060726

[3] => 18.475569353943605 -88.30062482830219

[4] => 18.487291543546217 -88.31985090252014

[5] => 18.484686681799133 -88.34594343181584

[6] => 18.485989117621315 -88.36654279704898

[7] => 18.476871859036027 -88.37615583415798

[8] => 18.49510589119781 -88.40224836345367

[9] => 18.478174354235335 -88.44482038493693

….

[164] => 18.14315877533503 -87.9022376682663

[165] => 18.16044934189305 -87.92489697002266

[166] => 18.16044934189305 -88.02995373271435

[167] => 18.410310718038836 -88.03630833016227

[168] => 18.41059802826527 -88.03557809904612

if i write:

$point = “18.511268 -88.289952 ”

it’s work fine, but when i write $point inside a while structure (i get many points from a table) it’s don’t work, because coordinate 18.511268 -88.289952 says outside when must be inside.

i am thinking this mistake is because i have many points (543) to validate inside a while structure, so, the server’s memory may be is “confused” like a result of the operations.

please help me, thank you.

* note that the first and last position are the same in $polygons.

MichaelPost authorHi,

I don’t see why there would be an issue with the use of

while. Since it works when you run the script with a single point, it should give the same result for that particular point when checking multiple points. The only thing that comes to mind would be that a variable is not reset properly in thatwhileloop, but it’s really difficult to say without seeing the code.As shown in the sample code above, you can put all the points in the $points array, and they will all be checked in the

foreachloop. Have you tried fetching all you points from the table (usingwhile) to populate the $points array and then running the point-in-polygon script in theforeach, as in that sample?Regards,

Michaël