# CFLib.org – Common Function Library Project

## PointInPolygon(polygon, point)

##### Last updated December 07, 2004

Version: 1 | Requires: CF5 | Library: MathLib

Description:
Determines if the given point is within the given n-sided polygon. The argument polygon expects a space delimited list of points. Each point is in itself a comma delimited pair of value. Example: "206,94 173,124 126,168 163,207" The argument point is nothing more than a common delimited list of two numbers. Example: "258,147"

Return Values:
Returns a boolean.

Example:

``````<cfset polygon = "206,94 173,124 126,168 163,207 219,229 259,203 284,141 274,105 255,87 229,77">
<cfset point1 = "258,147">
<cfset point2 = "139,197">

<cfif PointInPolygon(polygon, point1)>
The point1 IS within the polygon
<cfelse>
The point1 IS NOT within the polygon
</cfif>

<cfif PointInPolygon(polygon, point2)>
The point2 IS within the polygon
<cfelse>
The point2 IS NOT within the polygon
</cfif>
``````

Parameters:

Name Description Required
polygon A space-delimited list of coordinates. Yes
point A comma-delimited coordinate. Yes

Full UDF Source:

``````/**
* Determines if the given point is within the given n-sided polygon.
*
* @param polygon      A space-delimited list of coordinates. (Required)
* @param point      A comma-delimited coordinate. (Required)
* @return Returns a boolean.
* @author Joshua L. Olson (joshua@waetech.com)
* @version 1, December 7, 2004
*/
function PointInPolygon(polygon, point) {
var polygon_arr = ListToArray(polygon, " ");
var polygon_arr_length = 0;

var intersections = 0;

var test_point_x = Val(ListFirst(point, ","));
var test_point_y = Val(ListLast(point, ","));

var i = "1";
var dx = "0";
var dy = "0";
var cx = "0";

var point_1 = "";
var point_2 = "";
var point_1_x = "";
var point_1_y = "";
var point_2_x = "";
var point_2_y = "";
var cross_y = "";

polygon_arr_length = ArrayLen(polygon_arr);

// Terminate early if this is not a complete polygon.
if (polygon_arr_length LT "3") return false;

// Append the first element to the end of the array so that we complete the
// polygon, which is a prerequisite for this to work.
ArrayAppend(polygon_arr, polygon_arr);

for (i = "1"; i LTE polygon_arr_length; i = i + "1") {
// get the endpoints for the segment
point_1 = polygon_arr[i];
point_2 = polygon_arr[i + "1"];

point_1_x = Val(ListFirst(point_1, ","));
point_1_y = Val(ListLast(point_1, ","));

point_2_x = Val(ListFirst(point_2, ","));
point_2_y = Val(ListLast(point_2, ","));

// Determine if segment crosses vector starting at point and extending right

// Check that the line segment crosses the horizontal line extended left and
// right from the given point.  We consider end-points on the horizontal line to
// be above the horizontal line.

cross_y = ((point_1_y LT test_point_y) AND (point_2_y GTE
test_point_y)) OR
((point_2_y LT test_point_y) AND (point_1_y GTE test_point_y));

if (cross_y) {
// The segment crosses the horizontal plane.  Now determine if it's to the right
// or left of the given point.

dx = point_2_x - point_1_x;
dy = point_2_y - point_1_y;

// cx is the point at which the segment crosses the horizontal plane of the
// given point.  This is a basic geometric calculation.
cx = point_1_x + (dx * (test_point_y - point_1_y) / dy);

// If the crossing point is to the right of the given point, count it
if (cx GT test_point_x)
intersections = (intersections + 1) MOD 2;
}

}
// An odd number of intersections indicates that the point is within the polygon

return intersections IS 1;
}
``````

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