## PointInPolygon(polygon, point)

##### Last updated December 7, 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[1]);
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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