Finding Middle point of Polygon

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hi to all
Please help me, i want to find the middle lattitude and longitude of a polygon in gmap using sql server or C# or javascripts please help

thanks in advance

Posted 13-Jun-12 2:10am

Pardeep singh from Chandigarh

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3 solutions

Solution 3

this is a JavaScript function who get a Polygon and return a Point. you can use this function to calculate center of a Polygon.

Function:

JavaScript

function getCenterOfPolygon(polygon){
	var PI=22/7
	var X=0;
	var Y=0;
	var Z=0;
	polygon.getPath().forEach(function (vertex, inex) {
		lat1=vertex.lat();
		lon1=vertex.lng();
		lat1 = lat1 * PI/180
		lon1 = lon1 * PI/180
		X += Math.cos(lat1) * Math.cos(lon1)
		Y += Math.cos(lat1) * Math.sin(lon1)
		Z += Math.sin(lat1)
	})
	Lon = Math.atan2(Y, X)
	Hyp = Math.sqrt(X * X + Y * Y)
	Lat = Math.atan2(Z, Hyp)
	Lat = Lat * 180/PI
	Lon = Lon * 180/PI 
	return new google.maps.LatLng(Lat,Lon);
}

Use:

JavaScript

var pt=getCenterOfPolygon(mapPolygon);
alert(pt.lat()+","+pt.lng());

Posted 13-Jun-12 19:39pm

csharpbd

Updated 13-Jun-12 19:42pm

v2

Comments

kimberly ping 24-Jan-15 0:06am

What is this algorithm called?

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**Zoltán Zörgő** · Accepted Answer · 2012-06-13T02:23:00

First of all define the "middle point" in terms of mathematical concepts.
If you mean the center of a polygon:
Regular Polygon case:
In the case of regular polygons the center is the point that is equidistant from each vertex or corner. It is also the center of the polygon's incircle and circumcircle.
Irregular Polygon case
Irregular polygons are not considered as having a center, since there is unlikely to be any one point equally distant form each vertex. However, an irregular polygon can have a centroid, or center of gravity.
If you mean the centroid of a polygon see this article: http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/[^].
You can also calculate a vector mean, by calculating a mean for longitude and latitude values respectively.

Joshi, Rushikesh · Accepted Answer · 2012-06-13T04:45:00

Solution 1 is well detailed and thank you Zoltan

Below is simplified version

Consider polygon (Pentagon) with co-ordinates (x1,y1); (x2,y2); (x3,y3); (x4,y4); (x5,y5) then centroid should be

Centroid X coord = (x1+x2+x3+x4+x5) / 5
Centroid Y coord = (y1+y2+y3+y4+y5) / 5

You can use X as latitude and Y as longitude and can point Centroid.

If you are using any mapping tool/library then that library itself should have this functionality to create a polygon with centroid.

If you are creating any functionality on a DigitalMap then attached formulas might help you in future http://williams.best.vwh.net/avform.htm[^].

Also this http://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u33.html#SEC33.4.1[^] might help you to generate source code for your formulas.

Cheers and best of luck!

Thanks
Rushikesh Joshi