getCenter of Polygon (Centroid)

[ximex]

Example:
If i want to get draw in the middle of a polygon a icon, i need the center of this polygon.

Samplecode:

L.Polygon.prototype.getCenter = function(){
var pts = this._latlngs;

var twicearea = 0;
var p1, p2, f;
var x = 0, y = 0;
var nPts = pts.length;

for(var i=0, j=nPts-1;i<nPts;j=i++) {
    p1=pts[i];
    p2=pts[j];
    twicearea+=p1.lat*p2.lng;
    twicearea-=p1.lng*p2.lat;

    f=p1.lat*p2.lng-p2.lat*p1.lng;

    x+=(p1.lat+p2.lat)*f;
    y+=(p1.lng+p2.lng)*f;
}
f=twicearea*3;
return {lat: x/f,lng: y/f};

}

Problem: This code only works for a non-self-intersecting closed polygon

Rectangle: Much easier and no problems with self-intersection!

Source: https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon

[mourner]

Nice suggestion, will consider this. Thanks!

[ximex]

We found a little mistake in the function. Here you can read the small discussion: https://plus.google.com/u/0/108220049326938062364/posts/beV4PQYM58x

The problem only exits if the polygon is very small (~5x5meters). This code works with very small polygons too.

var pts = this._latlngs;
var off = pts[0];
var twicearea = 0;
var x = 0;
var y = 0;
var nPts = pts.length;
var p1,p2;
var f;
for (var i = 0, j = nPts - 1; i < nPts; j = i++) {
p1 = pts[i];
p2 = pts[j];
f = (p1.lat - off.lat) * (p2.lng - off.lng) - (p2.lat - off.lat) * (p1.lng - off.lng);
twicearea += f;
x += (p1.lat + p2.lat - 2 * off.lat) * f;
y += (p1.lng + p2.lng - 2 * off.lng) * f;
}
f = twicearea * 3;
return {
lat: x / f + off.lat,
lng: y / f + off.lng
};

[ximex]

Another little improvment: return value should be a L.LatLng() object.

return new L.LatLng(
x / f + off.lat,
y / f + off.lng
);

[hampelm]

Just wanted to note that this fn would be very helpful for the mapping I've been doing recently -- would love to see it in Leaflet.

[whyvez]

same here! Love your work... thank you!

[mourner]

Just a quick note on this: I started getting this into Leaflet core 88ad667 but eventually decided that I'd better do that after the vectors refactoring that I'm doing now #155

[mourner]

Done as a part of #2290, along with polyline centroids