Center of gravity of a polygon

Question

I am trying to write a PHP function that will calculate the center of gravity of a polygon.

I\'ve looked at the other similar questions but I can\'t seem to find a s

Answer 1

in cold c++ and while assuming that you have a Vec2 struct with x and y properties :

const Vec2 findCentroid(Vec2* pts, size_t nPts){
    Vec2 off = pts[0];
    float twicearea = 0;
    float x = 0;
    float y = 0;
    Vec2 p1, p2;
    float f;
    for (int i = 0, j = nPts - 1; i < nPts; j = i++) {
        p1 = pts[i];
        p2 = pts[j];
        f = (p1.x - off.x) * (p2.y - off.y) - (p2.x - off.x) * (p1.y - off.y);
        twicearea += f;
        x += (p1.x + p2.x - 2 * off.x) * f;
        y += (p1.y + p2.y - 2 * off.y) * f;
    }

    f = twicearea * 3;

    return Vec2(x / f + off.x, y / f + off.y);
}

and in javascript :

function findCentroid(pts, nPts) {
    var off = pts[0];
    var twicearea = 0;
    var x = 0;
    var y = 0;
    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 {
    X: x / f + off.lat,
    Y: y / f + off.lng
    };
}

or in good old c and while assuming that you have a Point struct with x and y properties :

const Point centroidForPoly(const int numVerts, const Point* verts)
{
    float sum = 0.0f;
    Point vsum = 0;

    for (int i = 0; i