polygon-utilities-n1.js

var polygon={
    area: function(points){
        var sum=0, n=points.length;

        if(points[0][0] != points[n-1][0] || points[0][1] != points[n-1][1]){
            sum += (points[n-1][0]*points[0][1] - points[0][0]*points[n-1][1]);
        }

        for(var i=0; i < n-1; ++i){
            sum += (points[i][0]*points[i+1][1] - points[i+1][0]*points[i][1]);
        }

        return sum/2;
    },
    length: function(points){
        var l=0, n=points.length;

        if(points[0][0] != points[n-1][0] || points[0][1] != points[n-1][1]){
            l += Math.sqrt(Math.pow(points[0][1] - points[n-1][1], 2) + Math.pow(points[0][0] - points[n-1][0], 2));
        }

        for(var i=0; i < n-1; ++i){
            l += Math.sqrt( Math.pow(points[i][1] - points[i+1][1], 2) + Math.pow(points[i][0] - points[i+1][0], 2) );
        }

        return l;
    },
    is_clockwise: function(points){
        // return this.area(points) < 0 ? false : true; // visual coherence
        return this.area(points) < 0 ? true : false; // numerical coherence
    },
    centroid: function(points){
        var A=this.area(points), cx=0, cy=0, n=points.length;

        if(points[0][0] != points[n-1][0] || points[0][1] != points[n-1][1]){
            cx += ( (points[n-1][0] + points[0][0]) * (points[n-1][0]*points[0][1] - points[0][0]*points[n-1][1]) );
            cy += ( (points[n-1][1] + points[0][1]) * (points[n-1][0]*points[0][1] - points[0][0]*points[n-1][1]) );
        }

        for(var i=0; i < n-1; ++i){
            cx += ( (points[i][0] + points[i+1][0]) * (points[i][0]*points[i+1][1] - points[i+1][0]*points[i][1]) );
            cy += ( (points[i][1] + points[i+1][1]) * (points[i][0]*points[i+1][1] - points[i+1][0]*points[i][1]) );
        }

        return [(1/(6*A))*cx, (1/(6*A))*cy];
    }
}

var points=[[123,332],[262,367],[314,500],[390,378],[465,303],[436,262],[477,123],[343,181],[222,100],[233,245]];

console.log('area: ' + polygon.area(points));
console.log('clockwise: ' + polygon.is_clockwise(points));
console.log('length: ' + polygon.length(points));
console.log('centroid: ' + polygon.centroid(points));