Detect if a set of points in an array that are the vertices of a complex polygon were defined in a clockwise or counterclockwise order?

Question

EDIT: I updated the program with the answer and it works great!

I am making a program (feel free to try it out) that lets users draw polygons which it then triangulates.

Answer 1

Compute the polygon area using the shoelace formula, but without the absolute value sign. If the result is positive, the points are ordered counterclockwise, and if negative - clockwise.

function polygonArea() { 
    var area = 0;
    for (var i = 0; i < vertices.length; i++) {
        j = (i + 1) % vertices.length;
        area += vertices[i].x * vertices[j].y;
        area -= vertices[j].x * vertices[i].y;
    }
    return area / 2;
}
var clockwise = polygonArea() > 0;