Are 2 polygons colliding both concave and convex polys are allowed

// polygon objects are an array of vertices forming the polygon
//     var polygon1=[{x:100,y:100},{x:150,y:150},{x:50,y:150},...];
// The polygons can be both concave and convex
// return true if the 2 polygons are colliding 

function polygonsCollide(p1,p2){
    // turn vertices into line points
    var lines1=verticesToLinePoints(p1);
    var lines2=verticesToLinePoints(p2);
    // test each poly1 side vs each poly2 side for intersections
    for(i=0; i<lines1.length; i++){
    for(j=0; j<lines2.length; j++){
        // test if sides intersect
        var p0=lines1[i][0];
        var p1=lines1[i][1];
        var p2=lines2[j][0];
        var p3=lines2[j][1];
        // found an intersection -- polys do collide
        if(lineSegmentsCollide(p0,p1,p2,p3)){return(true);}
    }}
    // none of the sides intersect
    return(false);
}
// helper: turn vertices into line points
function verticesToLinePoints(p){
    // make sure polys are self-closing
    if(!(p[0].x==p[p.length-1].x && p[0].y==p[p.length-1].y)){
        p.push({x:p[0].x,y:p[0].y});
    }
    var lines=[];
    for(var i=1;i<p.length;i++){
        var p1=p[i-1];
        var p2=p[i];
        lines.push([ 
            {x:p1.x, y:p1.y},
            {x:p2.x, y:p2.y}
        ]);
    }
    return(lines);
}
// helper: test line intersections
// point object: {x:, y:}
// p0 & p1 form one segment, p2 & p3 form the second segment
// Get interseting point of 2 line segments (if any)
// Attribution: http://paulbourke.net/geometry/pointlineplane/
function lineSegmentsCollide(p0,p1,p2,p3) {
    var unknownA = (p3.x-p2.x) * (p0.y-p2.y) - (p3.y-p2.y) * (p0.x-p2.x);
    var unknownB = (p1.x-p0.x) * (p0.y-p2.y) - (p1.y-p0.y) * (p0.x-p2.x);
    var denominator  = (p3.y-p2.y) * (p1.x-p0.x) - (p3.x-p2.x) * (p1.y-p0.y);        

    // Test if Coincident
    // If the denominator and numerator for the ua and ub are 0
    //    then the two lines are coincident.    
    if(unknownA==0 && unknownB==0 && denominator==0){return(null);}

    // Test if Parallel 
    // If the denominator for the equations for ua and ub is 0
    //     then the two lines are parallel. 
    if (denominator == 0) return null;

    // test if line segments are colliding
    unknownA /= denominator;
    unknownB /= denominator;
    var isIntersecting=(unknownA>=0 && unknownA<=1 && unknownB>=0 && unknownB<=1)

    return(isIntersecting);
}