linesIntersect.js

function open_segments_intersect(a1, a2, b1, b2) {
  if ((max(a1.x, a2.x) <= min(b1.x, b2.x)) || // a is left of b
      (max(b1.x, b2.x) <= min(a1.x, a2.x)) ||
      (max(a1.y, a2.y) <= min(b1.y, b2.y)) || // a is above b (in coordinates where (0,0) is topleft)
      (max(b1.y, b2.y) <= min(a1.y, a2.y))
     ) {return false;}
  else if ((vcross(vsub(b1,a1),vsub(a2,a1)) * vcross(vsub(b2,a1),vsub(a2,a1)) < 0) && // replace these with <= to make the segments act closed.
           (vcross(vsub(a1,b1),vsub(b2,b1)) * vcross(vsub(a2,b1),vsub(b2,b1)) < 0)) {return true;}
  else {return false;}
}

function vsub(a, b) {
  return {x: a.x - b.x, y, a.y - b.y}
}

function vcross(a, b) {
  return a.x * b.y - b.x * a.y;
}

pointInPolygon.js

/**
     * checks if a point is inside of a concave or convex polygon TESTED
     * polygon: array of {x:1, y: 1} objects
     */
    pointInPolygon = function (point, polygon){
        var i,
            j,
            c = 0,
            pointX = point.x,
            pointY = point.y;
            
        for (i = 0, j = polygon.length - 1, len = polygon.length; i < len; j = i++){
            
            if (((polygon[i].y > pointY) != (polygon[j].y > pointY)) && (pointX < (polygon[j].x - polygon[i].x) * (pointY - polygon[i].y) / (polygon[j].y - polygon[i].y) + polygon[i].x)){
                c = !c;
            }
        }
        return c;
    }