Openlayers battles - Is this polygon convex or not?

This would be pretty easy - I thought - if it were only a wonderful Openlayers function e.g polygon.isConvex(). But it wasn’t, or at least I could find it in version 2.13.1. I was searching the internet, trying to find the simplest solution, because I was sure there is a more elegant and shorter solution than hacking with angles.
Finally StackOverflow came to my help (as always :). In this thread I found the most suitable algorithm for my need.

A polygon is a set of points in a list where the consecutive points form the boundary. It is much easier to figure out whether a polygon is convex or not (and you don't have to calculate any angles, either):

For each consecutive pair of edges of the polygon (each triplet of points), compute the z-component of the cross product of the vectors defined by the edges pointing towards the points in increasing order. Take the cross product of these vectors:

 given p[k], p[k+1], p[k+2] each with coordinates x, y:
 dx1 = x[k+1]-x[k]
 dy1 = y[k+1]-y[k]
 dx2 = x[k+2]-x[k+1]
 dy2 = y[k+2]-y[k+1]
 zcrossproduct = dx1*dy2 - dy1*dx2

The polygon is convex if the z-components of the cross products are either all positive or all negative. Otherwise the polygon is nonconvex.

If there are N points, make sure you calculate N cross products, e.g. be sure to use the triplets (p[N-2],p[N-1],p[0]) and (p[N-1],p[0],p[1]).

You can checkout my Javascript implementation of this algorithm here.

Openlayers concave shape example

Batman vs Superman - AngularJS 2 example with Firebase

You can checkout the demo application here. Batman vs Superman - Angular 2 example site Code of the application is available here. If you have any comments or improvement ideas, feel free to share with me!