Create random polygon with CGAL in c++ (adaption of MATLAB algorithm)

I need to create random polygons with n vertices and decided to use CGAL. I found an algorithm for this using Delaunay triangulations implemented in MATlab: https://stackoverflow.com/a/9008916/9519322

I started to adapt it to c++, but I don't know how to handle vertices and (boundary) edges in CGAL and don't understand the follwing MATlab commands.

Could somebody help me to get a working adaption of the algorithm in c++?

assert(n >= 3);

std::random_device rd;
std::mt19937 mt(rd());
std::uniform_real_distribution<double> dist(std::nextafter(0.0, 1.0), 1.0);


int fudge = (int)ceil((double)n/10);

std::vector<Point_2> points;

for (int i = 0; i < n + fudge; ++i)
{
    points.emplace_back(dist(mt), dist(mt));
}

Delaunay dt;
dt.insert(points.begin(), points.end());

// get boundary edges of dt
// remaining

I've adapted the other algorithm of the thread yet, but it creates only star shaped polygons.