Proper way of adding CGAL points api-wise

I have a triangle defined by its three vertices. The vertices are of type Point = CGAL::Point_2<K> with a Simple_cartersian<double> kernel.

I want to randomly sample this triangle and for that I use a formula (https://math.stackexchange.com/questions/18686/uniform-random-point-in-triangle-in-3d) which adds the three vertices of the triangle multiplied by some random factors.

                Point = Point(0, 0) +                                                //
                        (1 - std::sqrt(r1)) * (standardTriangle[0] - Point(0, 0)) +  //
                        (std::sqrt(r1) * (1 - r2)) * (standardTriangle[1] - Point(0, 0)) +
                        (r2 * std::sqrt(r1)) * (standardTriangle[2] - Point(0, 0)));

This looks very cumbersome, as I need to convert the points to vector by substracting Point(0,0) and then I need to add everything to a Point on the origin.

Looks more natural to just do something like the following

                Point = (1 - std::sqrt(r1)) * standardTriangle[0] +  //
                        (std::sqrt(r1) * (1 - r2)) * standardTriangle[1] +
                        (r2 * std::sqrt(r1)) * standardTriangle[2]);

Adding and removing points from the origin is really the only way to sum points, even though mathematically this is not correct?

Solution

You might want to use the barycenter() function.

In case you need another sampling there is one available in CGAL. See here