Generate Non-Degenerate Point Set in 2D - C++

I want to create a large set of random point cloud in 2D plane that are non-degenerate (no 3 points in a straight line in the whole set). I have a naive solution which generates a random float pair P_new(x,y) and checks with every pair of points (P1, P2) generated till now if point (P1, P2, P) lie in same line or not. This takes O(n^2) checks for each new point added to the list making the whole complexity O(n^3) which is very slow if I want to generate more than 4000 points (takes more than 40 mins). Is there a faster way to generate these set of non-degenerate points?