Currently, Eddy is reading this paper "On the Expected Complexity of Random Convex Hulls". It states that the expected number of vertices of the convex hull of N points, chosen uniformly and independently from a disk is OOO, and OOO for the case a convex polygon with K sides, and so on. Eddy thinks it's very interesting and now wants to research something about it. But, it seems too hard to start with something like disk or polygon. Thus, as his first step in the research, Eddy first chooses a triangle. Now, Eddy wants to find out the expected number of points on the convex hull when uniformly randomly picking N points within the triangle. However, Eddy can't find any way to solve this problem. As his best friend, you come to help Eddy finish his research debut.
Currently, Eddy is reading this paper "On the Expected Complexity of Random Convex Hulls"(1997). It states that the expected number of vertices of the convex hull of N points, chosen uniformly and independently from a disk is O(N13)O(N^{frac{1}{3}})O(N31), and O(KlogN)O(K log N)O(KlogN) for the case a convex polygon with K sides, and so on. Eddy thinks it's very interesting and now wants to research something about it. But, it seems too hard to start with something like disk or polygon. Thus, as his first step in the research, Eddy first chooses a triangle. Now, Eddy wants to find out the expected number of points on the convex hull when uniformly randomly picking N points within the triangle. However, Eddy can't find any way to solve this problem. As his best friend, you come to help Eddy finish his research debut.
