Consider this problem
**I have a land consisting of $n$ trees. Since the trees are favorites to cows, I have a big problem saving them. So, I have planned to make a fence around the trees. I want the fence to be convex (curves are allowed) and the minimum distance from any tree to the fence is at least $d$ units. And I definitely want a single big fence that covers all trees.
You are given all the information of the trees, to be specific, the land is shown as a $2D$ plane and the trees are plotted as $2D$ points. You have to find the perimeter of the fence that I need to create as described above. And you have to minimize the perimeter.**
One tree, a circular fence is needed
I was told the solution for $n>3$ was the perimeter of the convex hull $+2\pi d$
where $d$ is the minimum distance I must maintain from each point (tree).
But how?
Edit : I couldn't add the pictures. So,the links Image 1 and 2