Algorithm: How to generate a virtual box to include all the points

Algorithm: How to generate a virtual box to include all the points

I am thinking to use a algorithm to create a virtual box to include all
the points in. Here is the example:
1) Original points:
2) The result should look like this:
I've tried to use convex hull algorithm, however, the result will include
white space in the virtual box which is not what I want. It is better to
remove as much as white space. (space that not includes any points). (Each
point has x and y value)
If you guys can provide some idea that will be great. Thanks!!!