Polygon shape margin in Java

Question

I have a simple array of geo points. This array represents a non crossing polygon. I have an algorithm that can calculate if a geo point is inside the polygon or not.

This is how my class looks like:

public class Polygon
{
   List<LatLng> vertexes;
}

However sometimes in order to work the report I need to have a tolerance so I need to make a margin around the original polygon. That means the new polygon must have the same shape but to be bigger by r (value).

Does anyone have an idea how this can be implemented in Java having in mind that my original polygon class has a list of LatLng points.