The next two examples are to convince you that such a partition always exists.
Here is a large example where we apply the algorithm to a region with 2048 points
.
Given a convex polygon and a set of points, we want to partition the polygon into convex pieces of equal area so that each piece contains one point.
Here we take the convex hull of the continental USA as our polygon
and the 48 state capitals as our points:
The next two examples are to convince you that such a partition always exists.
Here is a large example where we apply the algorithm to a region with 2048 points
.