An algorithmic approach to convex fair partitions of convex polygons

Abstract

A convex fair partition of a convex polygonal region is defined as a partition on which all regions are convex and have equal area and equal perimeter. In this article we describe an algorithm that finds such fair partition. • The Fair Partitions method finds a fair partition for any given convex polygon and any given number of regions. • Our method relies on two well-known methods: Lloyd's algorithm and the Normal Flow Algorithm. • The method proposed in this article can be used in various contexts and many real-world applications.

Keywords

• Convex Fair Partitions Algorithm