A measure of non-convexity in the plane and the Minkowski sum

TL;DR

This paper introduces a measure of non-convexity for planar polygons and proves that it remains stable under Minkowski sums for regions close to convex, ensuring the sum's topological simplicity.

Contribution

It defines a new non-convexity measure for polygons and proves its invariance under Minkowski sums for nearly convex regions.

Findings

Non-convexity measure does not decrease under Minkowski sum for near-convex regions

Minkowski sum of such regions has no holes

The measure helps understand the topological properties of Minkowski sums

Abstract

In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for "not far from convex" regions this measure does not decrease under the Minkowski sum operation, and guarantees that the Minkowski sum has no "holes".