Robust NFP generation for Nesting problems

TL;DR

This paper introduces a simple, efficient algorithm for generating No-Fit-Polygons in nesting problems, improving geometric accuracy and computational efficiency for irregular 2D piece placement.

Contribution

A novel simplified NFP generation algorithm that reduces numerical errors and handles complex geometries effectively in nesting applications.

Findings

Reduces computational cost of overlap verification.

Improves accuracy of NFP representation.

Handles high-vertex complexity in real-world scenarios.

Abstract

Cutting and packing problems arise in a large variety of industrial applications, where there is a need to cut pieces from a large object, or placing them inside a containers, without overlap. When the pieces or the containers have irregular outline, the problem is classified as a Nesting problem. The geometrical challenges of the Nesting problem are addressed by focusing on the geometric aspect of the 2D pieces and containers involved. The challenges of the geometrical component are mainly derived from the complexity of the pieces, due to high number of vertices, which is common when dealing with real world scenarios. This complexity is challenging for current algorithms to process efficiently and effectively, leading to high computational cost and less satisfactory results, particularly when dealing with overlap verification operations. Usually, when tackling Nesting problems, the overlap verification process between two objects is done through the use of a structure known as No-Fit-Polygon (NFP). In this work, the generation of the NFP is achieved through a simple algorithm which produces a simplified shape while reducing numerical precision errors and fully representing the region that forms the NFP including positions with perfect fits.