Decoupling Geometry from Optimization in 2D Irregular Cutting and Packing Problems: an Open-Source Collision Detection Engine

TL;DR

This work tackles irregular 2D cutting and packing by decoupling geometry from optimization through a reusable Collision Detection Engine (CDE) that handles geometric feasibility. It introduces hazards as a unifying constraint model, a two-phase broad/narrow collision workflow implemented with a quadtree-backed broad phase, and precise edge-intersection and inclusion tests for robustness. To accelerate decisions, it adds a fail-fast surrogate using poles and piers, and further reduces complexity with polygon simplification, all within an open-source Rust implementation called jagua-rs. The paper provides a practical foundation for researchers to plug in their optimization methods while relying on a performant, extensible geometry layer, with validation via microbenchmarking and practical workflows like the sparrow project.

Abstract

Addressing irregular cutting and packing (C&P) optimization problems poses two distinct challenges: the geometric challenge of determining whether or not an item can be placed feasibly at a certain position, and the optimization challenge of finding a good solution according to some objective function. Until now, those tackling such problems have had to address both challenges simultaneously, requiring two distinct sets of expertise and a lot of research & development effort. One way to lower this barrier is to decouple the two challenges. In this paper we introduce a powerful collision detection engine (CDE) for 2D irregular C&P problems which assumes full responsibility for the geometric challenge. The CDE (i) allows users to focus with full confidence on their optimization challenge by abstracting geometry away and (ii) enables independent advances to propagate to all optimization algorithms built atop it. We present a set of core principles and design philosophies to model a general and adaptable CDE focused on maximizing performance, accuracy and robustness. These principles are accompanied by a concrete open-source implementation called $\texttt{jagua-rs}$. This paper together with its implementation serves as a catalyst for future advances in irregular C&P problems by providing a solid foundation which can either be used as it currently exists or be further improved upon.

Figures (16)

• Figure 1: Example solution of a leather nesting instance.
• Figure 2: Fundamental interaction between the CDE and an optimization algorithm for irregular C&P problems.
• Figure 3: Types of collision between a pair of simple polygons.
• Figure 4: Different types of hazards.
• Figure 5: The collision function.