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.

翻译：解决不规则切割与装箱优化问题面临两大挑战：一是几何挑战，即判断物品在特定位置是否可行放置；二是优化挑战，即根据目标函数寻找优质解。迄今为止，研究者必须同时应对这两类挑战，这需要兼备两种专业知识并投入大量研发精力。降低该门槛的途径之一是将两类挑战解耦。本文针对二维不规则切割与装箱问题提出一种功能强大的碰撞检测引擎，该引擎全面承担几何挑战的处理责任。该碰撞检测引擎具有双重价值：其一，通过抽象化几何问题，让研究者能专注于优化挑战；其二，支持在其基础上构建的所有优化算法实现独立改进的传导。我们提出一套核心原则与设计理念，构建了注重性能最大化、精确性与鲁棒性的通用适配型碰撞检测引擎模型。这些原则已通过名为$\texttt{jagua-rs}$的具体开源实现得到实践。本文及其实现方案为不规则切割与装箱问题的未来发展提供坚实基础，既可直接应用于现有场景，也可作为持续改进的起点，从而推动该领域的研究进程。