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：解决不规则切割与排样优化问题面临两个独立挑战：几何层面需判定物品在特定位置是否可行放置，优化层面需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个挑战，这需要两类专业知识及大量研发投入。降低该门槛的途径之一是将两个挑战解耦。本文针对二维不规则切割与排样问题提出一个功能强大的碰撞检测引擎，该引擎全面承担几何层面的挑战。该碰撞检测引擎具有以下特性：（i）通过几何抽象化使用户能专注于优化挑战；（ii）支持在其基础上构建的所有优化算法实现独立进展的传导。我们提出一套核心原则与设计理念，构建了注重性能、精度与鲁棒性最大化的通用自适应碰撞检测引擎模型。这些原则已通过名为$\texttt{jagua-rs}$的具体开源实现得到实践。本文及其实现方案通过提供可即用或持续改进的坚实基础，为不规则切割与排样问题的未来进展发挥催化作用。