Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered fragments, is fundamental to numerous applications, and yet most of the literature has focused thus far on less realistic puzzles whose pieces are identical squares. Here we formalize a new type of jigsaw puzzle where the pieces are general convex polygons generated by cutting through a global polygonal shape with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer's sequence. We analyze the theoretical properties of such puzzles, including the inherent challenges in solving them once pieces are contaminated with geometrical noise. To cope with such difficulties and obtain tractable solutions, we abstract the problem as a multi-body spring-mass dynamical system endowed with hierarchical loop constraints and a layered reconstruction process. We define evaluation metrics and present experimental results to indicate that such puzzles are solvable completely automatically.

中文翻译：

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懒惰的餐饮业者拼图：模型、属性和基于机械系统的求解器

拼图解决，即从一组不重叠的无序片段构建一个连贯的整体的问题，是许多应用程序的基础，但迄今为止，大多数文献都集中在不太现实的拼图上，这些拼图的部分是相同的正方形。在这里，我们形式化了一种新型的拼图游戏，其中的碎片是通过使用任意数量的直线切割切割全局多边形形状而生成的通用凸多边形，这是一种受著名的 Lazy 餐饮服务商序列启发的生成模型。我们分析了此类谜题的理论特性，包括一旦棋子被几何噪声污染后解决它们的固有挑战。为了应对这些困难并获得易于处理的解决方案，我们将问题抽象为具有分层循环约束和分层重建过程的多体弹簧质量动力系统。我们定义了评估指标并展示了实验结果，以表明此类谜题可以完全自动解决。