People of all ages enjoy solving geometric puzzles. However, finding suitable puzzles, e.g., puzzles with a moderate level of difficulty or puzzles with intellectually stimulating shapes can be difficult. In addition, designing innovative and appealing puzzles requires demanding effort and, typically, involves many trial and error processes. In this paper, we introduce a computational approach for designing geometric puzzles. Existing approaches employ bottom-up, constructive algorithms to generate puzzle pieces; therefore, intervening in the piece generation procedure is difficult. Differing from existing approaches that generate puzzles automatically or semi-automatically, we propose a top-down, partitioning-based approach, that enables us to control and edit piece shapes. With a subtle modification, the proposed algorithm can be easily extended to both 3D polycube and 2D polyomino puzzle design. To generate a variety of piece shapes, the proposed approach involves a capacity-constrained graph partitioning algorithm combined with polyomino tiling. We demonstrate the versatility of the proposed approach through various example designs, including fabricated puzzles, created using the proposed method.

中文翻译：

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多米诺拼图的计算设计

所有年龄段的人都喜欢解决几何难题。然而，找到合适的拼图，例如中等难度的拼图或具有智力刺激形状的拼图可能很困难。此外，设计创新且吸引人的谜题需要付出艰巨的努力，并且通常涉及许多反复试验的过程。在本文中，我们介绍了一种设计几何谜题的计算方法。现有方法采用自下而上的构造算法来生成拼图；因此，干预片段生成过程是困难的。与现有的自动或半自动生成拼图的方法不同，我们提出了一种自上而下、基于分区的方法，使我们能够控制和编辑棋子形状。经过细微的修饰，所提出的算法可以很容易地扩展到 3D polycube 和 2D polyomino 拼图设计。为了生成各种块形状，所提出的方法涉及一种容量受限的图分区算法，结合多联式拼贴。我们通过各种示例设计展示了所提出方法的多功能性，包括使用所提出的方法创建的制造拼图。