Chen, Rulin; Wang, Ziqi; Song, Peng; Bickel, BerndISTA
Interlocking puzzles are intriguing geometric games where the puzzle pieces are held together based on their geometric arrangement, preventing the puzzle from falling apart. High-level-of-difficulty, or simply high-level, interlocking puzzles are a subclass of interlocking puzzles that require multiple moves to take out the first subassembly from the puzzle. Solving a high-level interlocking puzzle is a challenging task since one has to explore many different configurations of the puzzle pieces until reaching a configuration where the first subassembly can be taken out. Designing a high-level interlocking puzzle with a user-specified level of difficulty is even harder since the puzzle pieces have to be interlocking in all the configurations before the first subassembly is taken out. In this paper, we present a computational approach to design high-level interlocking puzzles. The core idea is to represent all possible configurations of an interlocking puzzle as well as transitions among these configurations using a rooted, undirected graph called a disassembly graph and leverage this graph to find a disassembly plan that requires a minimal number of moves to take out the first subassembly from the puzzle. At the design stage, our algorithm iteratively constructs the geometry of each puzzle piece to expand the disassembly graph incrementally, aiming to achieve a user-specified level of difficulty. We show that our approach allows efficient generation of high-level interlocking puzzles of various shape complexities, including new solutions not attainable by state-of-the-art approaches.
ACM Transactions on Graphics
We thank the reviewers for the valuable comments, David Gontier for sharing the source code of the baseline design approach, Christian Hafner for proofreading the paper, Keenan Crane for the 3D model of Cow, and Thingiverse for the 3D models of Moai and Owl. This work was supported by the SUTD Start-up Research Grant (Number: SRG ISTD 2019 148), the Swiss National Science Foundation (NCCR Digital Fabrication Agreement #51NF40-141853), and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 715767 – MATERIALIZABLE).
Chen R, Wang Z, Song P, Bickel B. Computational design of high-level interlocking puzzles. ACM Transactions on Graphics. 2022;41(4). doi:10.1145/3528223.3530071
Chen, R., Wang, Z., Song, P., & Bickel, B. (2022). Computational design of high-level interlocking puzzles. ACM Transactions on Graphics. Association for Computing Machinery. https://doi.org/10.1145/3528223.3530071
Chen, Rulin, Ziqi Wang, Peng Song, and Bernd Bickel. “Computational Design of High-Level Interlocking Puzzles.” ACM Transactions on Graphics. Association for Computing Machinery, 2022. https://doi.org/10.1145/3528223.3530071.
R. Chen, Z. Wang, P. Song, and B. Bickel, “Computational design of high-level interlocking puzzles,” ACM Transactions on Graphics, vol. 41, no. 4. Association for Computing Machinery, 2022.
Chen R, Wang Z, Song P, Bickel B. 2022. Computational design of high-level interlocking puzzles. ACM Transactions on Graphics. 41(4), 150.
Chen, Rulin, et al. “Computational Design of High-Level Interlocking Puzzles.” ACM Transactions on Graphics, vol. 41, no. 4, 150, Association for Computing Machinery, 2022, doi:10.1145/3528223.3530071.
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