Computational design of polyomino puzzles

Kita, Naoki; Miyata, Kazunori

doi:10.1007/s00371-020-01968-5

Cited by 6 publications

(2 citation statements)

References 30 publications

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“…Recently, Chen et al presented a computational design method of high-level interlocking puzzles [CWSB22], where multiple moves are required to take out the first subassembly from the puzzle. While those are bottom-up constructive approaches, Kita and Miyata proposed a top-down partitioning approach in designing polyomino puzzles to improve the controllability of the puzzle designers [KM21].…”

Section: Related Workmentioning

confidence: 99%

Dissection Puzzles Composed of Multicolor Polyominoes

Kita

2023

Computer Graphics Forum

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Dissection puzzles leverage geometric dissections, wherein a set of puzzle pieces can be reassembled in various configurations to yield unique geometric figures. Mathematically, a dissection between two 2D polygons can always be established. Consequently, researchers and puzzle enthusiasts strive to design unique dissection puzzles using the fewest pieces feasible. In this study, we introduce novel dissection puzzles crafted with multi‐colored polyominoes. Diverging from the traditional aim of establishing geometric dissection between two 2D polygons with the minimal piece count, we seek to identify a common pool of polyomino pieces with colored faces that can be configured into multiple distinct shapes and appearances. Moreover, we offer a method to identify an optimized sequence for rearranging pieces from one form to another, thus minimizing the total relocation distance. This approach can guide users in puzzle assembly and lessen their physical exertion when manually reconfiguring pieces. It could potentially also decrease power consumption when pieces are reorganized using robotic assistance. We showcase the efficacy of our proposed approach through a wide range of shapes and appearances.

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Section: Related Workmentioning

confidence: 99%

Dissection Puzzles Composed of Multicolor Polyominoes

Kita

2023

Computer Graphics Forum

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“…Motivated by recent advances in digital fabrication, the graphics community has raised a great interest in research on computational design for stylized fabrication [Bickel et al 2018]. Among this line of research, a number of computational methods and tools have been developed for personalized design and fabrication of various kinds of geometric puzzles, including 3D jigsaw puzzles [Elber and Kim 2022], polyomino puzzles [Kita and Miyata 2020;Lo et al 2009], dissection puzzles [Duncan et al 2017;Li et al 2018;Tang et al 2019;Zhou and Wang 2012], interlocking puzzles [Song et al 2012;Xin et al 2011], centrifugal puzzles [Kita and Saito 2020], and twisty puzzles that generalize the Rubik's cube mechanism [Sun and Zheng 2015].…”

Section: Introductionmentioning

confidence: 99%

Computational design of high-level interlocking puzzles

et al. 2022

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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.

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Jigsaw puzzle solving techniques and applications: a survey

Markaki

Panagiotakis

2022

Vis Comput

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Computational design of polyomino puzzles

Cited by 6 publications

References 30 publications

Dissection Puzzles Composed of Multicolor Polyominoes

Dissection Puzzles Composed of Multicolor Polyominoes

Computational design of high-level interlocking puzzles

Jigsaw puzzle solving techniques and applications: a survey

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