research-article

Computational design of twisty joints and puzzles

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Changxi ZhengAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 34, Issue 4

Article No.: 101, Pages 1 - 11

https://doi.org/10.1145/2766961

Published: 27 July 2015 Publication History

Abstract

We present the first computational method that allows ordinary users to create complex twisty joints and puzzles inspired by the Rubik's Cube mechanism. Given a user-supplied 3D model and a small subset of rotation axes, our method automatically adjusts those rotation axes and adds others to construct a "non-blocking" twisty joint in the shape of the 3D model. Our method outputs the shapes of pieces which can be directly 3D printed and assembled into an interlocking puzzle. We develop a group-theoretic approach to representing a wide class of twisty puzzles by establishing a connection between non-blocking twisty joints and the finite subgroups of the rotation group SO(3). The theoretical foundation enables us to build an efficient system for automatically completing the set of rotation axes and fast collision detection between pieces. We also generalize the Rubik's Cube mechanism to a large family of twisty puzzles.

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Cited By

Khan DBohak CViola I(2024)Dr. KID: Direct Remeshing and K-Set Isometric Decomposition for Scalable Physicalization of Organic ShapesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332659530:1(705-715)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3326595
Lu HLee TMa JXie Y(2024)Design optimisation of structures made of a small number of prescribed building blocksEngineering Structures10.1016/j.engstruct.2024.117686304(117686)Online publication date: Apr-2024
https://doi.org/10.1016/j.engstruct.2024.117686
Khan ASnow SMatthews B(2023)Participatory Design Tools: Leveraging Materiality and Familiarity to Adapt Unconventional Materials into Design ToolsProceedings of the 15th Conference on Creativity and Cognition10.1145/3591196.3593339(399-412)Online publication date: 19-Jun-2023
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Index Terms

Computational design of twisty joints and puzzles
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 34, Issue 4

August 2015

1307 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2809654

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Copyright © 2015 ACM.

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Publication History

Published: 27 July 2015

Published in TOG Volume 34, Issue 4

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Cited By

Khan DBohak CViola I(2024)Dr. KID: Direct Remeshing and K-Set Isometric Decomposition for Scalable Physicalization of Organic ShapesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.332659530:1(705-715)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3326595
Lu HLee TMa JXie Y(2024)Design optimisation of structures made of a small number of prescribed building blocksEngineering Structures10.1016/j.engstruct.2024.117686304(117686)Online publication date: Apr-2024
https://doi.org/10.1016/j.engstruct.2024.117686
Khan ASnow SMatthews B(2023)Participatory Design Tools: Leveraging Materiality and Familiarity to Adapt Unconventional Materials into Design ToolsProceedings of the 15th Conference on Creativity and Cognition10.1145/3591196.3593339(399-412)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3591196.3593339
Kita N(2023)Dissection Puzzles Composed of Multicolor PolyominoesComputer Graphics Forum10.1111/cgf.1496842:7Online publication date: 30-Oct-2023
https://doi.org/10.1111/cgf.14968
Rodríguez ACirio G(2022)True seamsACM Transactions on Graphics10.1145/3528223.353012841:4(1-16)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530128
Müller TEvans ASchied CKeller A(2022)Instant neural graphics primitives with a multiresolution hash encodingACM Transactions on Graphics10.1145/3528223.353012741:4(1-15)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530127
Grittmann PYazici ÖGeorgiev ISlusallek P(2022)Efficiency-aware multiple importance sampling for bidirectional rendering algorithmsACM Transactions on Graphics10.1145/3528223.353012641:4(1-12)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530126
Nimier-David MMüller TKeller AJakob W(2022)Unbiased inverse volume rendering with differential trackersACM Transactions on Graphics10.1145/3528223.353007341:4(1-20)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530073
Li XLi MJiang C(2022)Energetically consistent inelasticity for optimization time integrationACM Transactions on Graphics10.1145/3528223.353007241:4(1-16)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530072
Chen RWang ZSong PBickel B(2022)Computational design of high-level interlocking puzzlesACM Transactions on Graphics10.1145/3528223.353007141:4(1-15)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530071
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