Delian Metamorphoses

Hungerbühler, Norbert; Nüsken, Michael

doi:10.4171/em/26

Cited by 1 publication

(2 citation statements)

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“…C uboid ‐C ube dissection puzzle with six pieces, designed by Anton Hanegraaf in 1989. [Copyright figure: Hunger‐bμhler and Nμsken [HN06]]…”

Section: Introductionmentioning

confidence: 99%

“…It is more challenging due to representing more complex 3D shapes with a few common pieces and requiring higher degrees of freedom (DOF) to reconfigure the pieces into different assembly forms. Therefore, very few 3D dissection results have been reported [Thel8,Fre09,HN06, Fre97], which are elegant primitive 3D shapes, such as tetrahedrons, cubes and prisms, and were created by solving intricate math problems with analytic approaches; see Figure for an example. Unlike 2D dissection puzzles that are simply placed on a tabletop surface, 3D dissection puzzles are preferable to be steady for each assembly form; e.g., every puzzle piece is supported by its neighboring pieces and no puzzle piece should fall apart due to gravity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computational Design of Steady 3D Dissection Puzzles

Tang

Song

Wang

et al. 2019

Computer Graphics Forum

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Dissection puzzles require assembling a common set of pieces into multiple distinct forms. Existing works focus on creating 2D dissection puzzles that form primitive or naturalistic shapes. Unlike 2D dissection puzzles that could be supported on a tabletop surface, 3D dissection puzzles are preferable to be steady by themselves for each assembly form. In this work, we aim at computationally designing steady 3D dissection puzzles. We address this challenging problem with three key contributions. First, we take two voxelized shapes as inputs and dissect them into a common set of puzzle pieces, during which we allow slightly modifying the input shapes, preferably on their internal volume, to preserve the external appearance. Second, we formulate a formal model of generalized interlocking for connecting pieces into a steady assembly using both their geometric arrangements and friction. Third, we modify the geometry of each dissected puzzle piece based on the formal model such that each assembly form is steady accordingly. We demonstrate the effectiveness of our approach on a wide variety of shapes, compare it with the state‐of‐the‐art on 2D and 3D examples, and fabricate some of our designed puzzles to validate their steadiness.

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“…C uboid ‐C ube dissection puzzle with six pieces, designed by Anton Hanegraaf in 1989. [Copyright figure: Hunger‐bμhler and Nμsken [HN06]]…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%