Computational Design of Steady 3D Dissection Puzzles

Tang, Keke; Song, Peng; Wang, Xiaofei; Deng, Bailin; Fu, Chi‐Wing; Liu, Ligang

doi:10.1111/cgf.13638

Cited by 17 publications

(7 citation statements)

References 33 publications

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“…However, the method was demonstrated only on coarse discrete grids with simple target shapes. On the other hand, Tang et al presented a method to design steady 3D dissection puzzles with more complex targets by accepting slight modifications [TSW*19]. In addition to those methods that target 2D or 3D shapes represented as a discrete grid, Duncan et al proposed a dissection design technique that approximately dissects naturalistic 2D shapes [DYYT17].…”

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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“…Given a voxelized 3D shape, their method iteratively extracts pieces while enforcing a local interlocking condition among every three consecutive pieces; see Figure 17(a). This method was later extended to handle smooth non‐voxelized shapes for 3D printing [SFLF15] and to design 3D steady dissection puzzles [TSW ∗ 19].…”

Section: Structurally Stable Assembliesmentioning

confidence: 99%

“…On the other hand, global interlocking might impose too strict constraints on the assembly's geometry, as real assemblies usually do not have to experience arbitrary external forces. Hence, some research works relax the constraint of global interlocking, e.g., by allowing multiple keys in the final assembly [SFJ ∗ 17] or allowing parts to be immobilized by using geometric arrangement together with friction [TSW ∗ 19].…”

Section: Structurally Stable Assembliesmentioning

confidence: 99%

“…Unlike 2D dissection puzzles that can be supported on a table‐top surface, 3D dissection puzzles are preferable to be stable under gravity and during manipulation. Tang et al [TSW ∗ 19] addressed this problem by co‐decomposing two voxelized shapes and making the resulting assemblies stable based on a generalized interlocking model; see also Section 4.2. Their method allows slight modification on the input shapes, with preference on the interior to preserve the puzzle's external appearance.…”

Section: Reconfigurable Assembliesmentioning

confidence: 99%

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State of the Art on Computational Design of Assemblies with Rigid Parts

Wang

Song

Pauly

2021

Computer Graphics Forum

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An assembly refers to a collection of parts joined together to achieve a specific form and/or functionality. Designing assemblies is a non-trivial task as a slight local modification on a part's geometry or its joining method could have a global impact on the structural and/or functional performance of the whole assembly. Assemblies can be classified as structures that transmit force to carry loads and mechanisms that transfer motion and force to perform mechanical work. In this state-of-the-art report, we focus on computational design of structures with rigid parts, which generally can be formulated as a geometric modeling and optimization problem. We broadly classify existing computational design approaches, mainly from the computer graphics community, according to high-level design objectives, including fabricability, structural stability, reconfigurability, and tileability. Computational analysis of various aspects of assemblies is an integral component in these design approaches. We review different classes of computational analysis and design methods, discuss their strengths and limitations, make connections among them, and propose possible directions for future research.

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“…Several computational methods have been developed to construct interlocking assemblies for different applications, including puzzles [Song et al 2012;Tang et al 2019;Xin et al 2011], 3D printed objects Yao et al 2017a], laser-cut polyhedrons [Song et al 2016], and furniture Song et al 2017]. Zhang and Balkcom [2016] explored a small set of reusable voxel-like interlocking blocks for building 3D structures, while Wang et al [2018] developed a unified framework to design interlocking assemblies of different forms by leveraging a graph-based representation.…”

Section: Related Workmentioning

confidence: 99%

Design and structural optimization of topological interlocking assemblies

et al. 2019

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We study assemblies of convex rigid blocks regularly arranged to approximate a given freeform surface. Our designs rely solely on the geometric arrangement of blocks to form a stable assembly, neither requiring explicit connectors or complex joints, nor relying on friction between blocks. The convexity of the blocks simplifies fabrication, as they can be easily cut from different materials such as stone, wood, or foam. However, designing stable assemblies is challenging, since adjacent pairs of blocks are restricted in their relative motion only in the direction orthogonal to a single common planar interface surface. We show that despite this weak interaction, structurally stable, and in some cases, globally interlocking assemblies can be found for a variety of freeform designs. Our optimization algorithm is based on a theoretical link between static equilibrium conditions and a geometric, global interlocking property of the assembly---that an assembly is globally interlocking if and only if the equilibrium conditions are satisfied for arbitrary external forces and torques. Inspired by this connection, we define a measure of stability that spans from single-load equilibrium to global interlocking, motivated by tilt analysis experiments used in structural engineering. We use this measure to optimize the geometry of blocks to achieve a static equilibrium for a maximal cone of directions, as opposed to considering only self-load scenarios with a single gravity direction. In the limit, this optimization can achieve globally interlocking structures. We show how different geometric patterns give rise to a variety of design options and validate our results with physical prototypes.

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Computational Design of Steady 3D Dissection Puzzles

Cited by 17 publications

References 33 publications

Dissection Puzzles Composed of Multicolor Polyominoes

Dissection Puzzles Composed of Multicolor Polyominoes

State of the Art on Computational Design of Assemblies with Rigid Parts

Design and structural optimization of topological interlocking assemblies

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