Two-dimensional irregular packing problems: A review

Guo, Bingxuan; Hu, Jingwen; Li, Jingrui; Wu, Fenghe; Peng, Qingjin; Zhang, Quan

doi:10.3389/fmech.2022.966691

Cited by 14 publications

(9 citation statements)

References 139 publications

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“…The most efficient method for computing the NFP is through the Minkowski sum [Bennell and Song 2008], which incurs a complexity of at least O (𝑁 2 ) with 𝑁 being the number of edges in each polygon. The ultimate pose of each shape is then chosen from the potential pose set using simple heuristic rules as summarized in [Guo et al 2022], where prominent rules include bottom-left-first, maximal-packing-ratio, and minimalboundary-length. Unfortunately, even computing the exact NFP for hundreds and thousands of UV patches is intractable, and practical algorithms [Lévy et al 2002;Nöll and Strieker 2011] only consider horizontal or vertical boundaries.…”

Section: General Irregular Shape Packingmentioning

confidence: 99%

“…Given 𝑝 𝑖 and 𝑃 𝑖 −1 , the low-level packing algorithm needs to select the translation 𝑡 𝑖 and rotation 𝜃 𝑖 for 𝑝 𝑖 such that the packed shape 𝑃 𝑖 ≜ [𝑅(𝜃 𝑖 )𝑝 𝑖 + 𝑡 𝑖 ] ∪ 𝑃 𝑖 −1 is collision-free with a high packing ratio. Conventional packing algorithms [Guo et al 2022] would consider each patch independently and evenly sample 𝐾 rotations and consider all the possible translations under each rotation using NFP algorithm, leading to at least O (𝐾𝑁 2 ) complexity with 𝑁 being the total number of edges in 𝑝 𝑖 and 𝑃 𝑖 −1 , which is a major bottleneck of packing algorithms. And due to its myopic nature, the packing ratio is sub-optimal.…”

Section: Low-level Pose Network (Lpn)mentioning

confidence: 99%

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Learning Based 2D Irregular Shape Packing

Yang,

Pan,

et al. 2023

ACM Trans. Graph.

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2D irregular shape packing is a necessary step to arrange UV patches of a 3D model within a texture atlas for memory-efficient appearance rendering in computer graphics. Being a joint, combinatorial decision-making problem involving all patch positions and orientations, this problem has well-known NP-hard complexity. Prior solutions either assume a heuristic packing order or modify the upstream mesh cut and UV mapping to simplify the problem, which either limits the packing ratio or incurs robustness or generality issues. Instead, we introduce a learning-assisted 2D irregular shape packing method that achieves a high packing quality with minimal requirements from the input. Our method iteratively selects and groups subsets of UV patches into near-rectangular super patches, essentially reducing the problem to bin-packing, based on which a joint optimization is employed to further improve the packing ratio. In order to efficiently deal with large problem instances with hundreds of patches, we train deep neural policies to predict nearly rectangular patch subsets and determine their relative poses, leading to linear time scaling with the number of patches. We demonstrate the effectiveness of our method on three datasets for UV packing, where our method achieves a higher packing ratio over several widely used baselines with competitive computational speed.

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Section: General Irregular Shape Packingmentioning

confidence: 99%

Section: Low-level Pose Network (Lpn)mentioning

confidence: 99%

Learning Based 2D Irregular Shape Packing

Yang,

Pan,

et al. 2023

ACM Trans. Graph.

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“…Handling and shipping furniture pose challenges due to its bulkiness and often delicate nature. Specialized storage, transportation, and delivery logistics are required [12]. Additionally, planning the assembly of ready-to-assemble furniture, which non-specialists typically do, presents challenges [13].…”

Section: Introductionmentioning

confidence: 99%

Surveying Quality Management Methodologies in Wooden Furniture Production

Skorupińska,

Hitka,

Sydor

2024

Systems

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Furniture production is a specific industrial sector with a high human labor demand, a wide range of materials processed, and short production runs caused by high customization of end products. The difficulty of measuring the aesthetic requirements of customers is also specific to furniture. This review of academic papers identifies and explains effective quality management strategies in furniture production. The reviewed literature highlights a range of quality management methodologies, including concurrent engineering (CE), total quality management (TQM), lean manufacturing, lean six sigma, and kaizen. These strategies encompass a variety of pro-quality tools, such as 5S, statistical process control (SPC), quality function deployment (QFD), and failure mode and effects analysis (FMEA). The strengths of these quality management strategies lie in their ability to enhance efficiency, reduce waste, increase product diversity, and improve product quality. However, the weaknesses concern implementation challenges and the need for culture change within organizations. Successful quality management in furniture production requires tailoring strategies to the specific context of the furniture production industry. Additionally, the importance of sustainability in the furniture industry is emphasized, which entails incorporating circular economy principles and resource-efficient practices. The most important finding from the literature analysis is that early detection and correction of poor quality yields the most beneficial outcomes for the manufacturer. Therefore, it is essential to strengthen the rigor of quality testing and analysis during the early stages of product development. Consequently, a deep understanding of consumer perspectives on required furniture quality is crucial. The review identified two research gaps: (1) the impact of unnecessary product over-quality on the efficiency of furniture production and (2) the influence of replacing CAD drawings with a model-based definition (MBD) format on quality management in furniture production.

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“…Packing irregular objects (nesting) is one of the most challenging problems in packing issues. Special geometric tools are used for modeling irregular packing problems, such as raster point, direct trigonometry, no-fit polygon and phi-functions, to mention a few [24][25][26][27][28]. Irregular n-dimensional (n ≥ 4) packing problems arising in multi-resource project management can be found in [29].…”

Section: Introductionmentioning

confidence: 99%

A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

Litvinchev,

Fischer,

Romanova

et al. 2024

Mathematics

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Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems.

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Two-dimensional irregular packing problems: A review

Cited by 14 publications

References 139 publications

Learning Based 2D Irregular Shape Packing

Learning Based 2D Irregular Shape Packing

Surveying Quality Management Methodologies in Wooden Furniture Production

A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

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