Symmetrical Patterns of Ainu Heritage and Their Virtual and Physical Prototyping
Abstract
:1. Introduction
2. Basic Motifs
3. Pattern Digitization Methodology
Algorithm 1 Point Cloud Creation Algorithm  
1 Define:  Center Point P_{c} = (P_{cx},P_{cy}) ∈ ℜ^{2}, Initial Length d > 0, Initial Angle ϕ ∈ ℜ Instantaneous Distance (r_{i} ∈ ℜi = 0,1,…,n) Instantaneous Rotational Angle (θ_{i} ∈ ℜi = 0,1,…,n) 
2 Calculate:  P_{0} = (P_{0x}, P_{0y}) so that ${P}_{0x}={P}_{cx}+d\mathrm{cos}\varphi $ and ${P}_{0y}={P}_{cy}+d\mathrm{sin}\varphi $ 
3 Iterate:  For i = 0,1,…,n Rotate P_{0} by an angle θ_{i} around P_{c} in the counterclockwise direction to create P_{i} = (P_{ix},P_{iy}) so that
$${P}_{ix}={P}_{cx}+\left({P}_{0x}{P}_{cx}\right)\mathrm{cos}{\theta}_{i}\left({P}_{0y}{P}_{cy}\right)\mathrm{sin}{\theta}_{i}$$
$${P}_{iy}={P}_{cy}+\left({P}_{0x}{P}_{cx}\right)\mathrm{sin}{\theta}_{i}+\left({P}_{0y}{P}_{cy}\right)\mathrm{cos}{\theta}_{i}$$
$${P}_{eix}={P}_{cx}+\left({P}_{ix}{P}_{cx}\right)\left({r}_{i}/d\right)$$
$${P}_{eiy}={P}_{cy}+\left({P}_{iy}{P}_{cy}\right)\left({r}_{i}/d\right)$$

4 Output:  PC = (P_{ei}i = 0,1,…,n) 
4. Digitization of Hokkaido Ainu Motifs
4.1. Point Clouds of the Main Motifs
4.2. Point Cloud of the Synthetic Motifs
4.3. Point Cloud of the Plant Motifs
4.4. Virtual and Physical Prototypes of Ainu Patterns
5. Concluding Remarks
 (a)
 The indigenous people living in the northern part of Japan, known as Ainu, decorate their houses, clothing, ornaments, utensils, and spiritual goods using some unique patterns. Nowadays, goods crafted with Ainu patterns are cherished by many people in Japan and abroad, and different kinds of souvenirs and cultural artifacts carry these patterns, making these significant from both cultural and economic viewpoints.
 (b)
 The fourteen basic motifs underlying the patterns used by the Ainu community living in Hokkaido are elucidated through literature review.
 (c)
 The digital technology that can mimic the Ainu patternmaking craftsmanship is presented. It consists of three domains, namely, modeling domain, virtual prototyping domain, and physical prototyping domain. The modeling domain employs an algorithm. The algorithm recursively creates a point cloud to preserve the shape information of a given pattern. From a point cloud, a representative segment of a pattern can be copied several times, keeping the symmetry of the pattern. The virtual prototyping domain uses CAD systems to produce a solid CAD model of the given pattern directly from its point cloud. The physical prototyping domain uses a 3D printer to produce the physical prototype of the given pattern directly from the triangulation data of the solid CAD model.
 (d)
 Ten basic Hokkaido Ainu motifs and three synthesized motifs were digitized using the presented digital technology. The settings of the parameters to create the respective point clouds are also described elaborately.
 (e)
 The presented methodology helps avoid all sorts of sophisticated transformations and complicated computations that are needed when a scanning or imageprocessingbased digitization technique is used.
 (f)
 The outcomes of the study help preserve the cultural heritage as well as the craftsmanship underlying complex patterns not limited to Ainu community.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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No.  Motif  Name  No.  Motifs  Names 

1  Ayus  8  Skiurenmorew  
2  Morew  8  Morewetok  
3  Arusmorew  10  Punkar  
4  Sikikenumorew  11  Apapopiras(u) ke  
5  Sik  12  Apapoepuy  
6  Utasa  13    
7  Urenmorew  14   
i  Inputs  Outputs (PC)  

r_{i}  θ_{i}  
10  
15  
16  
20  
30 
Main Motifs  Instantaneous Rotational Angle  Instantaneous Distance  SegmentWise Point Clouds (PC)  Integrated Point Cloud 

Utasa  
Morew  
Sik  
Ayus 
Synthetic Motifs  Point Cloud(s) of Main Motif(s)  Inverted Point Cloud(s)  Integrated Point Clouds 

Urenmorew  
Sikurenmorew  
Motif Name  Instantaneous Rotational Angle  Instantaneous Distance  SegmentWise Point Cloud (PC)  Integrated Point Cloud 

Morewetok  
Apapo  
Virtual Models  Physical Models  Virtual Models  Physical Models 

Ayus  Sikurenmorew  
Morew  Morewetok  
Sik  Punkar  
Utasa  Apapopiras(u) ke  
Urenmorew  Apapoepuy 
Model  Point Clouds  Virtual Prototypes  Physical Prototypes 

1  
2  
3 
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Tashi; Ullah, A.S. Symmetrical Patterns of Ainu Heritage and Their Virtual and Physical Prototyping. Symmetry 2019, 11, 985. https://doi.org/10.3390/sym11080985
Tashi, Ullah AS. Symmetrical Patterns of Ainu Heritage and Their Virtual and Physical Prototyping. Symmetry. 2019; 11(8):985. https://doi.org/10.3390/sym11080985
Chicago/Turabian StyleTashi, and AMM Sharif Ullah. 2019. "Symmetrical Patterns of Ainu Heritage and Their Virtual and Physical Prototyping" Symmetry 11, no. 8: 985. https://doi.org/10.3390/sym11080985