## 4 Cultural Heritage Preservation
### CAD Modeling, Triangulation Modeling and AM  
Based on the Ainu motifs, three models, namely, Model-1, Model-2, and Model-3 are created. This section describes the CAD Modeling, Triangulation Modeling, and execution of AM, as described in Figure 3, of Model-1, Model-2, and Model-3. The Model-1 is created by using four Ski-uren-moreus and a Sik (shown in Figure 9b). Other three Ski-uren-moreus are obtained by rotation a Ski-uren-moreu as shown in Figure 11. The rotation is performed using Equations (A2) and (A3), where \(\theta=\pi/2\), \(\pi\), and \(3\pi/2\). Combining all the point-clouds, the point-cloud of Model-1 is obtained as shown in Figure 12a. Now, the point-clouds of Model-1 is transferred to commercially available CAD package for CAD modeling. The result of the CAD modeling is shown in Figure 12b. Once the CAD modeling is done, the triangulation modeling is performed simply by saving the CAD model into an STL data file using a CAD package (the details are not shown to avoid commercially). The result of triangulation modeling is shown in Figure 12c. The STL data generated from the triangulation modeling can be used to build a physical model of the Model-1 using AM devices (e.g., 3D printer) as shown in Figure 12d. In this case, an ordinary 3D printer is used (the details are not shown to avoid commerciality). Figure 11: Point-clouds of Ski-uren-moreu created using both the algorithmic approach and parametric-equation-based approach. Figure 12: Model-1 based on Ainu motifs. (**a**) Point-cloud; (**b**) Solid CAD model; (**c**) Triangulation data; (**d**) Physical model built by 3D printer. The Model-2 is created based on Moreu, Sik, and Utasa of main Ainu motifs. A total of twenty-four Moreus, eight Siks, one Utasa, and lines are used for creating the Model-2 as shown in Figure 13. The step-by-step point-clouds creation procedure of the Model-2 are as follows. Firstly, using Equation (A1), the point-cloud of Utasa and Square shape is created. Then, the point-cloud of two Moreu motifs are created so that they become symmetric about the \(y\)-axis. Next, the point-cloud of two lines are created to connect the point-clouds of the Moreu motifs to the point-cloud of a square. The same is done for the two other point-clouds of Moreu motifs, which are symmetrical about the \(y\)-axis. Then, point-cloud of Sik is created on top of the Moreu point-clouds. Now, the point-cloud of two connecting lines, Moreu, and Sik are rotated using Equations (A2) and (A3), where \(\theta=\pi/2\), \(\pi\), and \(3\pi/2\). The same operation is repeated using Equations (A2) and (A3), where \(\theta=\pi/4\), \(3\pi/4\), \(5\pi/4\), and \(7\pi/4\), to complete the required point-cloud. The result is shown in Figure 13a. The CAD modeling, triangulation modeling, and AM process of Model-2 are performed similarly to the Model-1, as shown in Figure 13.  
The Model-3 is created based on the Ainu motif shown in Figure 14a. It consists of Moreu, Sik, Ayusi, ellipses, curves, and lines. The point-cloud of Ayusi is created using the algorithmic approach and rest of the point-cloud are created using the parametric-equation-based approach which are in described in the previous section. Figure 14b shows the point-cloud of Ainu motif shown in Figure 14a. The CAD modeling, triangulation modeling, and AM process of Model-2 are performed similarly to the Model-1 and Model-2, as shown in Figure 14.  
As seen from Figure 13, the Model-2 and Model-3 are more complicated than the Model-1, thus it consumes more time. It worth mentioning that while creating the point-cloud, it is better to start first from the center of a model and go outward. This step helps calculate the size of the shape and its location on the \(x\)-\(y\) plane. As shown in Figures 12 and 13, the models correspond to the main motifs (see Table 1). One can combine other motifs (e.g., synthetic, and plant motifs) to creates other  
Figure 13: Model-2 based on Ainu motifs. (**a**) Point-cloud; (**b**) Solid CAD model; (**c**) Triangulation data; (**d**) Physical model built by 3D printing.