# Real-Time Physical Prototyping Tool Design Based on Shape-Changing Display
## 4 Results and Discussion
### Validation Experiments
#### 4.2.4 Discussion  
The results of the center-positioning algorithm demonstrate that expressiveness can be changed by implementing visual significance. The visual significance of an object's recognition can influence the expressiveness of the SCD. Better expressive quality can be achieved by providing visually significant features of the objects for additional weight-centering methods. For example, facial components, such as the nose, eyes, and lips, can be more significant expressors of the face than its overall shape. In this case, the proposed center-positioning algorithm moved the center points slightly closer to the visually significant features, using the method indicated in Section 3.2.2, to refine the density of the actuating vertices. As shown in Figure 15, the actuating vertex density on the surface varied depending on the location of the center position. The advantage of the dense actuating vertex is its robust SCD expressiveness of complicated surfaces, such as with the Sydney Opera House. By adding additional weights to the sail of the opera house, the center position changed and thus, the concave shape was better represented (Figure 15). In the face model presented in Table 3, the shapes of the nose and mouth in the additional weight results are clearer than those in the center-weight results. Because the center-positioning algorithm provides an optimization process for surface expressions, the shape difference can be increased. When the value of the model and the gradient function after the first iteration showing the largest change is sufficiently small (the maximum vertex length is 1/200), \(\lambda\) (step size) is 0.1, and all six models, except for the uneven cube, are created within 8-12 iterations. The bumpy cube model is symmetric; therefore, its position does not change, even when the center-positioning algorithm is rotated.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ground Truth** & **Mean** & **Center-Weight** & **Center** & **Center** & **Additional** \\
**Positioning** & **Positioning** & **Positioning** & **Positioning** & **Weight** \\
**(Fewer Iterations)** & **(More Iterations)** & **(More Iterations)** & **(More Iterations)** & **(More Iterations)** \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._Here, as described in Section 4.1, a \(2V\) icosphere SCD was implemented to demonstrate the practical feasibility and accuracy of 3D model reconstruction. We also confirmed the efficiency and effectiveness of the \(8V\)-resolution SCD. To produce an \(8V\) SCD, refer to Section 4.1.3; we redesigned the guide core to \(8V\), and an actuator appropriate for it was required. For an ideal \(8V\) SCD design, an actuator with the smallest possible size had to be used. Using Maxon RE13, one of the currently available universal motors, it was possible to design an actuator with an attachment surface area of 900 mm\({}^{2}\) or less by arranging the shaft axis in a radial direction (the motor took about 200 mm\({}^{2}\)). If the radius, \(r\), of the actuator installation space was set at 17 mm using Equation (2), as proposed in Section 3.1, the radius of the smallest \(8V\) SCD that could be manufactured would be approximately 226 mm. Considering the moving distance of the actuating pin, the approximate minimum and maximum diameters of the \(8V\) SCD that could be manufactured were 600 and 1000 mm, respectively.