## 3 Methodology
### Determining the Head/Face Required Dimensions  
To determine the required key feature points for the eyewear design (Figure 4), different types of eyewear products were analyzed and key feature points were correlated to head/face measurements as shown in Figure 5a,b. The selection of these key points is based on the feature points suggested in the literature [43; 55], and they were combined with points shown in Figure 4 and Table 1 to determine the relevant feature points for the eyewear design. Figure 3: Scanning tool. Figure 2: Photogrammetry image. Figure 4: Dimensioning of eyewear. Figure 5: (**a**) Orthogonal photo; (**b**) Feature points for head measurement. The relationship between eyewear size and the head feature points was stablished through a simple correlation to facilitate the control of parameters using Grasshopper. The following eyewear frame considerations were made:  
(1). If the frame is too narrow and the distance between the legs is too close, the lateral orbital tissues will be compressed, causing symptoms such as head distention and headache. Therefore, eyewear frame size and head size should have the following relationship. \[a_{1}+0.5a_{2}\geq B_{2}+B_{3}+B_{4} \tag{1}\]  
The angle of template should be calculated according to the Formula (2). \[a_{7}\approx\tan^{-1}\frac{B_{2}+B_{4}+B_{3}-B_{1}}{B_{5}+B_{6}} \tag{2}\]  
Additionally, to ensure comfortable wearing, the a8 radian of the eyewear frame is determined by the curve of the face, where a8 should be at a certain distance from the feature points 3, 4, 6, 7, 8, 9, 22. (2). When the length from the hinge of the frame to the point above the ear is too long, and the bending contour of the frame does not match the outline of the ear base, it is difficult for the frame to remain stable and in place. Therefore, the length of the temples can be calculated according to:  
\[a_{6}\approx B_{5}+B_{6} \tag{3}\]  
and the back leg angle of eyewear can be calculated using:  
\[a_{10}\approx\tan^{-1}\frac{B_{8}}{B_{9}} \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Eyewear Size Parameters** & **Size Name** & **Explanation of Size** & \begin{tabular}{c} **Head Feature Points Related** \\ **to the Eyewear Size** \\ **(Figure 5b)** \\ \end{tabular} \\ \hline \(a_{1}\) & Eye size & Indicates the width of the lens & 6,8,9 \\ \hline \(a_{2}\) & Bridge width & Connection section of lens & 4,5,6 \\ \hline \(a_{3}\) & Nose angle & \begin{tabular}{c} Decide where to contact the \\ eyewear and nose \\ \end{tabular} & 4,5,12,13,14 \\ \hline \(a_{4}\) & Lens height & \begin{tabular}{c} Height of glasses, determined by \\ appearance \\ \end{tabular} & 3,5,8,10,11 \\ \hline \(a_{5}\) & Height of frame & \begin{tabular}{c} Height of eyeglasses frame \\ section, determined by \\ appearance \\ \end{tabular} & \\ \hline \(a_{6}\) & The temple size & \begin{tabular}{c} Distance from eyewear frame \\ to ear \\ \end{tabular} & 7,22 \\ \hline \(a_{7}\) & Angle of temple & \
\begin{tabular}{c} The angle between the temple and \\ the symmetrical plane of head \\ \end{tabular} & 7,22 \\ \hline \(a_{8}\) & Curvature of eyewear frame & Curvature of the eyewear frame & 3,4,6,7,8,9,22 \\ \hline \(a_{9}\) & Thickness of frame &
\begin{tabular}{c} Thickness of eyewear frame \\ section, determined by \\ appearance \\ \end{tabular} & \\ \hline \(a_{10}\) & Back leg angle of eyewear & Back leg angle of glasses & 22,23 \\ \hline \(a_{11}\) & Angle of eyewear frame & Angle between frame and temple & 4,5,7,11 \\ \hline \(a_{12}\) & Thickness of temple & Thickness of temple & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Eyewear feature point for dimensioning. (3). The height and thickness of the front end of the nasal bone play an important determinant for the stability of the nose pads of the glasses. The shape of the nose pads varies greatly from one individual to another, so the supporting effect of the glasses varies greatly.