## 2 Theoretical Background
### Aesthetic Measure
#### 2.1.3 Cohesion  
When the size proportion, form direction and outline of form of each element and object are similar, this will result in the feeling of cohesion.  
From the view of product form design, similar proportions of length, width, and height facilitate the value of cohesion (\(CM\)). To analyze the cohesion of products, the information that has to be known includes two portions: the proportions of the object frame from three views and the proportional relationship between object and elements. Equation (12) depicts a quantitative method which could be used for the evaluation of cohesion.  
\[CM=\frac{\left|\begin{matrix}CM_{f(hb)}\left|+\left|CM_{f(hd)}\right|+\left| CM_{f(db)}\right|+\\ CM_{wo(hb)}\left|+\left|CM_{wo(hd)}\right|+\left|CM_{wo(db)}\right|\\ \hline\end{matrix}\right.,0\leq CM\leq 1 \tag{12}\]  
The values of \(CM_{f}\) are the overall framework relative proportions of object form, which are respectively defined as follows:  
\[CM_{f(hb)}=\left\{\begin{array}{l}c_{f(hb)}\,\ if\ c_{f(hb)}\leq 1\\ \frac{1}{c_{f(hb)}}\,\ if\ c_{f(hb)}>1\end{array}\right. \tag{13}\]  
\[c_{f(hb)}=h_{frame}/b_{frame} \tag{14}\]  
Figure 2: Vertical symmetry of an object; (**a**) Higher minimalism; (**b**) Lower minimalism.  
\[CM_{f(hd)}=\begin{cases}c_{f(hd)}&if\ c_{f(hd)}\leq 1\\ \frac{1}{c_{f(hd)}}&if\ c_{f(hd)}>1\end{cases} \tag{15}\]  
\[c_{f(hd)}=h_{frame}/d_{frame} \tag{16}\]  
\[CM_{f(db)}=\begin{cases}c_{f(db)}&if\ c_{f(db)}\leq 1\\ \frac{1}{c_{f(db)}}&if\ c_{f(db)}>1\end{cases} \tag{17}\]  
\[c_{f(db)}=d_{frame}/b_{frame} \tag{18}\]  
Among which \(h_{frame}\) is the height of overall form framework; \(b_{frame}\) is the width of overall form framework; \(d_{frame}\) is the depth of overall form framework; \(CM_{f(hb)}\) means the relative proportion of height to width of overall form framework; \(CM_{f(hd)}\) means the relative proportion of height to depth of overall form framework; \(CM_{f(db)}\) means the relative proportion of width to depth of overall form framework.  
\(CM_{wo}\) are the relative proportions of the framework of each element to the framework overall form, which are respectively defined as follows:  
\[CM_{wo(hb)}=\frac{\sum\limits_{i}^{n}t_{i(hb)}}{n} \tag{19}\]  
\[t_{i(hb)}=\begin{cases}c_{i(hb)},&if\ c_{i(hb)}\leq 1\\ \frac{1}{c_{i(hb)}},&if\ c_{i(hb)}>1\end{cases} \tag{20}\]  
\[c_{i(hb)}=\frac{h_{i}/b_{i}}{h_{frame}/b_{frame}} \tag{21}\]  
\[CM_{wo(hd)}=\frac{\sum\limits_{i}^{n}t_{i(hd)}}{n} \tag{22}\]  
\[t_{i(hd)}=\begin{cases}c_{i(hd)},&if\ c_{i(hd)}\leq 1\\ \frac{1}{c_{i(hd)}},&if\ c_{i(hd)}>1\end{cases} \tag{23}\]  
\[c_{i(hd)}=\frac{h_{i}/d_{i}}{h_{frame}/d_{frame}} \tag{24}\]  
\[CM_{wo(db)}=\frac{\sum\limits_{i}^{n}t_{i(db)}}{n} \tag{25}\]  
\[t_{i(db)}=\begin{cases}c_{i(db)},&if\ c_{i(db)}\leq 1\\ \frac{1}{c_{i(db)}},&if\ c_{i(db)}>1\end{cases} \tag{26}\]  
\[c_{i(db)}=\frac{d_{i}/b_{i}}{d_{frame}/b_{frame}} \tag{27}\]  
\(CM_{wo(hb)}\) is the relative proportion of height to width of each of the elements and the overall form framework; \(CM_{wo(hd)}\) is the relative proportion of height to depth of each of the elements and the overall form framework; \(CM_{wo(db)}\) is the relative proportion of width to depth of each of the elements and the overall form framework; \(h_{frame}\) is the height of the overall form framework; \(b_{frame}\) is the width of the overall form framework; \(d_{frame}\) is the depth of the overall form framework; \(h_{i}\) is the height of the element form; \(b_{i}\) is the width of the element form; \(d_{i}\) is the depth of the element form; \(n\) is the element quantity in the overall form.