## 2 Theoretical Background
### Aesthetic Measure
#### 2.1.1 Symmetry  
Symmetry is primarily used for testing of any duplication of elements along the axes, i.e., whether unit elements on one side of the centerline are exactly duplicated to the other side. Symmetry could be differentiated into three kinds, including vertical, horizontal, and diagonal symmetries, as shown in Figure 1. Thus, when analyzing the symmetry of an object, it needs to be cut into four portions: upper left, upper right, lower left and lower right. The symmetry of the object can be defined as Equation (1). \[SYM=1-\frac{|\mathrm{SYM}_{FV}|+|\mathrm{SYM}_{FH}|+|\mathrm{ SYM}_{FR}|}{9}\,\ 0\leq SYM\leq 1 \tag{1}\]  
Among which \(|\mathrm{SYM}|\) is the overall symmetry, \(|\mathrm{SYM}_{FV}|\) is the horizontal symmetry of front-view direction; \(|\mathrm{SYM}_{FH}|\) is the vertical symmetry of front-view direction; \(|\mathrm{SYM}_{FR}|\) is the diagonal symmetry of front-view direction. \(|\mathrm{SYM}_{RV}|\) is the vertical symmetry of right-view direction; \(|\mathrm{SYM}_{RR}|\) is the horizontal symmetry of right-view direction; \(|\mathrm{SYM}_{RR}|\) is the diagonal symmetry of right-view. \(|\mathrm{SYM}_{TH}|\) is the horizontal symmetry of top-view; \(|\mathrm{SYM}_{TD}|\) is the vertical symmetry of top-view; \(|\mathrm{SYM}_{TR}|\) is the diagonal symmetry of top-view. When the obtained SYM value approaches 1, the form has a higher level of symmetry. In calculating symmetrical aesthetic-perception equations, it is necessary to proceed with nondimensionalization in the calculation of equations to prevent a large difference in the numbers  
Figure 1: Symmetry of an object in (**a**) vertical, (**b**) horizontal, and (**c**) diagonal directions. of object shape sizes, which results in error in the process of calculating numbers. The factors of symmetry which have to be checked in each portion include: the centroid coordinates, the size of the overall frame, the centroid angle and the centroid distance. The \(yz\) plane is the plane of front view to be investigated. Equations (2)-(4) are used to evaluate these three types of symmetry. \[ \begin{array}{l}\left|\text{SYM}_{FV}\right|=\frac{\left|Y^{\prime}_{\text{ U}L}-Y^{\prime}_{\text{U}L}\right|+\left|Y^{\prime}_{\text{L}R}-Y^{\prime}_{ \text{U}L}\right|+\left|Z^{\prime}_{\text{U}L}-Z^{\prime}_{\text{L}L}\right|+ \left|Z^{\prime}_{\text{L}R}-Z^{\prime}_{\text{L}L}\right|+\\ \left|B^{\prime}_{\text{U}R}-B^{\prime}_{\text{L}L}\right|+\left|B^{\prime}_{ \text{L}R}-B^{\prime}_{\text{L}L}\right|+\left|H^{\prime}_{\text{U}R}-H^{ \prime}_{\text{U}L}\right|+\left|H^{\prime}_{\text{L}R}-H^{\prime}_{\text{L}L }\right|+\\ \left|\Theta^{\prime}_{\text{F}L\text{R}}-\Theta^{\prime}_{\text{F}L\text{L} }\right|+\left|\Theta^{\prime}_{\text{F}L\text{R}}-\Theta^{\prime}_{\text{F} L\text{L}}\right|+\left|R^{\prime}_{\text{F}L\text{R}}-R^{\prime}_{\text{F} L\text{L}}\right|+\left|R^{\prime}_{\text{F}L\text{R}}-R^{\prime}_{\text{F}L }\right|\\ 12\end{array}  \tag{2}\]  
\[ \begin{array}{l}\left|\text{SYM}_{FH}\right|=\frac{\left|Y^{\prime}_{\text{ U}L}-Y^{\prime}_{\text{L}L}\right|+\left|Y^{\prime}_{\text{U}R}-Y^{\prime}_{ \text{L}R}\right|+\left|Z^{\prime}_{\text{U}L}-Z^{\prime}_{\text{L}L}\right|+ \left|Z^{\prime}_{\text{U}R}-Z^{\prime}_{\text{L}R}\right|+\\ \left|B^{\prime}_{\text{L}L}-B^{\prime}_{\text{L}L}\right|+\left|B^{\prime}_{ \text{U}R}-B^{\prime}_{\text{L}R}\right|+\left|H^{\prime}_{\text{U}L}-H^{ \prime}_{\text{L}L}\right|+\left|H^{\prime}_{\text{U}R}-H^{\prime}_{\text{L} R}\right|+\\ \left|\Theta^{\prime}_{\text{F}L\text{U}}-\Theta^{\prime}_{\text{F}L\text{L} }\right|+\left|\Theta^{\prime}_{\text{F}L\text{R}}-\Theta^{\prime}_{\text{F} L\text{R}}\right|+\left|R^{\prime}_{\text{F}L\text{R}}-R^{\prime}_{\text{F} L\text{L}}\right|+\left|R^{\prime}_{\text{F}L\text{R}}-R^{\prime}_{\text{F}L }\right|\\ 12\end{array}  \tag{3}\]  
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