## 3 Results and Discussion
### Comparison of Methods  
The statistical method and function simulation method were used to simulate the color parameters in this study, with both of them dividing into three sub-methods (Figure 5). The colors of the two types of sapphire with different cut shapes were classified as the same color grade in the qualitative evaluation. But the color of each sapphire was not completely identical; instead, they had subtle differences. The purpose of the quantitative evaluation was to accurately distinguish the sapphire colors and reduce the limitations of the human eye evaluation. The standard deviation of each parameter was calculated (as shown in Figure 5) to observe the degree of dispersion of the color parameter. The method that gained a higher degree of dispersion (larger standard deviation) for color parameters made it easier to distinguish the color of each sapphire, which can be considered the optimal method. The parameters for simulating the two types of cut sapphire colors are shown in Figure 5, where A, M, and Z represent the average, median, and mode, respectively. For example, L-A, a-A, b-A, and C-A represent the lightness, **a** value, **b** value, and the chroma of the sapphire color obtained using the average of the \"fire\" region in Method 1 (statistical method), while L-A', a-A', b-A', and C-A' represent these same four parameters in Method 2 (function simulation method). The average of each set of the simulated color parameters was calculated to compare the advantages and disadvantages of the two simulation methods in evaluating color. The average and standard deviation of each set of **b** values obtained through the function simulation method and statistical method were similar (as shown in Table 3). The negative direction of the **b** value in the color space represents the blue perception. Therefore, the two methods used to simulate sapphire color had similar effects on its primary blue hue. To select the optimal method, it was necessary to observe the average and standard deviation of the other color parameters, namely **L**, **a**, and **C**. Figure 5: Box plots of the parameter distribution and standard deviation bar charts for the simulated sapphires’ color. **(a)** Box plots of the parameter distribution and standard deviation bar chart for the oval-shaped sapphires’ color that were simulated using the average; **(b)** box plots of the parameter distribution and standard deviation bar chart for the oval-shaped sapphires’ color that were simulated using the median; **(c)** box plots of the parameter distribution and standard deviation bar chart for the oval-shaped sapphires’ color that were simulated using the mode; **(d)** box plots of the parameter distribution and standard deviation bar chart for the pear-shaped sapphires’ color that were simulated using the average; **(e)** box plots of the parameter distribution and standard deviation bar chart for the pear-shaped sapphires’ color that were simulated using the median; and **(f)** box plots of the parameter distribution and standard deviation bar chart for the pear-shaped sapphires’ color that were simulated using the mode. Except for the lightness (**L**) of the oval-shaped sapphires simulated using the mode, the lightness average of the sapphire simulated by the function simulation method was higher than that simulated by the statistical method. Therefore, the simulated color by the function simulation method had higher lightness. The average of the **a** values of the sapphire color (both oval- and pear-shaped) simulated by the function simulation method was higher than those simulated by the statistical method. Except for the chroma (**C**) of sapphire color (both oval- and pear-shaped) simulated by the mode, the chroma's average of the sapphire simulated by the function simulation method was lower than that simulated by the statistical method. This indicates that the simulated color by the statistical method was more saturated.