Algorithm 1. Judgement Method of Square Symmetrical Environment

Input: A set of N points $R=\left\{\left(r_i,{\varphi }_i\right)\right|i=1,\dots ,N\}$

Output: Symmetrical environment or not

1: Convert raw data $R$ to coordinate data $P=\left\{\left(x_i,y_i\right)\right|i=1,\dots ,N\}$, ignore angle parameter

2: Calculate geometric centroid $P_{centroid}$

3: Calculate new distance data $R^{\prime }$ from $P$

4: Descending sort $R^{\prime }$ as $R^{″}$

5: Count the number of maximum values $nu{m}_{\max }$ and number of minimum values $nu{m}_{\min }$

6: If $(nu{m}_{\max }\ne 4||nu{m}_{\min }\ne 4)$ then

7: Environment is not square symmetrical

8: End if, terminate

9: Calculate the Euclidean distance between two adjacent points $d_{12}$, $d_{23}$, $d_{34}$, $d_{41}$ in turn

10: If $d_{12}$, $d_{23}$, $d_{34}$, $d_{41}$ are not equal then

11: Environment is not square symmetrical

12: End if, terminate

13: Fit 4 lines by connecting adjacent two points in turn from 4 maximum distance points

14: Count the vertical distances from the remaining points to the 4 lines

15: If all distances less than $\epsilon$ which infinitely close to zero then

16: Environment is square symmetrical

17: Save the G‒V distance to the G‒V index list

18: else

19: Environment is not square symmetrical

20: End if, terminate