Payana-Giraud Method

**Payan-Giraud method**

The Payan method is named after its creator, the Brazilian Philippe Payan (1908-1988), while the Giraud method is named after the French mathematician and mechanic, academician Denis Giraud (1894-1973).

First, it was necessary to reflect a point on the edge of a centrally symmetrical figure, then to find the point of reflection of the edges of the figure, and so on, taking into account that at each next step the number of mirrors under consideration increases by one. Thus, a general method was developed for searching for the “reverse” reflection of any point in n-symmetric polygons. At large volumes, it was also necessary to take into account the stages of coincidence and divergence of sequences of passes connected by the corresponding Boolean operators. In this case, the complexity of the algorithm reaches O(n2), since for each element it is necessary to calculate all the others.