Geometrical analysis of motion schemes on fencing experts from competition videos.

Geometrical fencing is a scientific approach to fencing pioneered by Camillo Agrippa in the XVIth century which consists of characterizing the geometrical structure of fencing movements. Many geometrical spaces are involved in a duel, which evolve over time according to the skills of the fencers and the game rules. In this article, the concept of motion scheme is introduced as a flexible geometrical structure to represent fencing spaces evolving over time. The method is applied to the video of a duel of the Olympic games 2016. Five main results are presented. First, decisive actions of the duel are deduced from the distance between fencers. Second, footwork is reconstructed from horizontal movements of the feet. Third, a kinematic model is developed and compared with data in the literature. Fourth, the lunge attack is characterized and compared with data in the literature. Fifth, the role of the free hand is studied in the case of protective and balancing gestures. These findings provide rich information on the geometrical structure of fencing movements as well as on the tactical-strategic choices made by the fencers in real competition conditions. Finally, four applications illustrate the scientific value of motion schemes in fencing and other sports.