Fig 1.
A duel at the Olympic games 2016.
Left: Steffen (Swiss). Right: Grumier (France). The blue markers represent the points of interest captured by video tracking. Source of the original video: [6].
Fig 2.
Landmark trajectories as 3D worldlines.
Each worldline represents the trajectory of a marker for Steffen (red), Grumier (blue) and the piste (gray). The front view (xt) reflects fencing actions dominated by the horizontal coordinate. A net movement of Steffen towards Grumier characterizes the direct thrust.
Fig 3.
It is a strategic region defined between the head, the sword hand and the top of the front foot.
Fig 4.
Illustrated motion scheme of frontal spaces.
It describes movements of frontal spaces from the initial state to the hit state for Steffen (red) and Grumier (blue). Only a few triangles have been drawn for clarity. The worldlines (gray) represent the barycenters of the frontal spaces. The yellow ball represents the touch. It shows how Steffen won the touch with a direct attack.
Fig 5.
Analysis of the mutual distance.
(A) Horizontal position of the barycenters of the frontal spaces, XSteffen(t) and XGrumier(t) respectively. (B) Mutual distance computed as |XSteffen(t) − XGrumier(t)|.
Fig 6.
Motion scheme of the frontal spaces.
The analysis of the mutual distance leads to a transition system for Steffen (red) and Grumier (blue). Each arrow represents a transition between two states realized by a frontal space.
Fig 7.
It is defined by the back foot, the crotch and the front foot. It captures important locomotion movements in the sagittal plane, such as step forward, step backward or lunge attack.
Fig 8.
Xcrotch is horizontal position of the crotch. is horizontal velocity of the front foot.
is horizontal velocity of the back foot. Each step corresponds to a velocity bump (gray area) delimited between a blue circle and a red cross.
Fig 9.
Xcrotch is horizontal position of the crotch. is horizontal velocity of the front foot.
is horizontal velocity of the back foot. Each step corresponds to a velocity bump (gray area) delimited between a blue circle and a red cross.
Fig 10.
The velocity bumps of Figs 8 and 9 determine a transition system. Each thick arrow represents a foot step forward (solid arrow) or backward (dotted arrow) for Steffen (red) and Grumier (blue). Each thin arrow (gray) represents a fencing action (small retreat, threat, retreat, attack).
Fig 11.
(A) It is composed of segments and joints. CS = trunk, CB = rear lower limb, CK = front thigh, KH = front leg, HT = front foot, ,
,
,
. (B) Implementation of this model based on video tracking.
Fig 12.
The average relative length of the five segments of the kinematic model is in the range 1 ± 0.1 except for a few peaks of standard deviation during offensive actions.
Fig 13.
(A) The trunk angle dramatically decreases during the Steffen’s attack. (B) The trunk angle decreases during the Grumier’s threat. (C) The crotch angle dramatically increases during the Steffen’s attack. (D) The crotch angle increases during the Grumier’s threat.
Fig 14.
Trunk and crotch angular velocities.
(A) Negative velocity peaks when closing the trunk during the Steffen’s attack. (B) Negative velocity peaks when closing the trunk during the Grumier’s threat. (C) Positive velocity peaks when opening the crotch during the Steffen’s attack. (D) Positive velocity peaks when opening the crotch during the Grumier’s threat.
Fig 15.
Light rectangles: ActiveROM, active range of motion from Faisal et al. [14]. Dark rectangles: WalkingROM, walking range of motion from Mentiplay et al. [15]. Red lines: average values of the angles. (A,B) The knee angles of Steffen and Grumier vary around the lower limit of WalkingROM, fencers bend their knees. (C,D) The ankle angles of Steffen and Grumier are mainly within WalkingROM.
Fig 16.
Knee and ankle angular velocities.
Light rectangles: MaxAV, maximum angular velocities for sport from Jessop et al. [16]. Dark rectangles: WalkingAV, angular velocities during walking from Mentiplay et al. [15]. (A,B,C,D) The knee and ankle angular velocities of Steffen and Grumier are mainly within WalkingAV and enhanced during their offensive actions.
Fig 17.
Motion scheme of the kinematic model.
Each segment represents a monotonic movement determined by an angular velocity bump in Figs 14 and 16.
Fig 18.
Correlation matrix of the motion scheme of the kinematic model.
(A) Each coefficient cij measures the correlation between rows i and j in the motion scheme of Fig 17. (B) The same matrix filtered by a threshold at 0.66 (∼ 2/3) reveals non-trivial coordination patterns common to Steffen and Grumier.
Fig 19.
It is defined by the body center (at of the trunk segment), the sword hand and the front foot (in the middle of the foot segment). These three points of interest are comparable to the mass center, the weapon and the front foot studied by Chen et al. [17] and Gutierrez-Davila et al. [18].
Fig 20.
Characterization of Steffen’s lunge attack.
Horizontal velocities are measured at the body center (solid line), sword hand (dashed line) and front foot (dash-dot line). Decisive movements are delimited by black dots (maximum velocity peaks) and white dots.
Fig 21.
Motion scheme of Steffen’s lunge attack.
The body center arrow describes the acceleration phase. The sword hand arrow describes the thrust to the touché. The front foot arrow describes the propulsion of one step forward. Maximum velocity peaks are indicated by black dots.
Fig 22.
Steffen’s normalized velocities match those of Chen et al. [17] at 97% and Gutierrez-Davila et al. [18] at 94%, which is good accuracy.
Table 1.
Peak velocities.
Fig 23.
It is defined by a line segment between the free hand and the body center. The free hand movement is evaluated relative to the body center.
Fig 24.
Trajectories of Steffen’s body center and free hand.
Decisive movements are delimited by white dots (variation changes). (A) Horizontal coordinates of body center (XBC, solid line) and free hand relative to body center (XFH/BC, dotted line). (B) Vertical coordinates of body center (YBC, solid line) and free hand relative to body center (YFH/BC, dotted line).
Fig 25.
Motion scheme of Steffen’s body center and free hand.
The protective gesture during the retreat is represented by arrows for the body center backward and the free hand up/down. The balancing gesture during the lunge attack is represented by arrows for the body center forward/downward and the free hand backward/upward.
Fig 26.
Steffen’s lunge in the duel Steffen-Grumier.
The touch at 3 seconds and the start 0.5 seconds before the touch are represented by dotted vertical lines. The motion scheme of the front foot (bottom plot) is monotonic with respect to the head, the crotch and the back foot. Source of the original video: [6].
Fig 27.
Borel’s fleche in a duel Borel-Svichkar (World Fencing Championships Wuxi, 2018).
The touch at 12 seconds and the start 0.5 seconds before the touch are represented by dotted vertical lines. The front foot abscissa remains virtually stable while it is sequentially overtaken by the head (state H), the crotch (state C) and the back foot (state B). The motion scheme of the front foot has three states H, C, B. Source of the original video: [21].
Fig 28.
Horizontal velocity of the sword hand during a counter-attack in a duel Borel-Fichera with double touch (Challenge SNCF Réseau, 2017).
The touch at 6.8 seconds and the start 1 second before the touch are represented by dotted vertical lines. Each velocity bump (top and middle plots) is delimited between a blue circle and a red cross. The motion scheme (bottom plot) gives subtle indications on the performance of the athletes. It reveals that the attack of Fichera is synchronized with the end of the parry of Borel (continuous vertical line around 6.6 seconds), and the counter-attack of Borel appears more concise than the attack of Fichera. Source of the original video: [22].
Fig 29.
Dominance in a duel between the defender Heinzer and attacker Borel (Championnats d’Europe d’escrime Torun, 2016).
The touch at 2.28 seconds and the start 2.25 seconds before the touch are represented by dotted vertical lines. The horizontal position of the center of the duel X (top plot) and its velocity (middle plot) were estimated between the barycenters of the frontal spaces. Borel executes a remarkably fluent direct thrust. The motion scheme (bottom plot) indicates the full dominance of the attacker Borel over the defender Heinzer. Source of the original video: [23].
Fig 30.
Dominance in a duel between the defender Bida and attacker Siklosi (World Championships Budapest, 2019).
The touch at 11.08 seconds and the start 2.25 seconds before the touch are represented by dotted vertical lines. The horizontal position of the center of the duel X (top plot) and its velocity (middle plot) were estimated between the barycenters of the frontal spaces. Siklosi executes an explosive direct thrust. The motion scheme (bottom plot) indicates alternating dominance between the defender Bida and the attacker Siklosi, which ends with the touch of Siklosi. Source of the original video: [24].
Fig 31.
Lasha Talakhadze in men’s weightlifting.
The video tracking was based on 9 points of interest represented by blue markers, including 3 fixed points of calibration, 2 points on the barbell and 4 anatomical points (forehead, crotch, wrist on the left, wrist on the right). Source of the original video: [25].
Fig 32.
Vertical positions of Talakhadze clean and jerk.
Curves of vertical positions (ordinate) of points of interest for Talakhadze and the barbell. The black vertical line at 13.64 seconds indicates when the barbell passes above the forehead.
Fig 33.
Motion scheme of Talakhadze clean and jerk.
The motion scheme for Talakhadze describes precise timing of movements. The continuous segments correspond to upward movements while the dotted segments correspond to downward movements. The black vertical line at 13.64 seconds indicates when the barbell passes over the forehead.