Loop Geometry of a COP Trajectory

Describes a centre-of-pressure trajectory as a loop: how far its end lands from its start, and whether the path crosses itself on the way.

Usage

pr_cop_shape(cop, close = TRUE)

Arguments

cop

A pr_cop object from pr_calc_cop(), or a data frame with x/y columns, or one with cop_row/cop_col columns as returned by pr_calc_cop_grid() and pr_frame_metrics() (cop_col is treated as x, cop_row as y).

close

Logical. Append the first point to the end before looking for crossings. Default TRUE.

Value

A one-row tibble::tibble with columns n_points (integer, after dropping missing coordinates), path_length, closure_dist, closure_ratio (closure_dist / path_length, NA for a stationary trajectory), self_intersects (logical) and n_crossings (integer).

Details

A stride that returns the rider to where they began traces a closed loop, and how that loop is shaped separates a clean, repeatable seat from a wandering one. Two numbers capture most of it:

• closure_dist — the straight-line distance from the last point back to the first, in whatever units the trajectory carries. Small relative to the path travelled means the trajectory came home.

• n_crossings — how many times the path cuts through itself. A simple oval crosses zero times; a figure-of-eight crosses once; a trajectory that scribbles crosses many times. self_intersects is n_crossings > 0.

With close = TRUE (default) the first point is appended to the end before the crossing sweep, so the closing chord counts as part of the loop — the right question for a cycle that should repeat. With close = FALSE only the path as travelled is examined. Either way closure_dist and path_length describe the open trajectory.

Crossings are counted with orientation tests on every pair of non-adjacent segments, an exact predicate with no tolerance to tune. Two segments that merely touch end to end, or that overlap along a line, are not counted; only a genuine transverse crossing is. The sweep is quadratic in the number of points, which is immaterial for one stride and worth remembering before feeding it a whole recording.

Units are the input's own and nothing is converted: a pr_cop from pr_calc_cop() is in millimetres, while cop_row/cop_col from pr_calc_cop_grid() or pr_frame_metrics() are in grid index units, so path_length and closure_dist follow suit. closure_ratio is dimensionless and comparable across both.

Missing coordinates are dropped pairwise before anything is measured — pr_calc_cop() returns NA for unloaded frames.

See also

pr_calc_cop_grid() and pr_frame_metrics() for trajectories in grid units, pr_calc_cop() for millimetres.

Other temporal structure functions: pr_calc_dominant_freq(), pr_calc_phase_map(), pr_calc_spectrum(), pr_calc_stride_cycles()

Examples

# A clean rectangle: comes home, never crosses itself.
square <- data.frame(x = c(0, 1, 1, 0), y = c(0, 0, 1, 1))
pr_cop_shape(square)
#> # A tibble: 1 × 6
#>   n_points path_length closure_dist closure_ratio self_intersects n_crossings
#>      <int>       <dbl>        <dbl>         <dbl> <lgl>                 <int>
#> 1        4           3            1         0.333 FALSE                     0

# A bow tie crosses once.
bow <- data.frame(x = c(0, 1, 0, 1), y = c(0, 0, 1, 1))
pr_cop_shape(bow)$n_crossings
#> [1] 1

# One stride of a real trajectory, in grid index units:
trial <- pr_example_trial("saddle_horse")
cycles <- pr_calc_stride_cycles(trial)
cop <- pr_calc_cop_grid(trial)
pr_cop_shape(cop[cycles$start_idx[1]:cycles$end_idx[1], ])
#> # A tibble: 1 × 6
#>   n_points path_length closure_dist closure_ratio self_intersects n_crossings
#>      <int>       <dbl>        <dbl>         <dbl> <lgl>                 <int>
#> 1       33        8.77        0.375        0.0427 TRUE                      9