Time point of maximum velocity

Computes the index of the peak velocity of a trajectory, defined by vectors of x and y coordinates, and assumed to be equidistant in time.

Usage

index_max_velocity(x_vector, y_vector)

Arguments

x_vector

x-coordinates of the executed path.

y_vector

y-coordinates of the executed path.

Value

Single number indicating the index of peak velocity (1 to +Inf).

Details

The supplied vectors are assumed to be ordered by time with equal time differences.

References

Pfister, R., Tonn, S., Schaaf, M., Wirth, R. (2024). mousetRajectory: Mouse tracking analyses for behavioral scientists. The Quantitative Methods for Psychology, 20(3), 217-229. doi:10.20982/tqmp.20.3.p217

Examples

x_vals <- c(0, 1, 2, 3, 6, 10, 12, 14, 15)
y_vals <- c(0, 0, 0, 0, 0, 0, 0, 0, 0)
index_max_velocity(x_vals, y_vals)
#> [1] 5
# velocity maximal between x_vals[5] and x_vals[6]

numbers <- seq(-(3 / 4) * pi, (3 / 4) * pi, by = 0.001)
y_vector <- sin(numbers)
plot(numbers, y_vector)
index_max_velocity(rep(0, length(numbers)), y_vector)
#> [1] 2357
abline(v = numbers[index_max_velocity(rep(0, length(numbers)), y_vector)])

which.max(cos(numbers)) # first derivative of sin, max at 0 degrees
#> [1] 2357