Curvature

Computes the curvature of a path, defined by vectors of x and y coordinates, as compared to an ideal path, as defined by the start and end points of the path.

Usage

curvature(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 curvature (1 to +Inf).

Details

The supplied vectors are assumed to be ordered by time.

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, 0, 0, 1, 2)
y_vals <- c(0, 1, 2, 2, 2)
plot(x_vals, y_vals, type = "l")
lines(c(0, 2), c(0, 2), lty = "dashed", lwd = 2) # ideal

curvature(x_vals, y_vals)
#> [1] 1.414214

x_vals <- c(0, 1, 2, 2, 2)
y_vals <- c(0, 0, 0, 1, 2)
plot(x_vals, y_vals, type = "l")
lines(c(0, 2), c(0, 2), lty = "dashed", lwd = 2) # ideal

curvature(x_vals, y_vals)
#> [1] 1.414214

x_vals <- c(0, 0, 1, 2, 2)
y_vals <- c(0, 1, 1, 1, 2)
plot(x_vals, y_vals, type = "l")
lines(c(0, 2), c(0, 2), lty = "dashed", lwd = 2) # ideal

curvature(x_vals, y_vals)
#> [1] 1.414214