curvature {mousetRajectory}

Curvature

Description

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.

Details

The supplied vectors are assumed to be ordered by time.

Value

Single number indicating the curvature (1 to +Inf).

References

Wirth, R., Foerster, A., Kunde, W., & Pfister, R. (2020). Design choices: Empirical recommendations for designing two-dimensional finger tracking experiments. Behavior Research Methods, 52, 2394 - 2416. doi:10.3758/s13428-020-01409-0

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)

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)

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)