Traj3DAcceleration: Approximates the acceleration of a 3-dimensional trajectory

In JimMcL/trajr: Animal Trajectory Analysis

Approximates the acceleration of a 3-dimensional trajectory

Description

Returns an approximation of the acceleration of a trajectory at each point using the second-order central finite differences.

Usage

Traj3DAcceleration(trj3d)

Arguments

trj3d

3-dimensional trajectory whose acceleration is to be calculated.

Details

trajr trajectories, which consist of straight line displacements between sampled locations, do not contain enough information to correctly derive velocity or acceleration. Since we have to assume a constant velocity at each step, the first derivative is discontinuous. Acceleration, therefore, is zero during each step and infinite at each change of velocity. The approximation implemented by this function assumes that acceleration occurs over a period of time: half the duration of the previous step plus half the duration of the next step.

The function Traj3DSpeed, despite its name, can be used to calculate the magnitude of the acceleration vectors returned by this function.

Value

Numeric matrix of 3D acceleration vectors. Each row represents the acceleration at a point in the trajectory. Columns are named "'x'", "'y'" and "'z'". The vector has an attribute, trj, with the trajectory as its value. The first and last values will always be NA, since acceleration cannot be estimated for those points.

See Also

Traj3DVelocity for calculating velocity, Traj3DResampleTime and Traj3DRediscretize to resample a trajectory to fixed time or length steps.

Examples

## Not run: 
library(rgl)

# Plot a trajectory and its acceleration in 3D, using the rgl package

# Function to add acceleration vectors as arrows to a 3D trajectory plot
Acc3DArrows <- function(acc, scale = 0.0001, trj3d = attr(acc, "trj3d"), ...) {
    cols <- c("x", "y", "z")
    sapply(seq_len(nrow(t3) - 2) + 1, function(r) {
           arrow3d(t3[r, cols], t3[r, cols] + acc[r, ] * scale, type = "extrusion", ...)
    })
}
plot3d(trj3d$x, trj3d$y, trj3d$z, type = 'l')
Acc3DArrows(Traj3DAcceleration(trj3d), col = 2)

## End(Not run)

JimMcL/trajr documentation built on Jan. 31, 2024, 12:57 a.m.