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Interpolate, average and differentiate rotations

Source: R/quaternion_interp.R
quat_slerp.Rd

  • quat_slerp(p, q, t): spherical linear interpolation, t = 0 giving p and t = 1 giving q, along the shorter arc.

  • quat_mean(q, weights): the average rotation, as the eigenvector of the largest eigenvalue of sum(w q q') (Markley et al. 2007). Unlike averaging components, it is unaffected by the sign ambiguity.

  • quat_continuous(q): flips signs so each row lies on the same side as the previous one. q and -q are the same rotation, so this changes no rotation, but smoothing or differentiating a series without it goes wrong wherever the sign jumps.

  • quat_angular_velocity(q, dt): angular velocity between successive rows, in radians per unit of dt, about the fixed frame's axes (frame = "fixed") or the body's own (frame = "body"). The first row is NA.

[Experimental] quat_angular_velocity() is experimental, and may change without a deprecation cycle: how it differences successive rows – here, each row against the one before – is to be settled with animetric's angular velocity from orientation (animovement/animetric#85). The other three are stable.

Rows with NA are skipped by quat_mean() and carried through by the others.

Usage

quat_slerp(p, q, t)

quat_mean(q, weights = NULL)

quat_continuous(q)

quat_angular_velocity(q, dt, frame = c("fixed", "body"))

Arguments

p, q

Quaternions; see quaternions.

t

Interpolation fraction(s), recycled against the rows.

weights

Optional non-negative weights, one per row.

dt

Time between rows: one value, or one per row.

frame

"fixed" or "body".

Value

A quaternion matrix; quat_mean() returns one row; quat_angular_velocity() returns a matrix with columns x, y, z.

Examples

a <- quat_from_axis_angle(c(0, 0, 1), 0)
b <- quat_from_axis_angle(c(0, 0, 1), pi / 2)
quat_slerp(a, b, 0.5)
#>              w x y         z
#> [1,] 0.9238795 0 0 0.3826834
quat_mean(rbind(a, b))
#>              w x y         z
#> [1,] 0.9238795 0 0 0.3826834

spin <- quat_from_axis_angle(c(0, 0, 1), seq(0, 1, by = 0.1))
quat_angular_velocity(spin, dt = 1 / 30)
#>        x  y  z
#>  [1,] NA NA NA
#>  [2,]  0  0  3
#>  [3,]  0  0  3
#>  [4,]  0  0  3
#>  [5,]  0  0  3
#>  [6,]  0  0  3
#>  [7,]  0  0  3
#>  [8,]  0  0  3
#>  [9,]  0  0  3
#> [10,]  0  0  3
#> [11,]  0  0  3