Quaternions from and to Euler angles — quat_from

Three rotations about coordinate axes, applied in sequence. There are twelve sequences: six Tait-Bryan ("ZYX", "XYZ", …, all three axes) and six proper Euler ("ZXZ", "XYX", …, first and last axis the same).

Intrinsic rotations are about the body's own axes, which move with each rotation. Intrinsic "ZYX" is yaw, pitch, roll.
Extrinsic rotations are about the fixed frame's axes. An intrinsic sequence equals the reversed extrinsic sequence with the angles reversed.

Neither sequence nor intrinsic has a default: an assumed convention is the classic source of Euler-angle bugs, so the call must say which is meant. Euler angles are a report format; store orientation as quaternions.

Usage

quat_from_euler(angles, sequence, intrinsic)

quat_to_euler(q, sequence, intrinsic)

Arguments

angles: Angles in radians: a vector of length 3, or three columns, in sequence order.
sequence: Three axes, e.g. "ZYX". Case is ignored.
intrinsic: TRUE for rotations about the moving body axes, FALSE for rotations about the fixed axes.
q: Quaternions; see quaternions.

Value

quat_from_euler(): a quaternion matrix. quat_to_euler(): a matrix with three columns in sequence order. The middle angle is in [-pi/2, pi/2] for Tait-Bryan sequences and [0, pi] for proper ones; the others are in (-pi, pi]. At gimbal lock the third angle is 0.

Examples

ypr <- c(pi / 2, 0.1, -0.2)
q <- quat_from_euler(ypr, sequence = "ZYX", intrinsic = TRUE)
quat_to_euler(q, sequence = "ZYX", intrinsic = TRUE)
#>           z_1 y_2  x_3
#> [1,] 1.570796 0.1 -0.2

# The same rotation, described extrinsically
quat_to_euler(q, sequence = "XYZ", intrinsic = FALSE)
#>       x_1 y_2      z_3
#> [1,] -0.2 0.1 1.570796