Quaternions from two body axes given as vectors

The orientation whose body axis axes[1] points along primary, and whose body axis axes[2] points towards secondary. Only the part of secondary perpendicular to primary is used, so it need not be at right angles to it; it only has to fix the roll about primary. The third axis completes a right-handed set.

This is how three points define an orientation: primary from one point to a second, and secondary from the first towards any third point off that line. With the default axes, primary is the body's forward axis (x) and the third point lies on the side of its y axis. With axes = c("y", "x"), primary runs across the body and secondary fixes which way is forward.

Usage

quat_from_vectors(primary, secondary, axes = c("x", "y"))

Arguments

primary

Vectors (length 3, or 3 columns) along body axis axes[1]. Need not be unit length.

secondary

Vectors (length 3, or 3 columns) towards body axis axes[2]. Need not be unit length or perpendicular to primary.

axes

Two distinct body axes from "x", "y", "z": the one primary is mapped onto, then the one secondary points towards.

Value

A quaternion matrix; see quaternions. A row is NA where either vector is missing or zero, or the two are parallel, since the roll is then undefined.

See also

quat_from_matrix(), which this builds the rotation for.

Examples

# Facing +y, with the body's left (+y) towards -x: a quarter turn about z
quat_from_vectors(c(0, 1, 0), c(-1, 0, 0))
#>              w x y         z
#> [1,] 0.7071068 0 0 0.7071068

# The secondary vector need not be perpendicular
quat_from_vectors(c(0, 1, 0), c(-1, 5, 0))
#>              w x y         z
#> [1,] 0.7071068 0 0 0.7071068

# Across the body: right-to-left along +y, forward towards +x
quat_from_vectors(c(0, 1, 0), c(1, 0, 0), axes = c("y", "x"))
#>      w x y z
#> [1,] 1 0 0 0