The angle between two vectors

Row-wise angle between direction vectors, as used for joint angles.

• With no axis, the included angle acos(u . v / |u||v|), in [0, pi].

• With an axis, both vectors are projected onto the plane perpendicular to it, and the angle turns from u to v about the axis by the right-hand rule, in [-pi, pi]. For 2D vectors, c(0, 0, 1) gives the signed angle from x toward y.

Vectors need not be unit length. A zero vector, or one parallel to the axis, gives NA.

Usage

angle_between(u, v, axis = NULL)

Arguments

u, v

Numeric vectors of length 2 or 3, or matrices or data frames with 2 or 3 columns and one row per vector. A single vector is recycled.

axis

NULL, or a vector (or one per row) of length 3.

Value

Numeric vector of angles in radians.

Examples

angle_between(c(1, 0), c(0, 1))
#> [1] 1.570796
angle_between(c(1, 0), c(0, 1), axis = c(0, 0, 1))
#> [1] 1.570796
angle_between(c(1, 0), c(0, 1), axis = c(0, 0, -1))
#> [1] -1.570796

# One angle per row
angle_between(rbind(c(1, 0, 0), c(0, 1, 0)), c(0, 0, 1))
#> [1] 1.570796 1.570796