Get a random unit vector at a given angle with another vector.

Get a random unit vector which is at angle radians of vector u. Note that u is expected to be a unit vector itself.

Usage

rand_vector_at_angle(u, angle)

Arguments

u

Unit vector with \(n\) components.

angle

Angle in radians.

Value

Random unit vector with \(n\) components which is at angle

radians with vector u.

Note

This function is stochastic. For reproducibility set a PRNG seed with set.seed.

Examples

u <- c(1.0, 0, 0.5, -0.5)            # Define a 4D vector
u <- u / norm(u, "2")                # Normalize the vector
v <- rand_vector_at_angle(u, pi / 4) # Get a vector at 45 degrees
arad <- acos((u %*% v) / norm(u,"2") * norm(v, "2")) # Get angle in radians
arad * 180 / pi # Convert to degrees, should be close to 45 degrees
#>      [,1]
#> [1,]   45