Computing two vectors that are perpendicular to third vector in 3D

Question

What is the best (fastest) way to compute two vectors that are perpendicular to the third vector(X) and also perpendicular to each other?

This is ho

Answer 1

I think the minimum maximum magnatude out of all element in a unit vector is always greater than 0.577, so you may be able to get away with this:

-> Reduce the problem of finding a perpendicular vector to a 3D vector to a 2D vector by finding any element whose magnatude is greater than say 0.5, then ignore a different element (use 0 in its place) and apply the perpendicular to a 2D vector formula in the remaining elements (for 2D x-axis=(ax,ay) -> y-axis=(-ay,ax))

let x-axis be represented by (ax,ay,az)

if (abs(ay) > 0.5) {
  y-axis = normalize((-ay,ax,0))
} else if (abs(az) > 0.5) {
  y-axis = normalize((0,-az,ay))
} else if (abs(ax) > 0.5) {
  y-axis = normalize((az,0,-ax))
} else {
  error("Impossible unit vector")
}