Function rotate_a_to_b

pub fn rotate_a_to_b<T>(a: Vector3<T>, b: Vector3<T>) -> Option<Quaternion<T>>
where
    T: Float,

Calculate the versor to rotate from vector a to vector b (Without singularity!).

This function calculates q satisfying b = point_rotation(q, a) when norm(a) = norm(b).

If norm(a) > 0 and norm(b) > 0, then q can be calculated with good accuracy no matter what the positional relationship between a and b is. However, this function does not guarantee what the axis of rotation will be. If you want the rotation axis to be orthogonal to vectors a and b, you can use rotate_a_to_b_shotest.

If you enter a zero vector either a or b, it returns None.

Examples

let a: Vector3<f64> = [1.5, -0.5, 0.2];
let b: Vector3<f64> = [0.1, 0.6, 1.0];
 
let q = rotate_a_to_b(a, b).unwrap();
let b_check = point_rotation(q, a);
 
let b_u = normalize(b);
let b_check_u = normalize(b_check);
assert!( (b_u[0] - b_check_u[0]).abs() < 1e-12 );
assert!( (b_u[1] - b_check_u[1]).abs() < 1e-12 );
assert!( (b_u[2] - b_check_u[2]).abs() < 1e-12 );