Direction vector to quaternion

Question

I have a unit vector (direction) which represent a rotation around Y axis,

and would like to turn this into a quaternion to represent the same rotation.

I use GLM library, but interested any library agnostic solution.

Should I pack the direction vector to a matrix then convert to quaternion? Is there a better way?

UPDATE: As I said the matrix solution works already, but there must be a shorter way, as i don't need all dimension only one (around Y):

glm::quat q = glm::conjugate(glm::toQuat(
    glm::lookAt(glm::vec3(from.getX(), from.getY(), from.getZ()),
                glm::vec3(from.getX(), from.getY(), from.getZ()) + direction,
                glm::vec3(0, 1, 0)
    )
));

Answer 1

From http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/

qx = ax * sin(angle/2)
qy = ay * sin(angle/2)
qz = az * sin(angle/2)
qw = cos(angle/2)

But since your vector represents the rotation, and is not the axis of rotation, we need to compute the angle. Your axis of rotation is just 0,1,0

angle = atan2( vector.x, vector.z ) // Note: I expected atan2(z,x) but OP reported success with atan2(x,z) instead! Switch around if you see 90° off.
qx = 0
qy = 1 * sin( angle/2 )
qz = 0
qw = cos( angle/2 )

NOTE: this even works for non-unit vectors, as atan2 will compute the correct angle for any length vector, as long as it is not zero.

Answer 2

Try to look in this way:

Vector3df sundirection = sun->GetDirectionTo();
Vector3df rotaxis = normalize( cross(Vector3df(1, 0, 0), sundirection));
double angle = acos(dot(Vector3df(1,0,0),sundirection));
Quaterniondf orient(angle, rotaxis);