How do I convert a Direction Vector to a Quaternion

Question

Let's say I have a Vector v which points into a certain direction. My question is straightforward: How do I construct a Quaternion out of this direction Vector so an object would look into the direction of the vector? I suppose I need the forward Vector of the Object to point into the same direction as the direction Vector. How would I do that using Quaternions? Or am I supposed to do something completely different? Thanks in advance.

Answer 1

I have found the answer:

Quaternion Quaternion::LookAt(Vector3f direction, Vector3f forward, Vector3f up) {

        Quaternion rot1 = RotationBetweenVectors(forward, direction);
        Vector3f right = Vector3f::CrossProduct(direction, up);
        up = Vector3f::CrossProduct(right, direction);
        Vector3f realUp(0, 1, 0);
        Vector3f newUp = rot1 * realUp;
        Quaternion rot2 = RotationBetweenVectors(newUp, up);
        Quaternion res = rot2 * rot1;

        return Quaternion(res.x, res.y, res.z, res.w);

    }

    Quaternion Quaternion::RotationBetweenVectors(Vector3f forward, Vector3f direction) {
        forward = Vector3f::Normalize(forward);
        direction = Vector3f::Normalize(direction);

        float cosTheta = Vector3f::DotProduct(forward, direction);
        Vector3f axis;

        if (cosTheta < -1 + 0.001f) {
            // special case when vectors in opposite directions:
            // there is no "ideal" rotation axis
            // So guess one; any will do as long as it's perpendicular to start
            axis = Vector3f::CrossProduct(Vector3f(0.0f, 0.0f, 1.0f), forward);

            if (axis.Length() * axis.Length() < 0.01)
                axis = Vector3f::CrossProduct(Vector3f(1.0f, 0.0f, 0.0f), forward);

            axis = Vector3f::Normalize(axis);
            return Quaternion(axis.x, axis.y, axis.z, DegreesToRadians(0));
        }

        axis = Vector3f::CrossProduct(forward, direction);
        float s = sqrt((1 + cosTheta) * 2);
        float invs = 1 / s;

        return Quaternion(
            axis.x * invs,
            axis.y * invs,
            axis.z * invs,
            s * 0.5f
        );
    }