Quaternion from direction (or forward) and up vectors

    //XYZ is a 3D vector class with components X, Y, and Z
    //Obvious thing but worth mentioning: if converting this to
    //use floats, make sure you convert all literal doubles
    //to end in f (1.0 becomes 1.0f, 0.5 becomes 0.5f, etc)

    public static Quaternion LookRotation(XYZ forward, XYZ up)
    {
        forward = forward.Normalize();

        XYZ vector = forward.Normalize();
        XYZ vector2 = up.CrossProduct(vector).Normalize();
        XYZ vector3 = vector.CrossProduct(vector2);
        var m00 = vector2.X;
        var m01 = vector2.Y;
        var m02 = vector2.Z;
        var m10 = vector3.X;
        var m11 = vector3.Y;
        var m12 = vector3.Z;
        var m20 = vector.X;
        var m21 = vector.Y;
        var m22 = vector.Z;

        double num8 = (m00 + m11) + m22;
        var quaternion = new Quaternion();
        if (num8 > 0.0)
        {
            var num = (double)Math.Sqrt(num8 + 1.0);
            quaternion.w = num * 0.5;
            num = 0.5 / num;
            quaternion.x = (m12 - m21) * num;
            quaternion.y = (m20 - m02) * num;
            quaternion.z = (m01 - m10) * num;
            return quaternion;
        }
        if ((m00 >= m11) && (m00 >= m22))
        {
            var num7 = (double)Math.Sqrt(((1.0 + m00) - m11) - m22);
            var num4 = 0.5 / num7;
            quaternion.x = 0.5 * num7;
            quaternion.y = (m01 + m10) * num4;
            quaternion.z = (m02 + m20) * num4;
            quaternion.w = (m12 - m21) * num4;
            return quaternion;
        }
        if (m11 > m22)
        {
            var num6 = (double)Math.Sqrt(((1.0 + m11) - m00) - m22);
            var num3 = 0.5 / num6;
            quaternion.x = (m10 + m01) * num3;
            quaternion.y = 0.5 * num6;
            quaternion.z = (m21 + m12) * num3;
            quaternion.w = (m20 - m02) * num3;
            return quaternion;
        }
        var num5 = (double)Math.Sqrt(((1.0 + m22) - m00) - m11);
        var num2 = 0.5 / num5;
        quaternion.x = (m20 + m02) * num2;
        quaternion.y = (m21 + m12) * num2;
        quaternion.z = 0.5 * num5;
        quaternion.w = (m01 - m10) * num2;
        return quaternion;
    }