I am trying to visualize a pointcloud centered around the origin. I also want to have a user controlled rotation for which I found the arcball.rMat is the model matrix, passed into the shader.inline QVector3D getArcballVector(const QPoint& pt, int width, int height){    QVector3D P = QVector3D(1.0*pt.x ()/width * 2 - 1.0,                            1.0*pt.y ()/height * 2 - 1.0,                            0);    P.setY (-P.y ());    float OP_squared = P.lengthSquared ();    if (OP_squared <= 1)        P.setZ (std::sqrt(1 - OP_squared));  // Pythagore    else        P.normalize ();  // nearest point    return P;}void PointCloud::mouseMoveEvent(QMouseEvent * e){    if(e->buttons ()==Qt::LeftButton)    {        if(!rotPos.isNull () && rotPos!=e->pos ())        {            //rotate using an arcBall for freeform rotation            QVector3D vec1 = getArcballVector (rotPos, width (), height ());            QVector3D vec2 = getArcballVector (e->pos (), width (), height ());            //use bisector to get half-angle cos and sin from dot and cross product            // for quaternion initialisation            QVector3D vec3 = vec1+vec2;            vec3.normalize ();            QVector3D rotaxis = QVector3D::crossProduct (vec1, vec3);            double cos = QVector3D::dotProduct (vec1, vec3);            QQuaternion quat (cos,rotaxis);            quat.normalize ();            //we want to left-multiply rMat with quat but that isn't available            //so we'll have to do it the long way around            QMatrix4x4 rot;            rot.rotate (quat);            rMat=rot*rMat;            updateGL ();        }        rotPos=e->pos ();    }}void PointCloud::mousePressEvent(QMouseEvent *e){    if(e->buttons ()==Qt::LeftButton)    {        rotPos=e->pos ();    }}One point to make is that most arcball examples use acos to get the rotation angle for the axis-angle representation and use that to create the matrix and only mention using quaternions in passing (and if they do use quaternions they still end up using axis-angle). I found that I can derive the quaternion values directly using the dot and cross products of the first vector with the bisector of the 2 vectors (vec3).Are there any glaring inefficiencies? I could move the update code to a QTimer activated slot but the usage of the program has the user mostly ignoring the screen while concentrating on the road.
User controlled rotation with arcBall
c++;matrix;opengl;qt