Qt Transform matrix

I need to manipulate QML items through QMatrix4x4, in order to apply some perspective transformations. Basically, I defined the class Transform to use an object QMatrix4x4 as argument for the transform field of the QML Item

class Transform : public QQuickTransform{
 Q_OBJECT

 Q_PROPERTY(QMatrix4x4 matrix READ matrix WRITE setMatrix NOTIFY matrixChanged)

 public:
 explicit Transform(QQuickItem *parent = 0);

 QMatrix4x4 matrix() const;
 void setMatrix(QMatrix4x4 matrix);

 virtual void applyTo(QMatrix4x4 *matrix) const;

 signals:
         void matrixChanged();

 private:
         QMatrix4x4 m_matrix;

};

where

void Transform::applyTo(QMatrix4x4 *matrix) const {
      *matrix *= m_matrix;
       matrix->optimize();
}

However, it seems that QML doesn't "define" the perspective matrix in the classical way. I've focused my tests mainly on the rotations (http://en.wikipedia.org/wiki/Rotation_matrix). Let's say I have a QML Item in x:200, y:200 and I apply the transform

transform: [Transform{matrix:mytra},Rotation {  axis { x: 1; y: 0; z: 0 } angle: 90 } ]

where mytra is the identity matrix. The method applyTo() receives the (rotation) matrix

     1    -0.195312         0       200         
     0    -0.195312         0       200         
     0            0         1         0         
     0 -0.000976562         0         1

but the "classical" one should be

     1    0         0       200         
     0    0        -1       200         
     0    1         0         0         
     0    0         0         1

I don't understand where this matrix comes from and how to adapt my matrix to qt. Thanks for the help.

The math Qt is performing is correct, but the frame of reference that Qt is using doesn't match up with what you are thinking.

Matrix Math:

So the components you are seeing in the math are adding shear in the x and y directions of image.

But the rotation that Qt does is about one of those axis. So if you want to do a standard 2D rotation, without shearing, you need to either not specify an axis or you specify the z axis.

The axis to rotate around. For simple (2D) rotation around a point, you do not need to specify an axis, as the default axis is the z axis (axis { x: 0; y: 0; z: 1 }).

http://qt-project.org/doc/qt-5/qml-qtquick-rotation.html

The rotation about the y axis looks like this: