[Rotating a cube using quaternion with respect to a fixed frame] – For beginners

Hello guys,

I hope that you all are ok.

So I created an application on Qt6 that rotates a cube using quaternions. The rotation is performed relative to the standard OpenGL coordinate system.

As I know, the standard OpenGL coordinate system is shown in the image below:

I added a fixed coordinate system to my scene (like the one shown in the image above). So when I insert the quaternion values ​​as follows: w=0.7, x=0.7, y=0.0, z=0.0, the cube rotates around the x axis of the coordinate system standard.

Then I had to change the orientation of the axes of this coordinate system as shown in the image below where:

x is the magenta axis

y is White’s axis

z is the yellow axis

and my goal is to rotate the cube using a quaternion but this time the new fixed coordinate systemI didn’t know how to do it but that’s what I’ve done so far.

In my paintGL() function, I started by drawing the fixed coordinate system and changing the orientation of its axes using rotate:

glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

//================Orbital Frame ==========================================//

glMatrixMode(GL_MODELVIEW);

glLoadIdentity();

gluLookAt(2.0,2.0,0.0, 0.0,0.0,-5.0,0.0,1.0,0.0);

glTranslatef(0.0,0.0,-5.0);

glRotatef(180.0,0.0,1.0,0.0);

glRotatef(-90.0,1.0,0.0,0.0);

glScalef(0.4,0.4,0.4);

glMatrixMode(GL_PROJECTION);

DrawOrbitalFrame();

Then in my program I have shader programs (Vertex and Fragment shader programs) which I used to draw a textured cube:

program.bind();

texture->bind();

// Calculate model view transformation

QMatrix4x4 localMatrix;

//QMatrix4x4 identity;

localMatrix.lookAt(QVector3D(2.0, 2.0, 0.0), QVector3D(0.0,0.0,-5.0),QVector3D(0.0,1.0,0.0));

localMatrix.translate(0.0, 0.0, -5.0);

localMatrix.scale(0.4,0.4,0.4);

quaternion = QQuaternion(quat_w, quat_x, quat_y, quat_z);

quaternion.normalize(); // Normalizing my quaternion

localMatrix.rotate(quaternion); // the quaternion in here corresponds to the one that can be manually inserted in the spin boxes in the ui

quaternion=csvquaternion;

localMatrix.rotate(quaternion); // the quaternion in here correponds to the one extracted from a QList

program.setUniformValue("mvp_matrix", projection * localMatrix);

update();

// Use texture unit 0 which contains cube.png

program.setUniformValue("texture", 0);

// Draw cube geometry

geometries->drawCubeGeometry(&program);

texture->release();

program.release();

The rotation is achieved using the rotate function but the object rotates around the axes of the standard coordinate system and not the new one.

Can anyone tell me what I can do to make it rotate around the new fixed coordinate system or give me a little advice on how to achieve this?

Thank you all.