Quaternion-Based Rotation in OpenGL

This is yet another blog about quaternion. Assuming that we have quaternion [q0, q1, q2, q3]. Can we directly use it to rotation object in OpenGL? The answer is yes. At first, let us normalize this quaternion (written with Java)

     norm = (float) Math.sqrt(q0*q0 + q1*q1 + q2*q2 + q3*q3);

    if (norm == 0)

    {

    return 0;

    }

    else

    {

    q0 = q0 / norm;

    q1 = q1 / norm;

    q2 = q2 / norm;

    q3 = q3 / norm;

    }

Then, glRotatef function in OpenGL is a natural fit for rotation using quaternion.

 

        // Rotate the object according to quaternion

        theta = (float) (Math.acos(q0) * 2);

        

        aNorm = (float) Math.sqrt(q1 * q1 + q2 * q2 + q3 * q3);

        if (aNorm != 0)

        {

        gl.glRotatef(theta*180f/PI, q1/aNorm, q2/aNorm, q3/aNorm);

        }

        else

        {

        gl.glRotatef(theta*180f/PI, q1, q2, q3);

        }

Note that except for quaternion, glRotatef can also be used for rotation along x, y or z axis. In that way, glRotatef needs to be called three times instead of once with quaternion-based method.

    glRotatef(xRot , 1.0, 0.0, 0.0);

    glRotatef(yRot , 0.0, 1.0, 0.0);

    glRotatef(zRot , 0.0, 0.0, 1.0);