Developer Journal 56

0 degrees from up vector. Good.
yaw 0, pitch 0, roll 0

2:24 PM
One of the hardest things to do is to keep going each day when you're feeling doubt and time pressures.

I tried comparing the angle between two quaternions and no luck. Quaternions could work differently to vectors in this way.

Nope. I think, I'm messing up defining an up quaternion.

4:28 PM
I hate quaternions. So much.

5:10 PM
Calculating the angle between an up vector and a direction vector only works in when I rotate in some directions.

5:30 PM
I can rotate objects as much as I like but I can't get the current rotation level back to check whether an object has rotated too far.

6:17 PM
Looking at the direction vector doesn't help. Perhaps, I can look

6:26 PM
GOT IT!
1) Create two up vectors (0, 1, 0). Call them Alpha and Bravo.
2) Rotate Bravo by the robot's orientation.
3) Calculate the angle between Alpha and Bravo.

45 degrees from up vector. Good.
yaw 0, pitch -45, roll 0

45 degrees from up vector. Good.
yaw -45, pitch -90, roll 90

45 degrees from up vector. Good.
yaw 0, pitch, 135, roll -180

45 degrees from up vector. Good.
yaw 45, -90, 90

45 degrees from up vector. Good.
yaw 0, pitch 45, roll 0

YES! YES! YES!

I don't know why this doesn't work when Bravo is (0, 0, -1) and I don't know how to do this with quaternions.

More screen shots to illustrate why using pitch and yaw to detect the extent of tipping over was difficult.

45 degrees from up vector. Good
yaw 0, pitch 0, roll -45

Up till now we could use the rule that a robot has tipped too far when either absolute pitch or absolute roll has exceeded 45 degrees.

46 degrees from up vector. Good.
yaw -34, pitch -18, roll -34

However, there are situations like this which makes using such a rule difficult.

Some code fragments to illustrate what I'm doing.

void Robot::Rotate( const Direction& dir ) {
    const float increment = 5.0f;
    float yaw = 0.0f;
    float pitch = 0.0f;
    float roll = 0.0f;
    switch( dir ) {
        case ROTATE_DOWN:
            pitch = Ogre::Degree( -increment ).valueRadians();
            break;
        case ROTATE_UP:
            pitch = Ogre::Degree( increment ).valueRadians();
            break;
        case ROTATE_LEFT:
            yaw = Ogre::Degree( increment ).valueRadians();
            break;
        case ROTATE_RIGHT:
            yaw = Ogre::Degree( -increment ).valueRadians();
            break;
        case ROLL_LEFT:
            roll = Ogre::Degree( -increment ).valueRadians();
            break;
        case ROLL_RIGHT:
            roll = Ogre::Degree( increment ).valueRadians();
            break;
        default:
            break;
    }

    // get transform
    btTransform transform;
    transform.setIdentity();
    transform = rigidBody->getCenterOfMassTransform();

    // modify transform
    btMatrix3x3 matrix3x3;
    matrix3x3.setEulerYPR( roll, yaw, pitch );
    transform.getBasis() *= matrix3x3;

    // apply transform    
    rigidBody->setCenterOfMassTransform( transform );  

    // debug
    transform.getBasis().getEulerYPR( roll, yaw, pitch );
    cout << "yaw : " << nint( Ogre::Radian( yaw ).valueDegrees() ) 
         << endl;     
    cout << "pitch : "  << nint( Ogre::Radian( pitch ).valueDegrees() ) 
         << endl;     
    cout << "roll : "  << nint( Ogre::Radian( roll ).valueDegrees() )
         << endl;         

    // WORKS!
    const btVector3 upVec( 0.0f, 1.0f, 0.0f );
    const btQuaternion rotQua = transform.getRotation();    
    btVector3 rotVec( 0.0f, 1.0f, 0.0f );
    rotVec = transform.getBasis() * rotVec;
    const float angle = upVec.angle( rotVec );

    // ARGH!
    //const btQuaternion upQua( btVector3( 1.0f, 0.0f, 0.0f ), 90.0f ); // up
    //const btQuaternion upQua( btVector3( 0.0f, 0.0f, 1.0f ), 0.0f ); // up
    //const btQuaternion upQua( btVector3( 0.0f, 1.0f, 0.0f ), 0.0f ); // up
    //btQuaternion rotQua( upQua );
    //rotQua = rotQua * transform.getRotation();
    //const float angle = upQua.angle( rotQua );
    
    cout << "angle: " << Ogre::Radian( angle ).valueDegrees() << endl;   
}

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